Narrow Results

The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarized in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d -1)-dimensional interface splits in disconnected pieces. Some phenomenological arguments are proposed to describe such interfaces. They show that the character of the interfacial fluctuations at d< 2 is not the same as provided by a formal analytic continuation from d-dimensional hypercubes with d≥2. It, probably, is true also for the related critical exponents.

This paper deals with numerical modeling of two-phase liquid jet breakup using the smoothed particle hydrodynamics (SPH) method. Simulation of multiphase flows involving fluids with a high-density ratio causes large pressure gradients at the interface and subsequently divergence of numerical solutions. A modified procedure extended by Monaghan and Rafiee is employed to stabilize the sharp interface between the fluids. Various test cases such as Rayleigh–Taylor instability, two-phase still water and air bubble rising in water have been conducted, by which the capability of accurately capturing the physics of multiphase flows is verified. The results of these simulations are in a good agreement with analytical and previous numerical solutions. Finally, the simulation of the breakup process of liquid jet into surrounding air is accomplished. The whole numerical solutions are accomplished for both Wendland and cubic spline kernel functions and Wendland kernel function gave more accurate results. Length of liquid breakup in Rayleigh regime is calculated for various flow conditions such as different Reynolds and Weber numbers. The results of breakup length demonstrate in satisfactory agreement with the experimental correlation. Finally, impinging distance and breakup length of a simple multijet setup are analyzed. The two-jet multijet has a longer breakup length than a three-jet one.

In this paper, I give an overview over a recently developed rigorous theory of finite-size scaling near first order transitions. Leaving out details of the mathematical proofs, the main emphasis is put on the underlying physical ideas and the discussion of the validity of the results for regions which are, in the sense of mathematical rigour, not covered by the original papers. I present both the finite-size scaling for cubic systems and for long cylinders, discussing also a recent controversy which stems from our work on the finite-size scaling of the mass gap in long cylinders.

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitude of the critical interfacial tension.

We apply the lattice-gas method to study droplet behavior. The ascending velocity and deformation of a drop under buoyancy are numerically analyzed. We develop an algorithm to adjust surface tension by changing collision rules, and deformation of a droplet is calculated with different surface tensions. The deformation of a drop driven by the pressure gradient under gravity is also investigated.

In the present paper, the surface tensions and interfacial energies for pure metals and alloys for different structures were predicted by combining with the evaluated thermodynamic parameters in the framework of the CALPHAD (Calculation of Phase Diagrams) method. It is shown that the calculated results are in good agreement with the existing experimental data. On the basis of the predicted values of surface tension and interfacial energy, the phase stability and phase diagram with nano-size particles can be calculated by considering the Gibbs-Thomson equation. The calculated results for pure Fe indicate that the fcc phase is more stable with the decreasing of size of particles, which is in agreement with the experimental data reported, and the phase diagram with nano-size particle can be calculated.

Within finite temperature Density Functional Theory, we have calculated the energy of the transitions from the ground state to the first two excited states in the electron bubbles in liquid helium at pressures from zero to about the solidification pressure. For ⁴He at low temperatures, our results are in very good agreement with infrared absorption experiments. We have found that the 1s – 2p transition energies are sensitive not only to the size of the electron bubble, but also to its surface thickness. We also present results for the infrared transitions in the case of liquid ³He.

A new simple correlation based on the principle of corresponding state is proposed to estimate the temperature-dependent surface tension of normal saturated liquids. The correlation is a linear one and strongly stands for 41 saturated normal liquids. The new correlation requires only the triple point temperature, triple point surface tension and critical point temperature as input and is able to represent the experimental surface tension data for these 41 saturated normal liquids with a mean absolute average percent deviation of 1.26% in the temperature regions considered. For most substances, the temperature covers the range from the triple temperature to the one beyond the boiling temperature.

A new simple correlation based on the principle of corresponding state is proposed to estimate the temperature-dependent surface tension of normal saturated liquids. The new correlation contains three coefficients obtained by fitting 17,051 surface tension data of 38 saturated normal liquids. These 38 liquids contain refrigerants, hydrocarbons and some other inorganic liquids. The new correlation requires only the triple point temperature, triple point surface tension and critical point temperature as input and is able to well represent the experimental surface tension data for each of the 38 saturated normal liquids from the triple temperature up to the point near the critical point. The new correlation gives absolute average deviations (AAD) values below 3% for all of these 38 liquids with the only exception being octane with AAD=4.30%. Thus, the new correlation gives better overall results in comparison with other correlations for these 38 normal saturated liquids.

In this paper, we analyzed the ability of Lielmezs–Herrick (LH) correlation for the temperature-dependent surface tension of 28 hydrocarbons. We found that compared with other published correlations, the original LH correlation stands well only for four fluids. By using new data in REFPROP database, we refitted the two parameters of LH correlation. Two sets values are obtained. One is the updated corresponding state LH correlation, which is fluid independent. The other is the two-parameter LH correlation, which is fluid dependent. We found that the former clearly improves the accuracy of the original LH correlation and the latter is the best among all of the correlations we know.

In this paper, we proposed a new one-parameter correlation for the surface tension of saturated fluids. This new correlation requires only the critical temperature as inputs and is tested by using the REFPROP data for 72 saturated fluids including refrigerants, alkanes and some other simple fluids such as argon, carbon dioxide, etc. It is found that this correlation well stands in the whole temperature range from the triple point to the critical point with high accuracy for 59 liquids with average absolute deviations (AADs) less than 5%, 50 liquids with AADs less than 3%, and 13 liquids with AADs less than 1%. These results are clearly better than those of the other available correlations. This correlation can be used to estimate the value of the surface tension of the corresponding liquids at any temperature point from the triple point to the critical point.

By the potential method, it was determined that regardless of the nature of the liquid, the surface tension coefficient is determined by $\sigma =2q\frac{(T_K-T)}{(T_K+T)}$. In this expression, $q$ is the specific heat of the surface formation, $T_k$ is the critical temperature. According to our approach, the specific heat of the surface formation (SHS) also depends on temperature: $q=q_m+\alpha \cdot (T-T_m)$ ($q_m$ — the specific heat of the surface formation at the mealting temperature, $\alpha$ — thermal coefficent of SHS). In this research work, the temperature dependence of the surface tension coefficient was calculated for seven dissimilar liquids. It was revealed that the calculated values of $\sigma$ are in satisfactory agreement with the available experimental values.

In this paper, a new corresponding state principle (CSP)-based model is proposed to calculate the surface tension of hydrocarbons based on the National Institute of Standards and Technology (NIST) database. This model requires the critical point temperature, the lowest temperature available for surface tension data and the corresponding maximum surface tension value as inputs. It includes two adjustable coefficients which are fitted by using NIST data of three hydrocarbons. To test the applicability of this model, we applied it to predict the surface tension values of other 16 hydrocarbons. For all the 19 hydrocarbons available in NIST database, the average absolute deviations of 16 hydrocarbons are less than 5%. We also compared this new proposed model with other three existing corresponding state models, and found that this model is the best in predicting the surface tension data of hydrocarbons.

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number $S_t$, Sisko fluid parameter $\beta$ and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and $S_t$ while their positions relocate towards the fluid–air interface with increasing $\beta$ and n. Thickness of uniform film decreases when the values of C and $S_t$ are increased whilst it increases with the increase of $\beta$ and n. Analogy between the Newtonian fluid and the Sisko fluid’s shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made.

The effect of the interaction between a disc and water-like particle on the wetting behavior of water-like phase between two discs has been investigated by free energy analysis and discontinuous molecular dynamic simulations. A detailed description for the partial wetting-complete wetting transition is provided and the analytical expressions describing the wetting behavior are obtained.

A new transport equation model is proposed for simulating cavitating flows in miniature machines. In the developed model, the surface tension, viscous force, and thermal effect of cavitation are considered to reflect their influence on the cavitation bubble growth. The cavitating flow in a miniature pump is calculated by applying the proposed cavitation model. The comparison between numerical results and experimental data indicates that the new cavitation model is applicable for simulating the cavitating flow in miniature machines.

The influences of magnetic field on thermodynamic, mechanical and electromagnetic properties of water including the specific heat, surface tension force, soaking effect or angle of contact, refraction index and electric conductivity are studied. From these investigations we know that the magnetic fields reduce the specific heat of water, increase the soaking degree and hydrophobicity of water to materials, depress its surface tension force and increase refractive index and electric conductivity of water relative to those of pure water. We can predict that these changes are caused by the changes of microscopic structures and distribution of water molecules under the action of a magnetic field. Therefore, our studies have important significations in science and has practical value of application of magnetized water.

Wetting of droplets on homogeneous and spherical concave rough surfaces is investigated based on thermodynamics. In this study, neglecting the droplet gravity and the thickness of the precursor film of the liquid–vapor interface, the three-phase system is divided into six parts using Gibbs concept of dividing surface. The system Helmholtz free energy is established based on thermodynamics. Supposing the temperature and chemical potential to be constant, a new generalized Young’s equation of the equilibrium contact angle for a spherical droplet on a spherical concave rough surfaces is obtained including the line tension effects. Under certain conditions, this generalized Young’s equation is the same as the Rusanov’s equation.

Based on the recent progress on both the temperature dependence of surface tension [H. L. Yi, J. X. Tian, A. Mulero and I. Cachading, J. Therm. Anal. Calorim.126 (2016) 1603, and the correlation between surface tension and viscosity of liquids [J. X. Tian and A. Mulero, Ind. Eng. Chem. Res.53 (2014) 9499], we derived a new multiple parameter correlation to describe the temperature-dependent viscosity of liquids. This correlation is verified by comparing with data from NIST Webbook for 35 saturated liquids including refrigerants, hydrocarbons and others, in a wide temperature range from the triple point temperature to the one very near to the critical temperature. Results show that this correlation predicts the NIST data with high accuracy with absolute average deviation (AAD) less than 1% for 21 liquids and more than 3% for only four liquids, and is clearly better than the popularly used Vogel–Fulcher–Tamman (VFT) correlation.

In this paper, we proposed two reduced quantities, based on which we found that the curves of surface tension versus temperature of different saturated fluids can collapse into a single curve. Then a corresponding state-based correlation is proposed and then checked for 66 saturated fluids including simple fluids such as argon, nitrogen, etc., and some refrigerants in the temperature range from the triple point temperature to 0.992 times the critical temperature. By comparing with NIST data, the proposed correlation reproduces NIST data with AAD $<$ 1% for 21 fluids, AAD $<$ 2% for 26 fluids, and AAD $<$ 5% for 46 fluids.