Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow

Abstract

Laminar pressure-driven suspension flows are studied in the situation of neutrally buoyant particles at finite Reynolds number. The numerical method is validated for homogeneous particle distribution (no lateral migration across the channel): the increase of particle slip velocities and particle stress with inertia and concentration is in agreement with former works in the literature. In the case of a two-phase channel flow with freely moving particles, migration towards the channel walls due to the Segré-Silberberg effect is observed, leading to the development of a non-uniform concentration profile in the wall-normal direction (the concentration peaks in the wall region and tends towards zero in the channel core). The particle accumulation in the region of highest shear favors the shear-induced particle interactions and agitation, the profile of which appears to be correlated to the concentration profile. A 1D model predicting particle agitation, based on the kinetic theory of granular flows in the quenched state regime when Stokes number St = O(1) and from numerical simulations when St < 1, fails to reproduce the agitation profile in the wall normal direction. Instead, the existence of secondary flows is clearly evidenced by long time simulations. These are composed of a succession of contra-rotating structures, correlated with the development of concentration waves in the transverse direction. The mechanism proposed to explain the onset of this transverse instability is based on the development of a lift force induced by spanwise gradient of the axial velocity fluctuations. The establishment of the concentration profile in the wall-normal direction therefore results from the combination of the mean flow Segré-Silberberg induced migration, which tends to stratify the suspension and secondary flows which tend to mix the particles over the channel cross section.