Numerical analysis of a rarefied gas flow past a volatile particle using the Boltzmann equation for hard-sphere molecules

Abstract

A spherical condensed phase with a uniform surface temperature that is placed in a slow uniform flow of its vapor gas is considered. The steady behavior of the gas accompanied by evaporation and condensation on the sphere is investigated mainly numerically on the basis of the Boltzmann equation for hard-sphere molecules. The numerical method is a combination of the hybrid-difference-scheme method, capable of describing the discontinuity of the velocity distribution function in the gas, and the numerical kernel method [Phys. Fluids A 5, 716 (1993)]. The velocity distribution function of the gas molecules, the macroscopic variables such as the density, velocity, and temperature of the gas, and the force (drag) acting on the sphere are obtained precisely for the whole range of the Knudsen number (the mean free path of the uniform flow divided by the radius of the condensed phase). In particular, the behavior of the discontinuity of the velocity distribution function in the gas is described accurately.

A new consistent discrete‐velocity model for the Boltzmann equation

“…However, a signiÿcant progress has been achieved in developing such methods in the last years [6][7][8][9]. In fact, the deterministic approaches are the ones to be preferred when a high numerical accuracy is of paramount importance [10][11][12]. Finally, a number of approaches were developed to increase the e ciency of deterministic calculations without sacriÿcing the accuracy [6; 7; 13].…”

Diffusiophoresis of a Spherical Volatile Particle

“…Therefore, the flow velocity field of gas B around the particle is more or less similar to that in the case of a uniform (noncondensable) gas flow past a sphere [12]. On the other hand, there is a uniform flow of gas A in the negative x 1 direction at infinity, so that the flow velocity field of gas A has, to some extent, a common feature with that in the case of a uniform vapor flow past a spherical condensed phase [14]. Thus, condensation takes place on the head (the part facing to the positive x 1 direction) of the particle and evaporation on the tail (the part facing to the negative x 1 direction) [see Fig.…”

A Lattice Boltzmann Method for a Binary Miscible Fluid Mixture and Its Application to a Heat-Transfer Problem

“…Applying the asymptotic theory proposed by Sone [18][19][20][21] where U is a characteristic flow speed, a reference density ρ A0 , a reference concentration ρ B0 , and a reference temperature T 0 :…”

“…Next we apply the asymptotic theory proposed by Sone [18][19][20][21] to the present LBM model and obtain the convection-diffusion equation for the diffusing component. Then we calculate a diffusion problem to demonstrate the validity of the proposed method.…”