Some Illustrative Calculations of Phase Separation with and without Shear and the influence of interaction boundaries on Phase Separation.

Now that we have established the type of critical phenomena exhibited by the LB model of fluid mixtures and a reduced variable description for some of the basic thermodynamic properties of this model fluid mixture, we can apply the LB model to the description of phase separation under a wide range of conditions. In this section, we will illustrate some phenomena we have investigated in connection with recent measurements.

The comparison of non-equilibrium phenomena such as fluid phase separation to LB model calculations requires the introduction of a dimensionless time unit that is common between the experimental and computational fluids. For fluid phase separation, it is conventional to express reduced time in terms of the mutual diffusion coefficient D_m and the correlation length, $\xi^-$^- [93,94,95]. We thus divide our computational time t by the average initial rate of phase separation, t_ps = 2( ^- )² / |D_m|, deduced from Cahn-Hilliard theory [11,93,94,95]. The mutual diffusion coefficient obtained for the Shan-Chen model studied in this paper for a viscosity matched binary mixture is given by,

$$D_m=\tau T \left[ \frac{1-{G'}^2n^1n^2}{1+G'(c_1n^2+c_2n^1)} -\frac{1}{2} \right]$$ (33)

where G' = 12G/T. All times below are reported in the dimensionless time = t/t_ps in our discussion of the LB model of fluid phase separation. Results are presented from simulations corresponding to a sytem size of 80³ in units of lattice spacing cubed.