Flows induced by diffusion in the presence of permeable solids

Results for flows induced by diffusion in the presence of solids immersed in a background density stratification are extended to include solids which allow for significant internal diffusion and flux of the solute across the fluid-solid interface. The strength of the induced flow as a function of the ratio of the diffusivities of the solute in the solid and fluid is predicted theoretically and shown to agree with simulations. The dynamic problem is investigated for constrained and freely settling solids whose internal concentration differs from the background, and a quasi-steady flow is investigated for solids in a linear background stratification which settle due to inward flux of the solute.