Henry’s law, surface tension, and surface adsorption in dilute binary mixtures

Density functional theory of gas-liquid phase separation in dilute binary mixtures

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas [Formula: see text] (the Gibbs energy of transfer) is considerably larger than the thermal energy [Formula: see text] for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by [Formula: see text], where [Formula: see text] is the solute density added in liquid. For [Formula: see text], phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Diffuse interface method for a compressible binary fluid

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO_{2} + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO_{2} + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO_{2} the smaller the surface tension and the easier the drop deforms.

Thermohydrodynamics of boiling in binary compressible fluids

We numerically study the thermohydrodynamics of boiling for a CO(2) + ethanol mixture on lyophilic and lyophobic surfaces in both closed and open systems, based on a diffuse interface model for a two-component system. The corresponding wetting boundary conditions for an isothermal system are proposed and verified in this paper. New phenomena due to the addition of another component, mainly the preferential evaporation of the more volatile component, are observed. In the open system and the closed system, the physical process shows very different characteristics. In the open system, except for the movement of the contact line, the qualitative features are rather similar for lyophobic and lyophilic surfaces. In the closed system, the vortices that are observed on a lyophobic surface are not seen on a lyophilic surface. More sophisticated wetting boundary conditions for nonisothermal, two-component systems might need to be further developed, taking into account the variations of density, temperature, and surface tension near the wall, while numerical results show that the boundary conditions proposed here also work well even in boiling, where the temperature is nonuniform.

Bubble and droplet motion in binary mixtures: Evaporation-condensation mechanism and Marangoni effect

Bubble and droplet motion in binary mixtures is studied in weak heat and diffusion fluxes and in gravity by solving the linearized hydrodynamic equations supplemented with appropriate surface boundary conditions. Without gravity, the velocity field is induced by evaporation and condensation at the interface and by the Marangoni effect due to a surface-tension gradient. In pure fluids, the latter nearly vanishes since the interface temperature tends to the coexistence temperature T_{cx}(p) even in heat flow. In binary mixtures, the velocity field can be much enhanced by the Marangoni effect above a crossover concentration c;{ *} inversely proportional to the radius R of the bubble or droplet. Here c;{ *} is usually very small for large R for non-azeotropic mixtures. The temperature and concentration deviations are also calculated.