Advective nonsolenoidal (∇⋅v≠0) flow driven by diffusion-induced density changes in strictly zero gravity is studied in a two-dimensional rectangular box. Our model, which is more general than the Oberbeck–Boussinesq model, is a precursor for the study of fluid flow that occurs due to density changes during isothermal interdiffusion in a binary liquid under the influence of stochastic microgravity (g-jitter). We consider perturbation expansions of mass fraction (w) of the second chemical component of a binary solution, pressure (p), velocity (v), and chemical flux (j) with respect to a small parameter α [=ρ0∂(1/ρ)/∂w], where ρ is the density and ρ0 is its value for some average composition. The total barycentric velocity field is given by the sum of an average flow, having a nonzero divergence, and a solenoidal flow derived from a pseudo-stream-function. At first order in α, we obtain a fourth order partial differential equation for this pseudo-stream-function. We solve this equation analytically in a quasi-steady-state approximation for an infinitely long diffusion couple by using transform techniques. We also solve it numerically for the full time-dependent problem for a finite domain. We conclude that such nonsolenoidal flows will dominate for sufficiently small gravity, for which the Oberbeck–Boussinesq approximation will certainly not be valid.

Perera, P. S., & Sekerka, R. F. (1997). Nonsolenoidal flow in a liquid diffusion couple. Physics of Fluids, 9(2), 376–391.