Lbm-DEM Analysis of Inertial Migration of Neutrally Buoyant  Particle Suspensions in Planar Poiseuille Flow

We establish a hybrid numerical framework for modelling solid-liquid multiphase flow based on 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 study the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow. The results show that the influence of particle concentration on the degree of inertial migration primarily depends on the characteristic channel Reynolds number Re₀, which is defined as the Reynolds number for the pure channel flow with the same condition but no particles. For relatively low Re₀(sayRe₀<20), evident migration behaviour is only observed at a very low particle concentration (<1%), although the migration behaviour can still be observed at a high concentration (≥10%) when Re₀>20.Furthermore, we discover a unique feature regarding the influence of the solid fraction on the flow field: the normalized Reynolds number (the actual Reynolds number in presence of particles divided by Re₀) can be well regressed by an exponential law. Finally, we introduce an empirical focusing number to characterise the degree of inertial migration, and find that when the focusing number is above a critical value, a fully inertial migration occurs; when it is below another critical value, particles are laterally unfocused.