Analysis of inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow with a coupled lattice Boltzmann method-discrete element method

In this study, a hybrid numerical framework for modelling solid-liquid multiphase flow is established with a single-relaxation-time lattice Boltzmann method and the discrete element method implemented with the Hertz contact theory. The numerical framework is then employed to systematically explore the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in planar Poiseuille flow. The results show that the influence of particle concentration on the migration is primarily determined by the characteristic channel Reynolds number Re0. For relatively low Re0 (Re0 < 20), the migration behaviour can only be observed at a very low particle concentration (≤5%). However, when Re0 > 20 the migration behaviour can be observed at a high concentration (≥20%). Furthermore, a focusing number Fc is proposed to characterise the degree of inertial migration. It was found that the inertial migration can be classified into three regimes depending on two critical values of the focusing number, Fc+ and Fc−: (i) when Fc > Fc+, a full inertial migration occurs; (ii) when Fc < Fc−, particles are laterally unfocused; and (iii) when Fc− < Fc < Fc+, a partially inertial migration takes place.