Hele-Shaw flow of a concentrated, non-colloidal suspension (INVITED)

Abstract eng:
This paper provides a set of macrotransport equations for determining the volume fraction and velocity distributions in the flow of Wrated suspension of rigid, spherical particles through a Hele-Shaw cell. In this problem, Taylor dispersion relaxes volume fraction gradients in the flow direction, with a dispersivity that is proportional to '1‘1‘B3 /a2, where TI is the local depth-averaged velocity, B is the half depth of the channel and a is the particle radius. Perpendicular to the flow, volume fraction gradients are relaxed by shear-induced migration at a rate proportional to |u| a2 / B . The model predicts that negative volume fraction gradients should relax in the flow direction, while positive ones should self-sharpen to an asymptotic distribution in an appropriate frame of reference. However, the latter distribution is unstable to perturbations normal to flow, leading to viscous miscible fingering with a preferred wavelength that scales as 35/3 /a2/3.

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