Advective nonsolenoidal (&bnabla;⋅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 &agr; [=&rgr;0∂(1/&rgr;)/∂w], where &rgr; is the density and &rgr;0is 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 &agr;, 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. ©1997 American Institute of Physics.