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It is of great significance to sort specific types of cells through a fast and efficient technology in biomedical research and clinical applications. In this study, commercial hollow glass beads were modified with 3-aminopropyltriethoxysilane (ATPES) and hyaluronic acid (HA) sequentially, which can capture HeLa cells with nearly 100% efficiency within 10min. The beads can specifically recognize and sort HeLa cells from a cell coculture of HeLa and L-929 depending on their strong buoyancy and good affinity with cancer cells. The job provides a facile, quick and low-cost cell sorting method, which has potential application in the fields of specific and efficient cell isolation.

In the frame of inviscid and incompressible fluids without taking into consideration of surface tension effects, the axisymmetric evolution of two buoyancy-driven bubbles in an infinite and initially stationary liquid are investigated numerically by VOF method. The numerical experiments are performed for two bubbles with same size, with the following one being half of the leading one, and with the leading one being half of the following one, and for different bubble distances. The ratio of gas density to liquid density is 0.001. It is found by numerical experiment that when the distance between the two bubbles is greater than or equal to one and half of the bigger bubble radius, the interaction is very weak and the two bubbles evolute like isolated ones rising in an infinite liquid. When the two bubbles come closer, the leading bubble itself evolutes like an isolated one rising in an infinite liquid. However, due to the smaller distance between the two bubbles, large pressure gradient forms in the liquid region near the top of the following bubble, which causes the upward stretch of its top part no matter what sizes of the two bubbles are. When the distance between the two bubbles is less than or equal to three-tenth of the bigger bubble radius, before the liquid jet behind the leading bubble fully developed, the top part of the following bubble has already been sucked into the leading one, giving a pear-like shape. Soon after the following bubble merges with the leading one. It is also found that for the smaller bubble, its transition to toroidal is always faster than that of the bigger one because of its smaller size. The mechanism of the above phenomena has been analyzed numerically.

To illustrate the role of Lorentz force on migration of nanopowders, CVFEM simulation has been reported in current research. The chamber contains hybrid nanomaterial and made up form porous media. Momentum equations have been modified for present paper with adding new source terms. The mentioned method works based on FEM in generation of mesh and calculation of gradient of scalars while it uses FVM approach for employing source terms. Testing with benchmark article shows the nice accuracy. Increase of permeability can enhance the speed of nanopowders and iso-temperature lines shapes become complicated. Impose of MHD creates new force against buoyancy and declines the velocity of the nanomaterial. Also, complication of isotherms declines with rise of Ha. With growth of Da, value of $\mathrm{\Psi }$ increases about 111% and 64.2% when $\mathrm{\text{Ha}}=0$ and 20, respectively. Also, augment of Ha results in reduction of velocity about 30% and 47.6% when $\mathrm{\text{Da}}=0.01$ and 100. Given $\mathrm{\text{Da}}=5\mathrm{\text{Ha}}=100$, Nu for $\mathrm{\text{Ra}}=\mathrm{\text{1e}}5$ is 6.83 times bigger than case with $log(\mathrm{\text{Ra}})=3$. Nu decreases to about 67.28% with increase of Ha when $\mathrm{\text{Da}}=100$, $\mathrm{\text{Ra}}=\mathrm{\text{1e}}5$. As Da increases, Nu rises about 62% when $\mathrm{\text{Ha}}=0$, $\mathrm{\text{Ra}}=\mathrm{\text{1e}}3$.

The flame motion of a pool fire on a small-scale burner has been experimentally investigated from the viewpoint of nonlinear dynamics, focusing on the relationship between the flame motion behavior and increasing burner diameter d. Hexane (C₆H₁₄) was used as a liquid fuel in the present study. For small burner diameters of up to d ≈ 10 mm, a stable conical flame was observed. The flame tip of the stable flame began to oscillate at low frequency (approximately 10 Hz) due to the buoyancy-driven hydrodynamic instability when d exceeded 13 mm. With further increase in d, the flame tip oscillation began to exhibit an interesting oscillation mode. These flame motions can be shown quantitatively by drawing an attractor, and evaluated by estimating the correlation dimension D_c. For d ≤ 10 mm, the attractor was a fixed point and D_c was approximately zero. When d reached 13 mm, the attractor became a limit cycle and D_c was estimated to be approximately unity, indicating a periodic motion. With larger burner diameters of up to d ≈ 50 mm, the trajectories of the attractor seemed to be rolled up and D_c approached approximately 2, indicating a quasi-periodic motion. These results indicate that the flame motion of the small-scale pool fire switches from stable to quasi-periodic, throughout periodic with increasing the burner diameter. The present results also show that a nonlinear analysis based on deterministic chaos theory, such as that using the attractor and the correlation dimension, would be a valid method by which to discuss the flame instability issue of the pool fire.

We discuss the structure of nonmonotonic reasoning. We suggest that an important aspect of nonmonotonic reasoning systems is the ordering relationship (preference structure) on the propositions in the knowledge. We suggest that this ordering relationship must be a weak order, a complete and transitive relationship. We provide a comprehensive discussion of some central issues in preference theory. In most real applications of nonmonotonic knowledge bases the ordering relationship available is often not complete. We suggest a mechanism for completing these relationships. The basic imperative used in providing this completion is to do it in such a manner as to add as few unjustified inferences as necessary. To formally accomplish this task we introduce a measure of buoyancy associated with a weak order and suggest that the preferred completion is the one with the maximal buoyancy.

A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ($𝜀)$ spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

Geometric and volumetric quantities are usually used to define the reference area for the prediction of aerodynamic coefficients of various aquatic mammals, airships and unmanned vehicle. However, reference area does not have a unique definition, especially for a hybrid buoyant aerial vehicle having hybrid lifting hull which resembles a Steller sea lion. The term square cube root of volume is traditionally used as reference area to nondimensionalize the aerodynamic forces for conventional as well as unconventional airships. Published experimental data are usually available for complete configuration at low speed and in nondimensionalized form. So, a generic model of an aircraft’s fuselage was first tested in a wind tunnel as a test case to first determine the lift force and then the influence of different choices of reference area on the lift. A hybrid lifting hull was numerically simulated for the prediction of lift as well as drag coefficients and their ratio. It was found that the volumetric term has undefined correlation with aerodynamic forces in both cases. Changes in aerodynamic coefficients are not prominent when using the wetted area as the reference area. Based on the predicted trends of aerodynamic coefficients and a deep literature survey, the projected planform area is proposed as the best option for reference area of a Steller sea lion as well as for hybrid lifting hull of a hybrid buoyant vehicle.

When modelling a flow in the atmosphere and the processes strongly influenced by it (e.g., the dispersion of air pollution), it is important to appreciate that the properties of both the flow itself and the dispersion are affected by the flow regime; i.e., whether the flow is turbulent (as is almost always the case in the atmosphere) or laminar. A second factor that might complicate atmospheric flow is stability, which depends on the nature of vertical temperature stratification.

In the first part of this chapter, we demonstrate the impact of vertical temperature stratification on flow structure, modelled via the Boussinesq approximation and by varying the Froude number (Fr). The flow is assumed to be laminar and is modelled in 2D.

Next, we review several approaches to treating turbulence in modelling studies, with an emphasis on an implicit large-eddy simulation. The results of Taylor—Green vortex computations performed using this method are compared with the results of a direct numerical simulation at moderate Reynolds numbers. Several quantities are considered, including the kinetic energy dissipation rate, probability density functions of turbulent fluctuations, and 3D energy spectra.

When a large number of bubbles exist in the water, an object may float on the surface or sink. The assumption of equivalent density is proposed in this article to explain the concrete example. According to the assumption, an object is floatable only if its density is less than the equivalent density of the water-bubble mixture. This conclusion is supported by the floating experiment and by measuring the pressure underwater to a satisfactory approximation.