Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition

We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases, and the long-range molecular interaction is mimicked by introducing a pairwise interaction force. Double distribution functions are employed, with the density distribution function for the mass and momentum conservation laws and an innovative total kinetic energy distribution function for the energy conservation law. The recovered mesomacroscopic governing equations are fully consistent with kinetic theory, and thermodynamic consistency is naturally satisfied.

Figure 1

Distributions of (a) density $\rho$, (b) velocity $u_x$, (c) temperature $T_r$, and (d) pressure $p_{\mathrm{EOS}}$ at time $t=0.401\times {10}^7$, $0.803\times {10}^7$, $1.204\times {10}^7$, and $1.606\times {10}^7$, and (e) time evolution of the phase interface location $X_i$ for the one-dimensional Stefan problem.

Figure 2

Evolution of the square of the normalized droplet diameter $(D/D_0{)}^2$ with the normalized time $t^{*}={\alpha }_{v}t/D_0^2$ in the droplet evaporation process. Snapshots of the local density (left) and temperature (right) fields are also shown at time $t^{*}=12.716$, 38.147, 63.578, and 89.010, where the solid line in temperature field denotes the liquid-vapor phase interface.

Figure 3

Snapshots of the local temperature and velocity fields at different normalized times for (a) $\mathrm{Ste}=0.005$, (b) $\mathrm{Ste}=0.05$, and (c) $\mathrm{Ste}=0.5$, and (d) evolutions of the normalized total volume of the droplets $V/V_0$ with the normalized time $t^{*}={\alpha }_{v}t/D_0^2$ in the evaporation process of a large-small droplet pair. The solid and dotted lines in temperature field denote the liquid-vapor phase interface and its initial location, respectively.