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

Abstract

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.