Interfaces for the 21st Century: New Research Directions in Fluid Mechanics and Materials Science

The following sections are included:

• PREFACE

• CONTENTS

We have been studying the motion of sedimenting, surface gravity currents and the resultant motion of particles through the interface between a heavy, ambient fluid and a lighter surface layer (Maxworthy [1,2]). As noted by Green [3] and Chen [4] this latter motion has many features in common with double-diffusive interfaces, but further study has revealed a similarity to a wide range of problems involving the stability and morphology of interfaces in general. Some of these similarities have been discussed before (Michalland [5] and others) in another context and we discuss these and related applications.

A thin liquid drop on a flat surface will spread under the action of gravity and capillarity. In this paper, the effect of mass loss on the size and lifetime of the drop is determined. The simple case of a uniform and constant rate of depletion is analysed in detail. An example of a physical mechanism that results in mass loss is when the surface supporting the drop is heated and the drop loses mass by evaporation. The dynamic behaviour of the contact angle is found, and it is shown that there is no simple relationship between contact angle and speed when mass loss is present.

The plane spreading of a viscous melt on a horizontal plate, driven by gravitational forces, for isothermal conditions represents already a problem with a free liquid/gas interface. This problem has been treated in the literature both theoretically and experimentally (cf., Huppert [1], Didden and Maxworthy [2]). If heat is removed at the plate or at the liquid/gas interface, we may have solidification of the melt in the proximity of these locations and, thus, further free interfaces (solid/liquid) will be present in the problem. This has relevance for several applied problems in engineering and geophysics. Model experiments with metallic (Pr < 1) and oxide (Pr ≫ 1) melts have been conducted in a plane spreading geometry for constant pouring of the melt. The experiments feature (i) isothermal conditions and (ii) basal cooling. Thus, the experiments are suitable to examine the influence of a basal crust on the spreading flow. Further, an asymptotic model is presented, which for Pr ≫ 1 captures the spreading of an oxide melt in the presence of a thin crust. Hereby the liquid/gas interface and the solidified zone (solid/liquid interface) are predicted. A comparison of experimental and theoretical results completes the picture.

Channel roll waves are observed to amplify, accelerate, coalesce, and coarsen downstream. It is shown here that such strongly nonlinear dynamics are driven by localized interfacial coherent structures in the form of equilibrium hydraulic jumps. Their localized structure, due to a balance among inertia, kinematics, and dissipation, allows us to normalize the amplitude of every jump along a channel into a single value via a power-law scaling. The same scaling applies for the differential speed between an equilibrium jump and a non-equilibrium one that results from coalescence. We are then able to produce a texture-invariant coarsening rate that is favorably compared to experimental and numerical results.

Various methods, both passive and active, of controlling interfacial instabilities are first discussed briefly in order to provide a framework. Attention is then focused on active control with feedback when thermocapillarity is used to suppress instability. For the case of Bénard-Marangoni convection, the results of Or et al. [1] for large-wavelength disturbances involving surface deformation are compared to those of Bau [2] who used a different control law. Extension of the results is then made to the control of a viscous film flowing down a heated, inclined wall.

The problem of pattern formation in thin liquid films with neutral and with electrically charged, insoluble surfactants is addressed. A thin fluid film bounded by a wall is modeled by a set of N + 1 nonlinear evolution equations for the film thickness and for the concentrations of N species of surfactants on the free interface. A weakly nonlinear analysis for the case of a film with neutral surfactants predicts the appearance of morphological patterns with a homogeneous distribution of surfactants that is confirmed by numerical simulations. For the case of electrically charged, surface-active molecules, the system displays patterns with varying film thickness and an inhomogeneous distribution of surfactants. In both cases, morphological patterns are explained in terms of the competition between attractive and repulsive forces. The variable surfactant concentration for electrically charged, surface-active molecules is due to the competition between diffusion and ion migration. In this case, surface-tension gradients lead to the formation of roll cells driven by Marangoni convection.

We summarize and elaborate upon molecular dynamics results bearing on the microscopic properties of the flow near a moving contact line, such as slip, rheology, fluctuations and hysteresis, and present some new work on contact-line motion in dewetting.

A large number of computational problems and physical phenomena involve the motion of interfaces separating two or more regions. These can include problems in such areas as fluid mechanics, combustion, materials science, meteorology, and computer vision. In these problems, challenging issues often involve interfaces that change topology, form sharp corners and singularities, depend on delicate geometric quantities such as curvature and normal direction, and involve subtle feedback between the physics and chemistry of the interface and the position/motion of the front itself. In this paper, we will explain some of the issues involved in tracking interfaces, focus on a particular set of numerical techniques that arise from an implicit representation of the interface, and provide an overview of some of the applications that are possible with this view.

Direct numerical simulations of multiphase flows are discussed. The Navier-Stokes equations are solved by a finite-difference/front-tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to inertial and viscous effects. Studies of the motion of a few two- and three-dimensional, finite-Reynolds-number, buoyant bubbles in a periodic domain are reviewed. A parallel version of the method makes it possible to use large grids and resolve flows containing bubbles. Applications of the numerical method to other multiphase flows are also discussed.

In a previously-developed phase-field model of solidification that includes convection in the melt [1], the two phases are represented as viscous liquids, where the putative solid phase has a viscosity much larger than the liquid phase. In this paper, we report numerical computations on a simplified form of this model that represents the growth of a two-dimensional dendrite in a thin gap between two parallel thermally-insulting plates. In these computations, flow in the liquid arises because of the differing densities of the solid and liquid phases.

We develop a thermodynamically consistent phase field model for solidification of a multicomponent alloy, including hydrodynamics. The solid is treated as a very viscous fluid. The model is based on an entropy functional that includes gradient-entropy corrections for internal-energy density, partial-mass densities, and phase field. It allows for external forces and chemical reactions, and incorporates nonclassical temperature and chemical potentials, defined as functional derivatives. Korteweg stresses related to inhomogeneities in all of these quantities appear in momentum and energy balances.

A linear morphological stability analysis of a planar interface in interface reaction-controlled growth is presented. We allow the mobility of the interface to be a function of the elastic stress, and find that the stress-dependent mobility can be either stabilizing or destabilizing. We find that a stress-dependent mobility can be the dominant factor leading to instability at small stresses. The predictions are compared to the recent experiments by Barvosa-Carter et al. In agreement with their conclusions, we find that the experiments were performed in a parameter range where the stress-dependent mobility is the dominant cause of instability. The prediction of the critical wavenumber and amplification rate of the instability is consistent with the experimental results.

Dendritic-growth experiments conducted aboard the space shuttle Columbia's USMP-4 mission as part of the Isothermal Dendritic Growth Experiment (IDGE) are described. Video data reveals that pivalic acid dendrites growing in the diffusion-controlled environment of low-earth orbit exhibit a range of transient or non-steady-state behaviors. The observed transient features of the growth process continue to be studied, with the objective of elucidating the mechanisms responsible for these behaviors. While not yet clear, experimental factors may be responsible such as the long-range thermal interactions between the dendrite and its neighbors or container. It is also considered that the transient behaviors may arise from fundamental characteristics of isothermal, diffusion-limited, dendritic growth.

One of the challenges in predicting the solidification and melting of multi-component materials is to describe the evolution of mushy layers: regions of mixed phase in which solid and liquid coexist in intimate contact. If mush is treated as a distinct phase of matter then it is necessary to determine the conditions that apply at, and control, its interfaces with adjacent solid and liquid regions. At a mush–liquid interface, different conditions apply depending on the direction of fluid flow, with which solute is advected, relative to the direction of advance or retreat of the phase boundary. A mathematically complete set of interfacial conditions is presented for the case of steady solidification or melting and is used to determine states of buoyancy-driven convection in a mushy layer.

Peritectic alloys show a great variety of solidification microstructures. In recent years analytical theories of dendritic growth and of transient growth with nucleation ahead of the moving interface have been applied to describe the essentials of phase and microstructure selection. Coupled peritectic two-phase growth was also recently observed. Among the manyfold microstructures; banded structures, controlled by nucleation, convection, and solute trapping are very important in peritectics. Finally, consecutive phase transformations (liquid/solid and solid/solid) take place and lead to two transformation fronts, each one having its own growth behaviour. This multitude of structures constitutes a great challenge for theoretical analysis.

We describe a mean field, free-energy model that allows the computation of realistic phase diagrams for a particular set of ordering transitions in face-centered-cubic (FCC) binary alloys. The model is based on a sixth-order Landau expansion of the free-energy function in terms of the three nonconserved order parameters that describe ordering on the underlying FCC lattice. When combined with appropriate gradient-energy terms, this model will allow the self-consistent calculation of energetic and kinetic anisotropies of phase boundaries in future work.

We consider contact-line effects in directional solidification of a dilute binary alloy in a Hele-Shaw cell. We find steady basic-state solutions that satisfy the contact-angle conditions at the walls and then study their stability. Perturbation methods are used for values of the contact angle that are close to π/2, when the front is almost planar, while a numerical boundary integral method is used for arbitrary contact angles. We find that under physically realistic conditions the curved interface is less stable than the planar front, which is in agreement with experimental observations. The numerical solution is in agreement with the perturbation result in the region where the latter is valid.

A weakly nonlinear analysis is carried out in the framework of the same perturbation approach. As the deviation from the planar interface becomes more significant, the region of subcritical bifurcation is expanded. For values of thickness near one-half of the wavelength of the Mullins-Sekerka instability the three-dimensional steady-state structures can be observed even when the interface is normal to the wall; these structures are anti-symmetric with respect to the center plane of the Hele-Shaw cell. As the contact angle deviates from π/2, these shapes become unstable and the steady-state interface is symmetric with respect to the center plane.

For values of gap thickness much larger than the characteristic diffusion length we derive a long-wave evolution equation with appropriate boundary conditions at the walls and use it for numerical studies of strongly nonlinear evolution of the system. We find that formation of deep roots and secondary bifurcations are promoted due to contact-line effects for concave down (toward the solid) interfaces.

Film flows occur in various technical processes, in environmental sciences, and everyday life. Hence, they were the subject of many investigations, e.g., [1–5], to name a few. Here, we study the influence of a sharp edge on the surface shape and the velocity profile of a creeping steady thin film with high surface tension on an inclined plane. Within the framework of the lubrication assumption an asymptotic solution is constructed [6]. A parameter-free direct relation between the surface shape and the wall friction at the bottom is found that gives rise to an indirect detection of the wall friction by measuring the surface shape. It is shown that capillary effects make the surface shape rise to form a maximum in the near front of the edge similar to the problems with moving film fronts. The region of validity and the sensitivity of the asymptotic solution on the upstream and downstream boundary conditions and on the inclination angle are found by comparing with exact numerical results. A numerical parameter study with respect to the capillary number and inclination angle is performed. Depending on the parameter combinations various surface shapes can be obtained. The theoretical (analytical and numerical) results are verified by experiments.

Phase-field simulations have been used to study the evolution from a small nucleus to a dendrite in an undercooled melt, in the presence of convection. As a generic case for growth from solid boundaries, the nucleus is in one case assumed to be attached to a solid wall, and a shear flow parallel to the wall is assumed in the melt. The interaction between the melt flow and the growing dendrite results in a changed growth rate and morphology. One aspect that has been investigated is how the effective tilting of the main stem of the dendrite depends on the flow strength. It is shown that the major factor that determines the tilt angle is the selection of a nucleus with an optimal initial crystal orientation. We have also studied natural convection around a nucleus held in an undercooled melt.

The phase-field equations are solved together with the equations for viscous fluid flow using an adaptive finite element method. This method allows a large computional domain, so that a single dendrite in an effectively unbounded region can be studied.

We develop a model that describes the dynamics of a spreading and melting droplet on a heated substrate. The model, developed in the capillary-dominated limit, is geometrical in nature and couples the contact line, tri-junction, and phase-change dynamics. In this model the competition between spreading and melting is characterized by a single parameter that represents the ratio of the characteristic contact-line velocity to the characteristic melting velocity. A key component of the model for the spreading and melting droplet is an equation of motion for the solid. This equation of motion, which accounts for global effects through a balance of forces over the entire solid–liquid interface, including capillary forces at the tri-junction, acts in a natural way as the tri-junction condition. This is in contrast to models of tri-junction dynamics during solidification, where it is common to specify a tri-junction condition based on local physics alone. The tri-junction dynamics, as well as the contact angle, contact-line position, and other dynamic quantities for the spreading and melting droplet are predicted by the model and are compared to an isothermally spreading liquid droplet whose dynamics are controlled exclusively by the contact line. Our interest in this comparison has been motivated by experiments performed by Glick (1998) in which polystyrene spheres show different spreading characteristics when subject to these two different thermal configurations. We find that in general the differences between the dynamics of a spreading and melting droplet compared with that of an isothermally spreading droplet are increased as increases, that is, when the characteristic contact-line speed is greater than the characteristic melting speed. The presence of the solid phase in the spreading and melting configuration inhibits spreading relative to an isothermally spreading drop of the same initial geometry. Finally, we find that increasing the effect of spreading promotes melting.

The behavior of thin liquid films and liquid droplets is of fundamental importance in many natural and technological processes, such as the coating of surfaces, the recovery of oil from porous media, the development of microfluidic devices, and a host of applications in material processing. It is well known that the behavior of fluid systems can be greatly affected by forces such as capillarity, thermocapillarity, and the wetting characteristics of the material system when in a negligible or a reduced gravitational environment. Although the control of liquid droplets and films has been attained through many methods, we seek an approach whereby thermocapillarity effects are used to prescribe the motion of liquid droplets.

We examine the behavior of a three-dimensional liquid droplet on a non-uniformly heated or cooled horizontal solid surface. For a thin viscous droplet, lubrication theory was used to derive a two-dimensional evolution equation that includes the effects of viscosity, gravity, surface tension, slip at the contact line, and thermocapillarity. The evolution equation was coupled to a dynamic contact-line condition, relating the contact-line speed to the apparent contact angles, to describe the bulk motion of the droplet. The behavior of the droplet was examined in terms of the imposed thermal field on the solid surface, which includes a mean temperature and a constant temperature gradient superimposed on the mean value. This non-uniformity in the thermal conditions initiates a thermocapillary flow within the droplet that drives bulk migration down the temperature gradient. However, for certain values of the heating parameters, the system exhibits an instability characterized by a slight elongation of the contact line and highlighted by the formation of a dimple at the center of the droplet. When both thermal parameters are active, we show that the instability can be stabilized by a sufficiently large imposed thermal gradient. The critical value at which the interface shape transitions back to a non-dimpled steady state increases with uniform heating of the solid surface. Hysteresis behavior in the critical values in forward and backward traces along the steady-state solution branches is demonstrated and suggests a subcritical instability.

The instability also appears under axisymmetric or uniform heating conditions. The results indicate that a critical uniform heating value exists above which the droplet transitions from an axisymmetric configuration to a non-axisymmetric state with the interface shape again characterized by a dimple at the droplet center. For the axisymmetric instability, there was no transition back to a non-dimpled state at larger heating values. A stability analysis for the axisymmetric and three-dimensional droplet will be conducted to confirm the behavior observed in this study.

Although seismologists do not yet agree on the details of the depth dependence, the longitudinal variations, and perhaps even the strength, to a first approximation the inner core has been inferred to be elastically anisotropic, with the direction parallel to the rotation axis fast. Many hypotheses have been suggested as a cause for the anisotropy, all involving a lattice-preferred orientation, but the physical reality of many of them has not yet been demonstrated.

Using ice as an analog material for high-pressure, hexagonal-closest-packed iron, a series of laboratory experiments have been carried out in which salt-water is solidified from the center of a rotating, hemispherical shell. The experiments reveal more rapid growth of the solid near the pole than the equator, presumably because the Coriolis force inhibits convection within the tangent cylinder parallel to the rotation axis and circumscribing the inner core. Unlike in the Earth where pressure effects are important, in the experiments this leads to colder temperatures within the tangent cylinder. Because of the small length and time scales of the experiments it is not possible to study subsequent solid-state flow, but the experiments do demonstrate that the equilibrium solidification surface is not spherical. Using polarized light on thin sections of the ice, the columnar nature of the dendritic crystals is apparent, with the a-axes lying in the direction of growth. The experiments show how fluid flow in the melt may affect the solidification texture. The laboratory model suggests how a solidification texture is frozen in, from which further textural changes may develop.

Channel convection through the porous, dendritic mushy zone in solidifying alloys results from a nonlinear focusing mechanism, whereby liquid enriched in the solute melts dendrites as it convects away from the solid. The local melting reduces the Darcy friction and increases the flow speed to form a convective channel. However, it has been predicted that an applied magnetic field might prevent channels from forming because, as the Lorentz force replaces the Darcy friction as the primary resistance to flow, the focusing mechanism no longer operates. We find that an applied magnetic field can suppress channel convection when Q_m, the mushy zone Chandrasekhar number, exceeds order one. Q_m is a measure of the ratio of the Lorentz force to the Darcy friction. The longitudinal macrosegregation is not affected by the absence of channels, suggesting such channels are not always primarily responsible for the mass flux between the mushy zone and the melt and/or that convection in the mushy zone can occur without channels forming.

Williams and Davis (1982) derived a lubrication model for the evolution of thin films under the influence of van der Waals forces and surface tension. More recently, Zhang and Lister (1999) showed that this model has an infinite set of similarity solutions corresponding to finite-time film rupture. In this poster we discuss the dynamics and stability of thin-film rupture in planar and axisymmetric geometries. As the film thickness decreases, the planar state loses stability; we discuss the structure of the bifurcating solutions in both geometries. Loss of stability can lead to finite-time rupture of the thin film.

We have developed a systematic technique for calculating self-similar rupture solutions and determining their linear stability. The dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. For the problem of axisymmetric van-der-Waals-driven rupture, we identify a unique stable similarity solution for point rupture of a thin film and identify a new mode of rupture – annular "ring rupture."

The following sections are included:

• A front-capturing method for liquid-vapor flows with phase-change

• Front-tracking without connectivity

BACKGROUND: Intravascular gas embolism (IGE) is the entrapment of gas bubbles in the circulation and can occur in decompression sickness or during cardiopulmonary bypass. These IGE are harmful because they temporarily block blood flow causing local ischemia in the surrounding tissue. Altering the interfacial tension and contact-line mechanics at the bubble/blood/vessel interface with a surfaceactive agent changes the bubble conformation and dynamics. To determine the potential therapeutic benefit of manipulating interfacial forces, we investigated the effects of the surfactant, Antifoam 1510-US, on the dynamics of bubble entrapment and break-up in the intact rat cremaster circulation.

METHODS: The animals used in the experiments were handled according to NIH guidelines. Adult male Wistar rats (n = 6) were anesthetized, instrumented, and divided evenly into two groups, control, and those receiving a 2.5 ml pretreatment bolus of diluted Antifoam, raising the surfactant concentration to 1.5% of the total blood volume. Air bubbles (4 μl) were injected through the femoral artery and observed in the cremaster circulation over time with video-microscopy. Dimensions of the bubbles (0.2–10.0 nl), as well as other parameters relating to embolism dynamics, were measured from the video-taped recording.

RESULTS: The arterial vessels in the cremaster circulation of rats receiving the pre-treatment of Antifoam showed a much greater degree of constriction (~ 65%) than the arterioles of the control rats. This increased vasoconstriction in the pretreated animals, coupled with surfactant at the interface, lead to bubble elongation and caused bubble pinch-off into several smaller bubbles, not seen in the controls.

CONCLUSIONS: Addition of exogenous surfactant increased deformability of the IGE. This permitted a smaller radius of curvature at the ends of the bubble and allowed for bubble narrowing, elongation, and eventual bubble pinch-off. The pinch-off phenomena induced by surfactant may clinically create multiple smaller bubbles more apt to traverse the microcirculation and lodge in smaller vessels. This might maintain vital organ blood flow and reduce tissue damage.

A binary melt is hypercooled when it is cooled to a temperature below its solidus. In the isothermal limit planar solidification fronts propagate at a constant velocity determined by the kinetic undercooling and are subject to a long-wavelength morphological instability if speeds fall below a critical value. In this letter we examine the adiabatic limit where the accumulation of a small latent heat release causes the velocity of the interface to slowly decrease through its critical value. The evolution of the hypercooled interface is governed by a damped Kuramoto-Sivashinsky (dKS) equation with coefficients that vary as the interface decelerates. Using this equation we show that morphological transitions are delayed by an amount that reflects both the time the system spends in a stable state and the magnitude of the damping. For a sufficiently large latent heat of fusion the long-wavelength morphological instability is annihilated. Finally, the adiabatic dKS equation predicts late-stage coarsening of the microstructure with length scales that increase as t^1/2. In finite systems this coarsening removes the morphological instability.

The drainage of a thick non-aqueous film with a surfactant will be studied theoretically and compared with experimental results. Although the film is thin physically, the film is thick enough so that intermolecular forces acting across the film are not important. In the experiment, a thin film is suspended vertically from a wire frame over a bath and gravity drives the drainage of the film back into the bath. Lubrication theory is applied to the situation and the thin film is patched to the bath. Surfactant-transport, Marangoni, and surface-viscous effects are included in theoretical models. Models have been formulated that span the range of drainage regimes, which correspond to the range from rigid to mobile films. Computed and analytical results show that films may be made rigid by surface-viscous or Marangoni effects. Similarity solutions are found in some cases.

Understanding the transport of surfactant and liquid in the lung is of great importance in designing treatment for respiratory distress syndrome (RDS), and in understanding clearance from the lung. The standard method, surfactant replacement therapy (SRT), for treating this deficiency is to instill exogenous surfactant into the lung. It spreads in the small airways due to Marangoni flows. After the initial transient spreading, the surfactant concentrations at generation 7 (the approximate start of the Marangoni region) and generation 18 (the approximate start of the alveolated region) are essentially constant, so that a steady background surface tension gradient is established. Most of the surfactant transport in SRT takes place once this background gradient is established. On the other hand, liquid and surfactant clearance in normal lungs occur because production of surfactant in the alveoli results in lower surface tensions there than in the airways. This surface tension gradient causes flows towards the trachea. We consider a thin film lining a stretchable tube with a radius that depends on axial position to model airway branching and examine the effects of axial and radial wall oscillations on surfactant and liquid transport. Evolution equations for the film thickness, surface-surfactant concentration, and bulk-surfactant concentration are derived from conservation of momentum, conservation of fluid mass, and conservation of surfactant mass. The model is general and allows for choices of (1) interfacial linear sorption kinetics or squeeze-out phenomena; (2) uniform or linear membrane wall strain; (3) higher (SRT) or lower (liquid and surfactant clearance) concentration at the proximal end of the domain; (4) various strain amplitudes; and (5) various breathing-cycle periods. The evolution equations are solved using the methods of lines, and the cycle-average transport of both surfactant and liquid is computed. While the transport of surfactant on the surface and in the bulk varies greatly with strain amplitude, the transport does not vary as much with cycling period at a given strain amplitude in our model of SRT. As the transport of surfactant into the alveolar region is considerably higher when the strain amplitude is large, it may be advantageous to use large tidal volumes and large breathing-cycle periods with SRT in order to gain larger surfactant (both surface and bulk) transport. Our model of liquid and surfactant clearance predicts that large breathing-cycle periods and strain amplitudes result in greater clearance.

We have experimentally examined the effects of common soluble surfactants on gas bubbles in liquid flows in inclined tubes. Air bubbles of known size (λ = 0.8, 1.0, 1.5) are held stationary under minimum flow conditions in tubes oriented at specific inclination angles (α = 45°, 90°). Sodium Dodecyl Sulfate (SDS) or Triton X-100 (TX100) is infused into the bulk flow at specific bulk concentrations (Γ = 10% CMC, 100% CMC). In addition to recording pressure and flow waveforms, we capture images of the bubbles before and during exposure to the surfactant. The modification of the interfacial properties by the surfactant results in bubble behavior ranging from interfacial deformation to deformation plus axial translation to bubble detachment from the wall plus axial translation. Correspondingly, we observe modification of the measured pressure gradient within the test section of the tube. These surfactant-mediated responses are dependent upon the interrelated effects of Γ, λ, α, and the surfactant characteristics. Specifically, a high bulk concentration of surfactant produces more rapid bubble modification and increases the potential for bubble detachment. The potential for detachment increases further as bubble volume is increased. In both vertical tubes where contact forces are not important and in non-vertical tubes the infusion of surfactant may lead to axial translation either with or against the bulk flow. Finally, surfactants that are more effective at modifying contact properties produce bubble-shape and pressure-gradient changes more rapidly. This investigation demonstrates the ability of surfactants to potentially dislodge dried gas bubbles through the manipulation of interfacial properties.

Buckling instabilities are not restricted to solids; they can occur in thin layers of Newtonian fluids. Here we investigate two types of buckling. The first experiment is an instability in a thin viscous layer that lies in a cylindrical annular geometry. As the shear rate becomes larger than a critical threshold, the viscous film deforms sinuously without changing its thickness leading to ripples arranged like the spoke of a bicycle wheel. The ripples appear because the shear gives rise to tensile and compressive stress; the latter are responsible for out-of-plane motions of the sheet. Linear stability analysis predicts the critical shear rate at which the instability occurs as well as the wavelength and angular frequency of the instability. This analysis is compared to the results of our experiments.

The second scenario of a buckling of a viscous sheet occurs when a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble it bursts so slowly as to collapse under its own weight simultaneously, and folds into a wavy structure. This rippling effect occurs for both elastic and viscous sheets, and a theory for its onset is formulated. The growth of the corrugation is governed by the competition between gravitational and bending forces (shearing).

Understanding and controlling how a liquid interface changes its topology from being singly connected to being multiply connected (as is the case with a drop dripping from a faucet) or from being bounded to being unbounded in a particular direction (as is the case in the selective-withdrawal problem) is crucial for the control of many manufacturing processes including the creation of emulsions and mono-dispersed sprays. Furthermore, the mathematics describing these types of topological changes is not understood very well. In my poster I will present two beautiful phenomena that explore and shed light on these issues. First, I will show results from experiments on the two fluid drop snap-off problem where fluid is dripped through an outside liquid medium that is viscous. I will then show results from experiments on the selective-withdrawal problem. Here, we lower a straw so that its orifice rests above a water-oil interface. We then withdraw the oil through the straw. By changing the rate of withdrawal we control a transition between having only oil being withdrawn and having water being entrained along with the oil.

A classic problem in surface gravity waves is that of two-dimensional sloshing modes in a channel of arbitrary shape. Exact solutions are known for vertical walls and for triangular containers with α, the angle subtended at the free surface, equal to 45° or 30°. At higher frequencies, the wave motion is confined near the free surface and only the shape of the container at the corners is important. Fox and Kuttler (ZAMP, 1983) conjectured the asymptotic form

Experiments designed to verify the theory have been successfully completed for odd values of n up to 13. Five geometries, including angles 60° and 135° for which μ is not an integer, were used and surface tension in the fluid minimized. The measured data was adjusted to account for the remaining surface tension and good agreement with the theory was obtained.

Two different-sized drops of one liquid immersed in a second, immiscible liquid will move relative to one another under the influence of gravity. When the drops come close together, they interact owing to hydrodynamic disturbances, and various outcomes are possible: separation of the drops, capture with or without coalescence of the drops, breakup of the smaller drop into two or more drops, or even a combination of capture and breakup phenomena. Interfacial deformation may promote any of the results, depending on the drop-to-medium viscosity ratio, the ratio of the smaller drop radius to the larger drop radius, the gravitational Bond number, which is a measure of how much the drops will deform, and the initial horizontal offset between the drops. This poster presents an experimental investigation into the parameter space governing two-drop interactions to compare with theoretical results obtained previously (Zinchenko, Rother, and Davis, J. Fluid Mech. 391, 249 (1999); Davis, Phys. Fluids 11, 1016 (1999)). Trajectories of two drops consisting of a mixture of glycerol and water moving through an external medium of castor oil are photographed and analyzed to check quantitative agreement with computer simulations.

Previous work on the flow of thin liquid films over inclined solid surfaces has shown the existence of two forms for the advancing leading edge. In an investigation to determine the speed of advance of the chevron-like form of this disturbance, it was observed that in a single experiment the other pattern, rivulets with sides parallel to the down-slope direction, occurred when using silicone oil on a glass surface. Subsequently an extensive series of tests could not replicate this single result on clean glass. Various contaminants were then applied to the glass, but only chevrons appeared when the silicone oil film flowed. Finally, a stain inhibitor for fabrics, Scotch-gard, was sprayed onto the glass and the silicone film produced rivulets at its leading edge. Hence, it was concluded that some unknown substance that yielded a similar effect must have been deposited on the glass plate that had produced, with but one exception, chevrons. The present tests also showed that clear Teflon film will also form rivulets with silicone oil. Moreover, the author obtained rivulets with glycerin on glass, in contrast to previously-reported results of others. The ultimate lesson that can be drawn is that even when the solid surface is diligently and well cleaned, molecular thin films might be present to alter the contact angle of the liquid at the solid boundary and, thereby, affect the type of leading-edge pattern that is observed in an experiment.

We report on measurements of the viscosity of Langmuir monolayers. Langmuir monolayers are comprised of amphiphilic molecules that are confined to the air-water interface. They exhibit a rich two-dimensional phase behavior that includes the usual gas, liquid, and solid phases, as well as a number of phases that are analogs of three-dimensional smectic liquid crystals. We have built a Couette viscometer that is capable of measuring velocity profiles, viscosity, and the complex shear modulus of monolayer films. The velocity profiles are obtained by imaging the monolayer using a Brewster-angle microscope. The apparatus has been tested on both Newtonian and non-Newtonian phases, and the results for the velocity profiles are consistent with theoretical calculations.

It is known that the addition of divalent ions to the water will "stiffen" monolayers of fatty acids. This is due to the binding of two fatty acids by a single divalent molecule. The influence of divalent ions on the phase behavior has been studied, but the effects on the viscosity have not been studied in detail. We have made measurements of both the viscosity and the shear modulus and find that they increase by three orders of magnitude over a 10-hour time scale. Further, the evolution appears to occur with three distinct time scales. We directly measured the percentage of Ca⁺⁺ ions bound to the monolayer as a function of time by repeatedly transferring the monolayer onto a solid substrate. The multilayer formed by this process was rinsed in an acid to release the Ca⁺⁺ ions, and their concentration was measured with an ion meter. We found that the fraction of bound Ca⁺⁺ had a similar time evolution to the viscosity. Also, a simple ad-hoc model for the viscosity in terms of the percentage of bound Ca⁺⁺ is able to explain the time evolution. A more detailed study of this process will provide important insights into the fundamental nature of viscosity.

Little is detailed about surfactant effects on the contact angle, contact-angle hysteresis, and contact-line motion. Ultimately we are interested in wetting/dewetting phenomena related to intravascular gas embolism and its treatment with exogenous surfactants. We have therefore begun to characterize the relationships between contact angle, contact-angle hysteresis, spreading parameters, and surfactant moieties on various solid substrates.

Using a Wilhelmy-plate surface tensiometer, we measured the air-liquid surface tension, σ, of aqueous solutions of sodium dodecyl sulfate, (SDS) with and without 5% bovine serum albumin (BSA) present. By video image analysis, we evaluated a drop interfacial shape on a stationary flat horizontal substrate and on a flat slowly-rotating substrate (< 1°/second). Drop volumes were 40–80 μl and all measurements were recorded at room temperature in a sealed, humidified chamber 30 minutes after solution instillation into the experimental apparatus. Solid substrates included glass, acrylic, and stainless steel. We measured static, advancing, and receding contact angles, ϕ_s, ϕ_a, and ϕ_r, respectively, of drops of the same aqueous SDS ± BSA dilutions. We calculated S, the spreading parameter, based on ϕ_s.

The parameter σ cos ϕ incorporates both the surface tension and contact-angle effects needed to calculate a spreading coefficient. It is a measure of the adhesion force acting at the contact line. On glass, as SDS concentration increases, σ cos ϕ_s decreases monotonically to a minimum of 37.3 dyne/cm at and above the CMC. For both acrylic and stainless steel, as the SDS concentration increases, σ cos ϕ_s increases to a local maximum and then decreases to its plateau value (~33–34 dyne/cm) at and above the CMC. The variation of σ cos ϕ_s with concentration of SDS in the presence of BSA (which is surface active) maintains substrate dependence with a more narrow range of values. Competition between BSA and SDS for interfacial sites likely accounts for this. The contact-angle hysteresis (ϕ_a – ϕ_r) is nearly constant (~26°–30°) over the range of SDS concentrations. There is an 8-fold change in S, which tends from -19.2 to -2.4 as the SDS bulk concentration increases from 0 to the CMC.

The surfactant studied lowered interfacial tension, and reduced contact angles and the spreading coefficient with substrate dependence. These experiments help to explain a potential role that exogenous surfactants may have in the treatment of intravascular gas embolism. A particular surfactant delivered to the interface may significantly change the wetting potential of the liquid onto the solid and thereby increase or decrease the adhesion force acting on a trapped bubble. The exact influence of interactions of individual species (surfactant, protein, substrate) on the interfacial quantities measured in these experiments are not easily inferred. They must be derived by continued careful experimental analysis.

Dynamic wetting, spreading of a fluid over a solid surface, controls many natural phenomena and technological processes. When surface tension forces are important, the interface shape and local flow field very near the moving contact line control the macroscopic configuration of the fluid body. However, identifying the correct assumptions needed for predictive models of spreading is not trivial. Theoretically, the central difficulty is the unphysical stress singularity at the contact line arising when classical hydrodynamic assumptions are applied up to and including the moving contact line. The singularity suggests that very near the contact line (in an "inner" region), unique microphysical processes other than the classical hydrodynamic assumptions control the fluid motion. Thus, we must explore: what are these unique processes operating on the microscopic scale? And how can we find a legitimate boundary condition for the macroscopic problem?

Asymptotic expansions provide a description of the hydrodynamics near moving contact lines in a limited parameter range. These expansions and very accurate experiments provide a tool for answering the questions central to understanding the moving-contact-line problem. We have found that for a set of Newtonian polymer fluids (PDMS, polydimethylsiloxanes) on various surfaces, these asymptotic expansions describe the hydrodynamics at small capillary number, Ca < 0.1, and negligible Reynolds number, Re ~ 0. At higher Ca (with Re ~ 0) and moderate Re ~ 0.1 (with Ca < 10⁴), our experiments find that the curvature of the interface near the contact line is less than that predicted by the asymptotic expansions.

Having established the validity of the asymptotic analysis, we may now use it to probe the microphysical properties controlling the fluid motion on the inner scale. Although many processes have been suggested, no direct experimental identification of these processes exists. We must carefully use the tool provided by the asymptotic expansions to indirectly recover information on the inner scale hydrodynamics from our experiments. Use of static approximations or Tanner's Law in the analysis of experimental data leads to systematic errors that obscure the correct characterization of the inner hydrodynamics. We find that for PDMS, the parameters describing the inner hydrodynamics to in Ca, as Ca → 0, must vary with contact-line speed. This variation is complex and suggests that different mechanisms operate at different contact-line speeds. Further, the inner hydrodynamics vary, even for very closely-related systems. Use of Ca to scale the velocity does not unify the data for the different systems, implying that this is not the correct scaling of the fluid velocity in the inner region.

This work is devoted to a theoretical explanation of an effect observed during the study of freezing of ice in an axisymmetric container [1]. The experimental setup consists of a cylindrical glass container filled with water, which is immersed in a bath with hot water and is closed by a cold steel cover. After the temperature of the cover is reduced below 0°C, an ice front is formed. The solidification front observed on the ice had an asymmetric, circumferentially-periodic surface shape. Likewise, measurements of the temperature field showed a periodic structure.

It was assumed that the effect was due to an axisymmetry-breaking instability of the convective flow of water. Detailed numerical analysis of the stability of the basic axisymmetric flow with respect to all possible three-dimensional perturbations showed that an instability sets in with a relatively high azimuthal wavenumber k, which varies between 7 and 10. Details can be found in [2]. The corresponding pattern of the most unstable three-dimensional perturbation of the temperature is similar to the experimentally-observed temperature distribution. It is shown that the calculated instability is caused by the Rayleigh-Bénard mechanism, which leads to the appearance of a system of convective rolls distributed along the azimuthal direction inside a relatively thin convective layer.

The mechanics of separation of a thin interfacial liquid layer trapped between two parallel surfaces was studied in a controlled manner. The liquid of choice was a silicone oil with constant surface tension, but variable viscosity. Different viscosities, layer thicknesses, and separation velocities were used to determine the separation behavior and its dependence on viscous fingering and capillary number. Force, displacement, and time data were recorded for all experimental runs and the plots used to gain preliminary insight into this process. Qualitative flow-visualization data has also been recorded to corroborate the trends in the onset of viscous fingering with the predictions of a simple interfacial stability analysis.

The dynamics of free-surface flows and in particular the mechanisms for singularity formation at the interface of fluids with different physical properties constitute a problem of high theoretical as well as practical interest. The applications are abundant and include the functioning of such commonplace devices as ink-jet printers and fuel injectors, and processes such as oil extraction and fiber spinning. While considerable theoretical and computational advances have been achieved in our understanding of the problem in the inviscid and Stokes limits, the analyses at intermediate Reynolds numbers remain scarce and inconclusive.

We present a general computational algorithm able to describe different kinds of axially symmetric, free-surface flows for arbitrary Reynolds numbers. The distinctive feature of the proposed algorithm is that the interface is treated as a mathematical singularity corresponding to the discontinuous change in the fluid properties, rather than being artificially smeared over a finite region, as is usually done. This should allow one to numerically simulate the singularity formation with precision adequate for comparison with experimental data.

The idea of the algorithm is to replace the mathematical problem involving multi-fluid flow with complicated boundary conditions imposed at the free interface(s) with a simpler problem involving a single-fluid flow with spatially (and temporally) varying viscosity and density, and with a surface-tension force acting at the interface(s), thus effectively getting rid of the boundary conditions. This is achieved by writing the Navier-Stokes equation and the incompressibility condition in the weak form by integrating these equations with an appropriately chosen weight. The obvious advantage of the finite-element formulation is that it contains no singularities associated with the jump in viscosity at the interface. The viscosity jump can be removed by performing integration by parts, effectively reducing the order of the equations by one. Furthermore, the singularity produced by the jump in pressure can also be removed by using weight functions that are themselves discontinuous at the interface.

Present implementation assumes no angular dependence and zero angular velocity, but the algorithm allows one to lift these assumptions at the expense of a slight complication in the formulas. The interface is advanced using a version of the interface-tracking technique based on the advection of massless markers with the velocity field computed on a fixed grid, although other thechniques such as the volume-of-fluid or the level-set method can be easily incorporated. Our preliminary results for the two-fluid, selective-withdrawal problem provide an illustration of the computational method.

We present molecular simulations of two classical interfacial phenomena in fluid mechanics.

The first is the Rayleigh-Taylor instability, arising when a heavier fluid is situated on top (with respect to a gravity field) of a lighter fluid. Our molecular techniques allow a novel approach to this problem. The instability is triggered by molecular thermal fluctuations instead of the artificial perturbations imposed in continuum simulations. Additionally, a direct comparison between miscible and immiscible Rayleigh-Taylor mixing is possible.

The second problem presented is the motion of a contact line in two dimensions. Molecular simulations of a fluid displacing a second immiscible fluid in a two-dimensional channel are performed. A continuum simulation of the same problem is employed to answer the following question: what continuum boundary conditions are required to reproduce the molecular interface shape? We found that by using the actual slip profile observed in our molecular simulations as a slip boundary condition and by setting the dynamic contact angle equal to the static value, that we could reproduce the molecular results satisfactorily in the range 0.059 < Ca < 0.072 [Phys. Rev. E 59, 2475 (1999)].

Solder-jet technology is targeted for use in high-density-electronics-assembly applications where 63Sn/37Pb solder is utilized as an attachment and/or structural material. Solder jetting relies on ink-jet printing technology to create and precisely place miniature molten-solder droplets (50–100 μm in diameter) on substrates or pads. These droplets solidify after impact, forming bump deposits that are subsequently used for the flip-chip bonding of electronic components on the substrate. Ink-jet-based solder deposition is low cost (no masks or screens are required), flexible, easily automated using digital technology, suitable for a manufacturing environment (does not operate in a vacuum), highly repeatable, and offers high resolution.

Even though solder jetting shows great promise to achieve solder deposition at pitch geometries well below what is feasible with existing techniques, there exists a few formidable challenges that must be overcome before commercialization. Because maximum throughput is an important requirement in electronic assembly, solder jetting is performed openly, but with local environmental control. A sheathing nitrogen-ring flow surrounds the solder jet to minimize solder oxidation that can drastically delay the atomization process and degrade the effective adherence of the solder deposits on the targets. Therefore, successful commercial implementation requires quantification of the influence of the ambient oxygen content on the surface properties of the molten solder jet.

The method employed to measure the surface tension of the molten solder jet is the oscillating-jet technique. When a liquid is forced through an elliptical capillary (aspect ratio ≈ 2), an oscillating jet forms. The stationary shape of this jet (wavelength and both semiaxes) is affected by the liquid/gas interface properties and is used to determine the surface tension as a function of distance from the orifice (surface age) using the analysis of Bechtel et al. [J. Fluid Mech. 293, 379 (1995)]. The jetting is performed in a controlled environment containing a known nitrogen/oxygen mixture. A CCD camera with a microscope lens is used to obtain images of the oscillating solder jet along both major axes. From these images, the wavelength and the semiaxes are determined at the beginning, middle, and end of successive wavelengths. This data along with other material properties is used to determine the dynamic surface tension of the molten solder along the direction of jet propagation. The experiment is repeated at oxygen mole concentrations ranging from 5ppm to 21% (air). In addition to the oscillating-jet experiments, a maximum-bubble-pressure apparatus is employed to determine the equilibrium values of surface tension of molten solder in controlled nitrogen/oxygen mixtures.

When a liquid droplet is placed on a flat solid surface, we may observe partial wetting or complete wetting of the surface depending on the static and dynamic contact angles. We present a simple mathematical model for this free boundary problem and a new numerical method to simulate this model. Our numerical algorithm is based on the modified immersed-interface method and the level-set formulation. Our numerical results agree with those experiments and analytic results in the literature. Topological changes are handled easily using our methods.

We examine experimentally and theoretically the breakdown of a straight contact line on a roller that rotates into a liquid. This breakdown occurs at a critical dimensionless speed (capillary number Ca_c) and precedes the industrially important air-entrainment phenomenon. A corn-syrup/water mixture with relatively low viscosity (0.3–0.7 Poise) is used as the test fluid. Our flow-visualization experiments indicate that the liquid interfacial velocity at the nearly critical air cusp above the contact line decelerates rapidly (by two orders of magnitude) over the short length of the cusp (a few capillary lengths). Moreover, Ca_c is found to be insensitive to agitation in the liquid phase, but extremely sensitive to obstacles placed above the cusp in the gas phase.

The evolution of the air flow coupled with changes in the shape of the air-liquid interface is of paramount importance in the stability of the two-dimensional air cusp, since air is dragged into the cusp by both the solid roller and the liquid phase. Both the injection drag forces and the length of the cusp increase with increasing roller speed. The build-up of stagnation pressure, however, saturates as the cusp flattens. Consequently, at a critical Ca, the steady-flow balance breaks down. The required pressure gradient for air ejection becomes impossible in two dimensions — a larger free-surface-curvature gradient is needed to push the air out of the longer flat cusp. Hence, the third dimension should be invoked and the formation of triangular air pockets along the contact line is initiated.

We support this physical mechanism for air entrainment via matched asymptotics. Momentum boundary layers on the gas side within the cusp and on the roller and below the cusp interface in the liquid are connected to each other and to inviscid outer solutions. The matching at the contact line requires a molecular model for the gas viscosity when the air-cusp width approaches the mean-free path of gas molecules. Of particular interest is the dependence of Ca_c on the inception length of the gas momentum boundary layer as specified by the position of a scraper — a potentially useful means of delaying air entrainment in industry.

Vibration-induced droplet ejection occurs when a liquid drop is placed on a vertically-vibrating surface. The vibration leads to the formation of capillary waves on the free surface of this primary drop. When the forcing amplitude is large enough, secondary droplets are ejected from the wave crests.

For low-frequency forcing a low-order, axisymmetric wave mode is excited in the primary drop. For large enough forcing amplitudes, a steep depression or crater forms in the center of the drop during the downward phase of the oscillation cycle. During the next phase the crater collapses and liquid flowing inward forms an upward, high-momentum jet at the center of the crater. One or more small droplets may fragment from the end of this jet to produce secondary droplet ejection. For large forcing frequencies the wave motion is chaotic. Secondary droplets are ejected from multiple locations on the free surface of the primary drop. At each ejection site, a crater forms before droplet ejection. As in the low-frequency case, the crater then collapses and a jet is formed at the center of the crater. One or more droplets may then be ejected from the end of the jet. Under certain conditions the entire primary drop will rapidly atomize.

An axisymmetric, Navier-Stokes solver, based on the MAC method, is used to simulate the low-frequency process. The solver includes a piecewise linear, volume-of- fluid method and a continuum-surface-force implementation of surface tension. The simulations capture the sequence of events discussed above: a crater is formed, which collapses to form a jet, from which secondary droplets are ejected. Comparison of a time sequence of calculated interface shapes to an experimental sequence shows good agreement. The simulations illustrate the large velocities that develop in the jet.

The simulations will be used to investigate the physical mechanism responsible for droplet ejection. The effect of the driving parameters and physical parameters on the ejection process, including the size and velocity of the secondary droplets, will be evaluated. This will be used to gain an understanding of high-frequency atomization which, in turn, will be applied to the design of systems involving spray formation. This technology has application in a wide range of aerospace, industrial, and biomedical applications. A heat transfer cell that utilizes this technology is under development for microelectronics-cooling applications. This cell is similar to a heat pipe, but has a higher liquid flow rate that results in a substantially higher heat transfer rate.

Liquefied natural gas (LNG) is stored in an insulated tank where heat transfer throught the tank wall into the liquid is released by the evaporative heat loss at the liquid/vapor interface inside the tank. Excess vapor is transported out and the vapor pressure is usually kept constant. When the tank is refilled (usually bottom filled) with new cargo, it has different constituent concentrations from the existing LNG in part due to the preferential evaporation of constituents. As a result the new LNG usually has higher density, and a stable stratification results.

The new LNG in the bottom, however, does not release heat efficiently due to the lack of an evaporating interface. As the heat builds up, the density approaches that of the upper layer and a reversal of the layers can occur.

In the present study, we examine this multiphase flow of liquid and gas mixtures by stability analysis, a dynamical-systems approach, and finite-difference computations. In particular, the conditions for the reversal and the elapsed time are presented.

In this work, we study steady and oscillatory thermocapillary and natural convective flows generated by a bubble on a heated solid surface. The dynamic characteristics of the time-dependent convection are captured using a combined numerical-experimental approach. The index of refraction fringe distribution patterns constructed numerically by taking an inverse Abel transform of the computed temperature fields are compared directly to the experimental Wollaston Prism (WP) interferograms for both steady state and oscillatory convection. The agreement between numerical predictions and experimental measurements is excellent in all cases. It is shown that below the critical Marangoni number, steady-state conditions are attainable. With increasing Ma number, there is a complete transition from steady state up to a final non-periodic fluctuating flow regime through several complicated symmetric and asymmetric oscillatory states. The most prevalent oscillatory mode corresponds to a symmetric up and down fluctuation of the temperature and flow fields associated with an axially travelling wave. Careful examination of the numerical results reveals that the origin of this class of convective instability is closely related to an intricate temporal coupling between large-scale thermal structures that develop in the fluid in the form of a cold finger and the temperature-sensitive surface of the bubble. Gravity and natural convection play an important role in the formation of these thermal structures and the initiation of the oscillatory convection. Consequently, at low-g, the time evolution of the temperature and flow fields around the bubble are very different from their 1-g counterparts for all Ma numbers.

We explore the computational performance of different models used to compute the flow of a thin film down an inclined plane, within the framework of the lubrication approximation. Our 1D computations show that the results and computational efficiency strongly depend on the model that is used to deal with the contact-line singularity. This study allowed us to develop efficient fully nonlinear 2D simulations. Preliminary 2D computational results concerning contact-line instability will be presented.

A flow-visualization technique for density fields in liquid and solidifying alloyed metals has been developed. Density fields have been visualized similar to interferometry conventions. Density fields include information on temperature and concentration. In alloys, concentration is the dominant signal, thus chemical segregation in the melt can be revealed. Natural convection and double-diffusive flows have been visualized along with solidification and melting. Some visualized results are challenging theoretical analysis.

We present numerical methods for computing the motion of two-dimensional bubbles or drops in a slow viscous flow. New methods are presented for both the solution of the governing fluid equations and for the time integration of the evolving interfaces. The interfacial velocity of the bubble or drop is found through the solution to an integral equation whose analytic formulation is based on complex-variable theory for the Stokes equations. The numerical methods are spectrally accurate and employ a fast multipole-based iterative solution procedure, which requires only operations where N is the number of nodes in the discretisation of the boundary. It is known that the dynamic equations for the interfacial motion become stiff as the curvature of the interface increases. A small-scale decomposition is performed to extract the dominant term driving the stiffness. By introducing an appropriate tangential velocity into the dynamics, this dominant term becomes linear. This leads to implicit time-integration schemes that are explicit in Fourier space. Examples will include the deformation of drops in an extensional flow and the viscous sintering of glass.

The presence of surface-active materials, ubiquitous at most gas/liquid interfaces and particularly at the air/water interface, has a pronounced effect on the stress balance at the interface, and this in turn is nonlinearly coupled to the bulk flow. Even with minute amounts of surfactants on a liquid free surface, the boundary conditions for the Navier-Stokes equations are functions of the interfacial viscoelastic properties. The Boussinesq-Scriven constitutive relation for stress at a Newtonian interface consists of three intrinsic properties of the interface. These are the surface tension, σ, the surface shear viscosity, μ_s and the surface dilatational viscosity, κ_s; consistent measurements of the latter have not yet been reported. These viscoelastic properties vary with the surfactant concentration at the interface, c. Here, we present a fundamental description of the interface and its coupling to the bulk flow and develop an axisymmetric Navier-Stokes numerical model. We perform both numerical studies using this model and experimental measurements of the liquid flow in an annular region bounded by stationary inner and outer cylinders and driven by a rotating floor. The difficulties in obtaining a clean free surface even when triply distilled water is used will be reported. DPIV measurements with a clean free surface will be presented. Computational results from our Navier-Stokes model that incorporates measured σ(c) and μ_s(c), and modeled κ_s(c) for hemicyanine (an insoluble surfactant) will be presented. The computations for surfactant cases are compared with the hydrodynamics of a clean interface and a no-slip rigid surface. These computations provide insight into the dynamics that result from the surfactant with a nonlinear equation of state and finite surface viscosity. In this presentation, we focus on low initial surfactant concentration cases where a contamination front is observed and find that its location varies linearly with the initial concentration.

Typically, when the Marangoni stress (due to surface-tension gradients) is dominating, the interface is thought of as immobile, acting as a no-slip surface. However, this is only true for the velocity components in the directions that would have lead to surfactant-concentration gradients. In the present axisymmetric swirling flow, this direction is radial. In the azimuthal direction, since the flow is axisymmetric, there are no azimuthal gradients and so there are no Marangoni stresses acting in that direction. Thus, in the radial direction, the Marangoni stress makes the interface act like a no-slip surface, but in the azimuthal direction it is essentially stress-free. This has fundamental consequences for models of contaminated interfaces that are not planar two-dimensional, where surfactant coverage does not simply mean that the interface is no-slip.

A liquid bridge between two solid surfaces is known as a capillary bridge and the stability of such bridges is relevant to materials processing as well as to other aspects of the management of liquids. For a cylindrical bridge in low gravity of radius R and length L, the slenderness S = L/2R has a natural (Rayleigh-Plateau) limit of π beyond which the bridge breaks. We demonstrate a novel method of suppressing the growth of this mode on an electrically conducting bridge surrounded by an insulating liquid of the same density in a Plateau tank. The shape of the bridge is optically sensed as in our related demonstration of acoustic stabilization [M. J. Marr-Lyon et al., J. Fluid Mech. 351, 345 (1997)]. In the present stabilization method the optical information is used to control the potentials on a pair of ring electrodes concentric with the bridge. Slenderness values can be made to reach 4.46 when the generalized feedback force for the mode of interest is taken to be proportional to the modal amplitude. At S = 4.49, the next higher mode (which is not controlled in our current experiments) is predicted to become unstable. The electrical conductivity of the bridge liquid need not be large.

In the absence of gravity, cylindrical capillary bridges consisting of liquid between two circular supports naturally become unstable and break when the length L of the bridge exceeds its circumference. This is the Rayleigh-Plateau limit where the slenderness S = L/2R is π and R is the bridge radius. In experiments performed aboard NASA's low-gravity KC-135 aircraft, it was found that acoustic radiation pressure can be used to stabilize capillary bridges against breakup. Capillary bridges composed of a mixture of water and glycerol were deployed in a 21 kHz ultrasonic standing wave in air. The bridges were extended to a slenderness as great as S = 4.1 prior to breaking. Bridges extended beyond π broke immediately when the ultrasound was turned off. In contrast with previous work [M. J. Marr-Lyon et al., J. Fluid Mech. 351, 345 (1997)], this stabilization method does not use active feedback; the stabilization is a passive effect of the sound field. The acoustic wavelength is chosen such that the average radiation pressure due to the sound field is a function of the local bridge radius, so that areas of larger radius are squeezed, and areas of smaller radius are expanded. The KC-135 environment, however, is poorly suited for exploring the limitations of this method and the passive acoustic stabilization method cannot be simulated in Plateau tanks.

High-accuracy numerical simulations are presented for the nonlinear evolution of directional solidification processes, both in the absence and in the presence of potential flow in the melt. To this end, a numerical method is employed that utilizes an analytical boundary-fitted coordinate transformation in conjunction with a combination of spectral and finite-difference discretizations. The flow field is computed by a boundary-element technique. The accuracy of the computational scheme is demonstrated by comparing the growth rates at small interfacial amplitudes with linear stability results.

In calculations with random initial perturbations, we observe the emergence of a large-amplitude dominant wavelength in agreement with the predictions by linear stability theory. Furthermore, the simulations demonstrate the stabilization of the solidification process by a uniform flow parallel to the interface. Results are presented as a function of wavenumber, morphological parameter, and parallel-flow velocity.

The evaporating meniscus of a perfectly wetting liquid exhibits an apparent contact angle Θ owing to small-scale, evaporatively driven flow in the contact region. Existing theory by Wayner predicts Θ and the heat flow as the solution of a free-boundary problem. Published simulations use that theory to model the behaviour of grooved heat pipes. In that application, the heat flow across the meniscus in a millimetre-sized groove is found by dividing the meniscus in two. The heat flow from the inner contact region is found from the theory of the small-scale flow. That across the outer visible meniscus is found by solving the two-dimensional conduction equation. The simulations cover scales from nanometres to millimetres. At the top end of this range, they include the geometry of the solid from which liquid evaporates. At the other end, they use the existing theory for the small-scale flow. This covers a continuum of behaviours. The extremes include the isothermal meniscus that does not show an apparent contact angle; and two forms of strongly evaporating menisci that do. The first of these occurs in the limit of vanishing flow resistance to evaporation. All evaporation then occurs from a quasi-parallel film at dimensions smaller than those on which Θ is established [1]. The second occurs in the limit of vanishing thermal resistance to evaporation. The contact region is then isothermal, and all heat flow occurs at dimensions larger than those on which Θ is established [2]. As there is no previous analysis of the existing theory, these possibilities are not recognised in the literature. Yet the case of vanishing thermal resistance is common in applications. By emphasising it, one obtains insight, and useful formulae for the heat-pipe problem….

In our present work we are investigating the formation and subsequent instability of vortex rings formed by drops impacting a pool. We are especially interested in two aspects of the problem: the vorticity-generation mechanism at the free surface and the instability of the vortex ring at early times after impact. This instability leads to shedding of large-scale structures into the vortex-ring wake that we refer to as petals. In some cases, the petals pinch at their tips forming small vortex rings that travel away from the central axis of the primary vortex ring. We refer to this structure as the blooming vortex ring. For a more thorough discussion of the vortex structure, see [1]…

Instabilities can develop at the "interface" between two miscible fluids that exhibit patterns very similar to those observed between immiscible fluids. For example, a layer of colored glycerine hanged-up below a glass plate and placed into a water tank gives rise to organized patterns. Also, a thin layer of glycerine falling into water is unstable and produces falling columns with a regular distance between each other. These similarities between miscible and immiscible fluids lead to the possible existance of an "effective surface tension" between miscible fluids. This effective tension has a meaning for short times only, and should tend to zero with time. It can be explained by the strong concentration gradient at the "interface."

Viscous fluids flowing down inclined planes are of special interest in the study of pattern formation and the transition to spatio-temporal chaos. At moderate Reynolds numbers, their dynamics is controlled by surface-tension effects and viscous dissipation. Making use of the slaving principle, one can eliminate most local internal flow variables that are essentially bound to follow the slow evolution of the film thickness h. Combining a systematic expansion of the Navier-Stokes equation in powers of a small dimensionless parameter measuring the amplitude of thickness gradients to a Galerkin approximation method involving a functional basis made of polynoms, we have derived several models of increasing accuracy and complexity [1]…

Recent resuspension experiments suggest that a possible interfacial tension exists between pure fluid and a suspension consisting of the same fluid and heavy, small, solid beads of identical size and density. Since little is known about interfacial phenomena in suspensions we experimentally investigated the formation and expansion of a suspension drop in the same fluid. To our surprise, the motion of the droplet exhibits all phenomena demonstrated by the classical experiments in which vortex rings of one liquid are created in another from drops falling from rest under gravity. Membranes formed even when the concentration of particles was smaller than 5%. We also observed the breaking of the torus by the Rayleigh-Taylor instability and the formation of a cascade of new rings. Two drops falling one behind the other penetrate but do not lose their distinct nature for several moments until they finally mix and move as a single drop. Larger drops typically create a long cylindrical tail of particles throughout the vessel that contains the clear liquid. This column is unstable and it breaks and forms small 'capillary droplets.' By making use of earlier investigations we were able to estimate the interfacial tension from the growth of the torus.

Containerless solidification, confining its melt by surface tension, is an important technique to produce very pure materials. The form of the solidified product is sensitive to conditions at the tri-junction between the solid, the melt, and the surrounding vapor. We reconsider the analysis of Anderson, Worster, and Davis (1996) to test whether a more simple tri-junction condition can model experimental behaviour when the flat solidifying interface is no longer imposed. We find that the simpler condition can describe the inflection point and cusp of the axisymmetric drop if the solid-liquid interface is no longer assumed to be flat. The solution is now checked asymptotically for large and small time and for short distances from the tri-junction condition.

We derive a fully continuous, macroscopic model for epitaxial film growth from an analogous, but microscopic, Monte-Carlo procedure. Our approach features an explicit adatom density that evolves subject to deposition, diffusion, nucleation, and edge-adsorption of adatoms and is coupled to a separate height evolution equation. A specific aim of this approach is to incorporate multi-species effects, which are important in many systems (e.g., YBCO). To this end, it is natural to make a distinction between an atom on the film surface but not yet incorporated into the film (i.e., in the surface-density field), and an atom that has become part of a completed unit cell (i.e., in the film-height field). Such a distinction is familiar in mesoscopic models involving diffusion on terraces and explicitly represented ledges, but is absent from existing continuum models. Thus, the multi-species version of this model has an evolution equation for the density of each species on the surface of the film.

Time-dependent thermal convection has been investigated experimentally in deformed liquid bridges of silicone oil with a Prandtl number Pr = 105. The temperature oscillations were measured by five thermocouples placed through the upper rod into different azimuthal positions in the liquid bridge some distance from the free surface. The signals from the thermocouples were taken for Fourier analysis and determination of their phase shift.

The experimentally obtained stability diagram (ΔT_cr,V) shows that the transition from axisymmetric steady flow to an oscillatory flow is very sensitive to variations in the volume. It consists of two different oscillatory instability branches belonging to different azimuthal wave numbers. Between them, there is a small range of volumes for which the steady flow is stable up to very high values of ΔT. For high Prandtl fluids, the branch on which ΔT_cr increases with increasing volume has an azimuthal wave number m = 1, and the descending branch has an azimuthal wave number m = 2. It was found that the beginning of the gap is linked to the upper contact angle α. The physical explanation of the stability diagram follows the arguments proposed by Shevtsova and Legros [Phys. Fluids 10, 1621 (1998)].

A detailed analysis of the power spectrum and phase shift of the thermocouple signals reveals that the instability begins as a mixed mode, with wave numbers m = 0 and m = 1, within a narrow interval of ΔT. This is followed by a nearly standing wave with wave number m = 1 that changes to an m = 1 travelling wave when ΔT > 1.2ΔT_cr.

It has been proven experimentally that if standing (or travelling) waves are established in the liquid bridge, they can exist indefinitely as long as experimental conditions are maintained constant.

To the best of our knowledge, there has been no previous experimental study of the influence of the average temperature inside the liquid bridge (the temperature of the cold rod) on the onset of instability. It is shown that the critical Marangoni number and critical wave number are very sensitive to the average temperature in the liquid bridge (e.g., to the temperature of the cold rod). Is this only an effect of temperature-dependent viscosity, or is it some other effect? The reason for such behaviour remains obscure.

We have also discovered the possibility of changing the most dangerous mode at the threshold of instability. By surrounding the liquid bridge with another cylindrical volume with a larger internal diameter and kept at a constant temperature, the critical mode m = 2 can be switched to m = 1.

Many molecular and colloidal systems exhibit coexistence of different phases, separated by interfacial regions with characteristic density/concentration profiles and curvatures. External stresses, temperature gradients, and chemical potentials drive such systems out of thermodynamic equilibrium, giving rise to distinct deformations and flows within and across interfacial boundaries that are coupled to those in the bulk. Dynamic interfacial phenomena occurring in multiphase and thermocapillary flows, and in processes such as wetting, coating, adhesion, friction, and lubrication, play a very important role in many physicochemical, biological, and industrial processes.

Molecular dynamics is a realistic tool for simulating these phenomena, but it is limited to small systems and short simulation times, in which statistical fluctuations mask local mean densities and flows. A surface-thermodynamic level of modeling is another approach that has been very useful in the past. It postulates separate constitutive relations between strains and dissipative contributions to the stresses (rheology) at Gibbsian (infinitesimally thin) dividing surfaces. However, these constitutive relations proliferate for interfacial and non-Newtonian systems, and are hard to parametrize experimentally. In addition, the Gibbsian approximation leads to unphysical singularities in some important dynamic processes, such as wetting.

We present a novel, convective-diffusive lattice-gas approach for modeling interfacial dynamics in multiphase flows. The equations of motion are expressed in terms of probabilities over microscopic lattice degrees of freedom consisting of molecular occupancies and Eulerian velocities at discrete lattice sites. In contrast to hydrodynamic lattice-gas and lattice-Boltzmann approaches, these velocities are not limited to discrete directions and magnitudes. Our method is based on a local self-consistent mean-field approximation for these probabilities and their moments, which are evolved by alternating discrete convective and dissipative timesteps, both subject to local conservation laws in discrete form. We model dissipation as a Markov-chain process corresponding to diffusion of the molecules and their momenta by short-range hopping that depends explicitly on molecular interactions, as well as on site occupancies and velocities.

We demonstrate applications of the isothermal version of this method to computational modeling of interfacial dynamics, wetting, and coating phenomena occurring in multiphase flows that are in contact with moving solid walls, as well as the use of a nonisothermal version of this method for modeling thermocapillary flows.

During the late stages of spinodal decomposition, domains reach their equilibrium concentrations and sharp interfaces develop. In fluids, surface-tension-induced flow creates a hydrodynamic coarsening mechanism assuming domains are interconnected. For symmetric binary fluids, scaling arguments predict a growth rate of length ~ time at low Reynolds number and length ~ time^(2/3) at high Reynolds number.

Using a level-set method, we find evidence of a universal curve approaching the length ~ time^(2/3) limit at large lengths (high Reynolds number). We find similar behavior in ternary systems. Growth behavior in ternary systems is rich due to the various possible topologies. For example, we find that growth of a disconnected phase may be promoted in the presence of two interconnected phases.

We analyze the development of compositional and surface nonuniformities during the growth of strained alloy films. A continuum model is derived for the evolution of the film surface and composition due to the processes of deposition and surface diffusion. The compositional stresses arising from compositional variations of different-size alloy components is incorporated into the elasticity problem for the epitaxial film, and the thermodynamics of stressed solids is used to derive the chemical potentials for surface diffusion. From this coupled free-boundary problem for the morphology, composition, and stress state, the stability characteristics of planar film growth is determined from a linear stability analysis. For the case of equal surface mobilities of the alloy components, we find that compositional stresses make the film more unstable to the formation of stress-driven surface undulations. The destabilization is greatest over a moderate range of deposition rates, but weak at fast and slow deposition rates. For the case of different surface mobilities of the alloy components, we find that the difference in surface mobilities can completely suppress the stress-driven morphological instability. The stabilization is not symmetric with respect to the compositional and misfit strains: it occurs in films with compressive (tensile) misfit, when one of the atomic species in the film is both large and slow (large and fast) relative to the other component. A feature of the stabilization due to mobility differences is the existence of a critical deposition rate for stabilization, above which the film is stable. The existence of a critical deposition rate suggests the possibility of growing controlled lateral composition modulations using the small-amplitude steady-state behavior of the system at deposition rates slightly below the critical condition.

Planar-flow casting (PFC) (i.e., melt-spinning or spin-casting) produces flat product by forcing molten metal onto a moving substrate (i.e., a spinning wheel) where it solidifies and leaves as a ribbon, strip, or foil. Heat and momentum fluxes dominate in the gap between the nozzle and the wheel.

Success of the planar-flow process depends on the dynamics and stability of a group of two- and three-phase contact regions. The stability of these contacts is crucial in spin-casting, impact-forming, die-casting, spray-forming, extrusion, or any casting process where bulk properties and surface quality are important. They must also be understood in the design of new processes that depend on rapid phase change and high throughput, whether to produce innovative materials or conventional materials more efficiently. The solidifying flow is distinguished by the following features:

• Meniscus: deformable molten-metal/gas interface,

• Tri-junction: 3-phase common-line with phase change,

• Dynamic contact-line: 3-phase common-line with slip,

• Solidification front: surface of solid/liquid phase change.

Results: Recent experimental results are based on casting aluminum/silicon (Al/Si) alloys with Si content ranging from 0% (0.999 pure Al) to about 12% Si, depending on the cast.

• Experiment: The movement of the upstream meniscus is coordinated with the contact exposure of the wheel, suggesting that the puddle length (or contact length) can respond to the heat-up of the wheel [1].

• Analysis: The flow structure within the puddle, predicted by a previous adhoc analysis [2,3] is rederived in a systematic way to clarify the appropriate scalings [4]. The resulting pressure field is tested against observation [5].

• Theory: Vorticity transport in solidification boundary layers has been elucidated [6]. Forming singularities are likely to be important in PFC where 'fresh' surface is created at high rates; contacting and forming singularities are illustrated in a simple context [7].

Several theoretical analyses have examined the stability of half zones, always assuming that the free surface of the liquid bridge is cylindrical, as it would be in a microgravity environment. However, recent experiments by different groups have shown that significant free-surface deformation can have a pronounced effect on the stability boundary. Here, experiments and a theoretical stability analysis consider the onset of oscillatory thermocapillary convection in half zones with significantly deformed free-surface profiles. Free-surface deformation is quantified by a volume ratio representing the volume of liquid in the bridge relative to the volume of a right circular cylinder of equal height and endwall radius.

The experiments mark the boundary for the onset of oscillatory flow in half zones with volume ratios ranging from 0.5 to 1.6. The theoretical analysis applies energy stability theory to steady, axisymmetric flow in the half zone under the conditions of the experiments. A comparison between the theoretical and experimental results show that the energy limits are above the experimental stability boundaries in clear contradiction to theory. An explanation for the exaggerated stability limits has not been determined although the results may provide new insights about the already well-researched instability mechanisms.

Ink-jet technology is targeted for use in conformal electronics manufacturing where a homogeneous nano-particle suspension is utilized as the structural material. The suspension is dispensed onto flexible substrates by means of a piezoelectric droplet generator device capable of producing droplets on the order of 30–60 μm in diameter. The droplet generator is driven by a square-pulse waveform in which the rise/fall voltage and dwell time are variable. The substrates containing the dispensed material are then cured at 300°C for 15 minutes to yield a finished product. This method of circuit production is attractive to the electronics industry for it: 1) minimizes material usage and chemical waste production, 2) reduces turnover time, and 3) is capable of rapid prototyping. Ink-jet printing technology offers the potential for highly compact, ultra-lightweight assemblies and, especially, for rapid product introductions and enhancements, which are becoming increasingly critical in today's competitive wireless communications market. Current attempts in producing circuit interconnections at Motorola have proven to be successful.

Although improved component tolerances and unique patterning capabilities have been verified using drop-on-demand ink-jet techniques at Motorola, it remains to be demonstrated whether it is capable of the reproducibility, robustness, and accuracy necessary for reliable production of commercial products. The repeatability of the process relies heavily on steady, satellite-free, droplet generations. To attain such optimum droplet generations it is essential to investigate the relation between the device excitation parameters/design and fluid properties. Previous studies show surface tension to be a critical fluid property in the generation of repeatable droplet formations. Therefore, quantification of the influence of surface tension in correlation with the device excitation parameters is required for successful commercial implementation.

To quantify the drop-formation process, a short-duration flash videography technique is employed with time-delay capabilities down to 1 μs. With this technique, it is possible to observe the droplet ejection and formation process as a function of various impulse excitation parameters. Key metrics, such as droplet size and velocity, are measured, and satellite occurrences are recorded to generate an extensive parameter matrix that assists in the optimization of the dispensing process.

Instability can occur in the displacement of two or more contiguous fluids when a less viscous fluid displaces a more viscous fluid. In Hele-Shaw flow, evolution of the instability leads to fingers of the less viscous fluid growing into the more viscous fluid as displacement proceeds. Viscous fingering has been observed in the displacement of colloidal suspensions. The operative physical principle in suspension fingering is that the effective viscosity of a dense suspension exceeds the viscosity of the pure carrier liquid and is a monotonically increasing function of the local particle volume fraction…

We investigate the interfacial dynamics of potential flow in a thin fluid sheet for varicose long-wave disturbances when surface forces and inertia are the dominant physical effects. A coupled set of evolutions equations is derived for the interfacial deflection and axial velocity. For sufficiently small amplitudes, spatially periodic disturbances on the film lead to counter-propagating waves whose wavespeeds depend on the initial data. For larger-amplitude initial data below a threshold, these standing-wave-type solutions persist. In this regime, general initial conditions lead to quasi-periodic solutions in time. However, there is a class of initial data for which the transients are simply travelling-wave solutions. Beyond this threshold, the film ruptures according to the similarity scales reported in Pugh and Shelley (1998), independent of the amplitude of the initial data above threshold. Near the rupture criterion, transients suggest a similarity solution that has a bounded velocity but is singular in its spatial gradient. Further, a similarity property of the evolution equations predicts the threshold criterion up to the evaluation of a single constant, which is obtained numerically.

The thermal effects of internal interfaces, like interphase, antiphase, and domain boundaries, stem from their possession of an internal-energy excess. In my presentation, I will analyze the influence of the interfacial thermal effects on the formation of microstructures. These effects have received very little attention in the literature; their study is long overdue. Thermal effects significantly change the phase diagrams of one-component materials, in particular, those of thin films. For very thin films with thicknesses only 5–20 times greater than the interfacial thickness, phase separation does not occur and equilibrium is achieved with homogeneous transition states that can never be obtained in bulk samples because of their absolute instability. The thermodynamic and dynamic explanations will be presented. This type of a thin-film phase diagram is important for electronic devices and integrated circuits, for the theory of amorphization, and for nanophase composite materials where small particles or thin whiskers capable of undergoing a transition are immersed into a poorly conducting matrix.

As large systems evolve far from equilibrium, they produce complicated fractal structures with high interfacial-area density, like dendrites during solidification, highly dispersed coexisting phases during martensitic transformation, or self-entangled domains of opposite ordering after continuous symmetry-breaking ordering below the critical temperature. I will elucidate the influence of different thermal effects on the general properties of evolving microstructures. One of them (the heat-trapping effect) is caused by temperature gradients across an interphase boundary that change the course of dynamics and allow the emergence of a metastable (superheated) phase in the growth stage of the transformation. Conditions for such a regime may be met in many organic materials, including polymers. Another thermal effect of interphase boundary motion that will be discussed in conjunction with structure formation is the surface creation and dissipation effect. The temperature gradients across antiphase-domain or grain boundaries stem from the transmission of energy across the interface and cause a drag effect, which changes the course of structural coarsening for the later stages of material evolution. An experimental setup designed to reveal this thermal drag is suggested.

We present an experimental study of spontaneous and forced wetting of 5CB in the nematic phase on silicon wafers. At room temperature, a droplet of 5CB completely wets the surface and the ellipsometric profile reveals the existence of a characteristic thickness (~ 200 Å). As the temperature is increased, this thickness increases and "diverges" at the nematic/isotropic transition. This is the signature of a wetting transition: a 5CB droplet in the isotropic phase does not wet the surface. The question that arises is: why does the wetting transition takes place at the nematic/isotropic transition? In the discussion, we propose a simple model that takes into account long-range interactions and we show that the balance between elastic, anchoring, and van der Waals energies may fix the wetting condition. The knowledge of the energy per unit surface area allows us to predict the stability of a thin nematic film. For 5CB spun-cast onto silicon wafers, thin films are unstable while thick ones are metastable. We then observe experimentally the characteristic spinodal or nucleation dewetting in the two cases.

The subject of this research is a process we call vibration-induced drop atomization (VIDA). The process starts with a small water drop (~ 1 cm in diameter) placed at the center of a horizontal, circular metal diaphragm. The diaphragm is fastened to a holder at its periphery and a piezoelectric disk is centrally mounted to its bottom side. Excitation of the piezoelectric disk by a sinusoidal voltage causes the diaphragm to vibrate in the vertical direction in its fundamental axisymmetric mode. When the excitation signal is held at a fixed frequency and the amplitude is slowly increased, different stages of free-surface motion on the drop are clearly observed. First, axisymmetric standing waves appear on the free surface for small values of the excitation amplitude. These waves have the same frequency as the excitation and are present at even very small excitation amplitudes. At a first critical excitation amplitude, an azimuthal instability is triggered along the contact line. It couples with the existing axisymmetric waves so that the free surface undergoes a transition to a non-axisymmetric wave form. Here, the most energetic spatial mode has a frequency that is the first subharmonic of the excitation frequency. This is a characteristic of the parametric instability seen in a standard Faraday-wave experiment. As the excitation amplitude increases further, the three-dimensional, free-surface waves increase in magnitude, spread over the entire free surface of the drop, and exhibit very complex, nonlinear spatial behaviors. At a second critical excitation amplitude, small secondary droplets begin to be ejected from the free-surface wave crests. When droplet ejection occurs, the ejection sites appear in a central region that covers about two-thirds of the free surface. After droplet ejection begins and for large enough excitation frequencies, complete atomization of the drop will suddenly occur as the result of a rapid increase in the rate of secondary droplet ejection — an event we call drop bursting…

Thin solid films are the basic structure in most microelectronic and optoelectronic devices. This is a direct result of the layer-by-layer manufacturing technique, which involves roughly a hundred steps of successive material deposition and patterning. During these processes, the device is often heated to high temperatures, and the solid components inside the device can deform. The deformation becomes more disruptive as the size of integrated circuits decreases. To continue this trend of miniaturization, the stability and evolution of thin solid films needs to be understood. In this poster, we will present the morphological instabilities and evolution of solid-film shapes commonly encountered in micro-devices, such as holes, wedges, rods, and steps.

During the last decade two analytical theories for free-dendrite growth, the microscopic solvability condition (MSC) theory and the interfacial wave (IFW) theory, were proposed in the areas of condensed-matter physics and material science. These theories were attempts to resolve the problem of selection in dendrite growth, and to explain the essence of pattern formation. This article attempts to clarify the differences and commonalities between these two theories and to compare the predictions of these theories with some of the latest numerical evidence and experimental data.

Since the MSC theory is the most well-developed for the two-dimensional case, the comparison of the theories with numerical simulations is made mainly by using, but is not restricted to, two-dimensional, numerical solutions for dendrite growth with anisotropy of surface tension. Such kinds of numerical simulations have been carried out by Wheeler et al. (1993), Provatas et al. (1998, 1999), and Karma et al. (1996, 1997) with the phase-field model, and by Ihle and Muller-Krumbhaar (1994) with the free-boundary-problem model.

It is seen that if the anisotropy parameter is not too small, the numerical simulations yield steady needle solutions, whose side-branching structures are not self-sustaining. This result supports the conclusions drawn by both the MSC and the IFW theories. However, the numerical simulations also showed that there exists "a smallest value of the anisotropy parameter," less than which "no steady needle solution was found." This numerical evidence appears to be in agreement with the IFW theory and to contradict the MSC theory.

The prediction of the IFW theory is also compared with the latest experimental data obtained by Glicksman et al. (private communication) in the microgravity environment and excellent overall agreement between both is found.

The interaction of convection and dendrite growth has been a subject of great interest in the area of material science in recent years. Experimental observations have shown that convective motion in the liquid may have a significant effect on dendrite growth. The existence of convection may significantly change the growth velocity of the tip and the micro-structure pattern. Preliminary investigations of dendrite growth with convection are usually focused on the special case of zero surface tension. The solution for this special case, as in the Ivantsov solution for dendrite growth with no convection, cannot resolve the problem of the selection of the tip velocity of the dendrite or the dynamics of pattern formation on the interface. However, this solution is expected to provide a basis for further investigations in the general case of dendrite growth with non-zero surface tension.

In the past several years, theoretical studies of steady dendrite growth in an external flow have been conducted by a number of authors (such as Ananth and Gill (1989, 1991); Benamar, Bouisson, and Pelce (1988); Saville and Beaghton (1988), etc.) both numerically and analytically. An analytical solution was obtained by Ananth and Gill in terms of the Oseen model of fluid dynamics, which led to a paraboloid shape for the interface. Their solution satisfies all the interface conditions, but does not satisfy a proper upstream far-field condition. In fact, their solution yields a non-vanishing perturbed flow in the upstream far field, which is not appropriate from a physical point of view.

Xu (1994) made the first attempt to derive an asymptotic-expansion solution in terms of the Navier-Stokes model of fluid dynamics for the case of the Prandtl number, Pr → ∞. Xu derived a matched-asymptotic-expansion solution for the problem. However, for simplicity, the problem formulated in Xu's work neglected the regular condition for the velocity field at the symmetry axis. Furthermore, the same as in Ananth and Gill's work, the upstream far-field condition for the stream function in the formulation was weakened.

In this paper, we attempt to reconsider this problem with a fully justified mathematical formulation. We assume that a dendrite is growing with a constant tip velocity U against the flow, which has a uniform velocity U_∞ in the far field. We study two limiting cases:

• the weak-flow case: U_∞ ≪ U,

• the strong-flow case: U_∞ ≫ U,

and derive uniformly valid asymptotic solutions.

A one-dimensional directional solidification problem is considered for the purpose of analyzing the relationship between the solution resulting from a phase-field model to that from a sharp-interface model. An asymptotic analysis based upon a large Stefan number is performed on the sharp-interface model. In the phase-field case, the large-Stefan-number expansion is coupled with a small-interface-thickness boundary-layer expansion. The results show agreement at leading order between the two models for the location of the solidification front and the temperature profiles in the solid and liquid phases. However, due to the non-zero interface thickness in the phase-field model, corrections to the sharp-interface location and temperature profiles develop. These corrections result from the conduction of latent heat over the diffuse interface. The magnitude of these corrections increases with the speed of the front due to the corresponding increase in the release of latent heat. By properly selecting the potential coupling the order parameter and temperature in the phase-field model, and by tuning the kinetic parameter, we are able to eliminate the corrections to the outer temperature profiles in the solid and liquid phases of the phase-field model. This in turn eliminates the correction to the location of the solidification front. Hence, the phase-field temperature profiles agree with the sharp-interface profiles, except near the solidification front, where there is smoothing over the diffuse interface and no jump in the temperature gradients.

The contact angle and the spreading process of a sessile drop are very crucial in many technological processes, such as painting and coating, material processing, film-cooling applications, lubrication, and boiling. Additionally, it is well known that the surface free energy of polymers cannot be directly measured for their elastic and viscous restraints. Thus, measurements of the liquid contact angle on polymer surfaces become extremely important in order to evaluate the surface free energy of polymers through indirect methods linked with the contact-angle data.

Since the occurrence of liquid evaporation is inevitable, the effects of evaporation on the contact angle and spreading become very important for a more complete understanding of these processes. It is of interest to note that evaporation can induce Marangoni-Bénard convection in sessile drops [1]. However, the impact of convection inside the drop on the wetting and spreading processes is not clear. The experimental methods used by previous investigators cannot simultaneously measure the spreading process and visualize the convection inside the drop. Based on the laser shadowgraphic system used by the present authors [2,3], a very simple optical procedure has been developed to measure the contact angle, the spreading speed, the evaporation rate, and to visualize the convection inside of a sessile drop simultaneously. Two CCD cameras were used to synchronously record the real-time diameter of the sessile drop, which is essential for determination of both the spreading speed and the evaporation rate, and the shadowgraphic image magnified by the sessile drop acting as a thin plano-convex lens. From the shadowgraph, the convection inside the drop can be observed, if any, and the image outer diameter, which links to the drop profile, can be measured. Simple equations have been derived to calculate the drop profile, including the instantaneous contact angle, height, and volume of the sessile drop, as well as the evaporation rate. The influence of convection inside the drop on the wetting and spreading processes can be figured out through comparison of the drop profiles with and without convection when the sessile drop is placed at different evaporation conditions.

The last event of the conference was a panel discussion session chaired by one of the conference organizers, Michael J. Miksis [1]. The panelists were distinguished scientists from the fields of fluid mechanics and materials science and each one is a major contributor to the study of interfaces in his respective fields of research. The panel members were Stephen H. Davis (fluid mechanics and materials science) [2], Joel Koplik (fluid mechanics) [3], Wilfried Kurz (materials science) [4], Tony Maxworthy (fluid mechanics) [5], Robert F. Sekerka (materials science) [6], and Gretar Tryggvason (fluid mechanics) [7]. The panelists were chosen to strike a balance between the fields of fluid mechanics and materials science and also between the activities of theoretical, experimental, and numerical research. Professor Miksis asked each panelist to give a short statement on the general problem or problems he would like to see solved or worked on in the future. The intent of the discussion session was to bring out the similarities between interfacial dynamics in fluid mechanics and materials science and to suggest future avenues for research and cooperation. This account of the discussion is paraphrased from the complete transcript and was written by the author to clearly and smoothly describe the main themes raised during the session. A complete transcript of the discussion session was sent to the National Science Foundation in fulfillment of their contract-support requirements [8].