Velocity distribution functions for a bidisperse, sedimenting particle-gas suspension

The velocity distribution function of a dilute bidisperse particle-gas suspension depends on the relative magnitudes of the viscous relaxation time, τ_v, and the time between successive collisions, τ_v. The The distribution functions in the two asymptotic limits, τ_c ≪ τ_v and τ_v ≪ τ_c, which were analysed previously are qualitatively very different. In the former limit, the leading-order distributions are Gaussian distributions about the mean velocity of the suspension, whereas in the latter case the distributions for the two species are singular at their respective terminal velocities. Here, we calculate the properties of the suspension for intermediate values of τ_v/τ_c by approximating the distribution function as a composite Gaussian distribution. This distribution reduces to a Gaussian distribution in the limit τ_v ≪ τ_c, in agreement with previous asymptotic analysis. In the intermediate regime, however, the composite Gaussian has a non-zero skewness, which is a salient feature of the distribution in the limit τ_v ≪ τ_c. We have also performed numerical calculations using the direct-simulation Monte Carlo method. The approximate values for the moments of the velocity distribution obtained using the composite Gaussian compare well with the full numerical solutions for all values of τ_v/τ_c.