Establishment of Concentration Profile for the Flow of a Binary Fluid Mixture

Abstract

A study is made of the establishment of concentration profile of the heavy species for a binary fluid mixture under a body force from a uniformly mixed upstream condition. An inviscid hydrodynamical model is adopted. Two cases are considered. In the first case the flow is a swirling motion and the body force is provided by the centrifugal action of the swirl. In the second case the flow is a duct flow confined between two parallel walls with potential body force. Use is made of a perturbation procedure in terms of an expansion of the reciprocal of a diffusive Péclet number to obtain a closed form zeroth-order solution. The orders of the higher-order correction terms are explicitly given. The interplay between Fickian and baro-diffusion is brought out, and asymptotic solutions far downstream of the inlet are explicitly calculated for a class of swirling flows. The problem bears on various phenomena where a knowledge of the concentration of the heavier component is important, such as in gaseous nuclear cavity reactor propulsion devices.