On the interplay between deformation and inertia on the lateral migration of hyperelastic particles in square channel flows

Direct numerical simulations of hyperelastic particles flowing through a square channel are performed to investigate the deformation and inertia effects on the lateral migration. We employ a fully Eulerian method, and parametrized the Reynolds number Re and the capillary number Ca. We mapped out particle focusing patterns in the channel cross-section. Two transition curves between the Center Equilibrium Position (CEP) and Diagonal Equilibrium Position (DEP) patterns and between the DEP and Midline Equilibrium Position (MEP) patterns are found to be given by constant Laplace numbers La (= Re/Ca). In particular, the stability of the CEP is analyzed using an asymptotic expansion approach to the migration force at low Re and Ca, and the theoretically obtained critical Laplace number accounts well for the CEP-DEP transition.