Suspension balance model: A finite-element implementation for contraction–expansion flows

Abstract

Shear-induced migration of particles relative to the bulk motion in suspensions is predicted to be strongly amplified by geometric singularities, making suspension balance model (SBM) computations near sharp corners sensitive to how the corner is represented. We introduce a curvature-based regularization in which sharp corners are replaced by a controllable radius r. Using a finite-element SBM formulation for planar (i.e., two-dimensional) contraction and expansion flows, we show that the corner localizes rapid rotation of principal strain directions and particle-stress gradients, causing wall depletion and a corner concentration envelope, and coupling these microstructural features to the separatrix that bounds recirculation. The method used yields a well-defined sharp-corner limit; recirculation measures vary with r over a finite range and then collapse onto an r-independent plateau below a crossover radius. This regularized framework allows quantitative comparison across geometries and inlet conditions and facilitates interpretation of particle migration and recirculation in complex geometries.