Inertial migration of sedimenting particles in a suspension flow through a Hele-Shaw cell

Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-suspension flow in a vertical Hele-Shaw cell is investigated. Using the method of matched asymptotic expansions, an asymptotic model of the transverse migration of sedimenting particles is constructed. The particle migration in the horizontal section of the cell is caused by an inertial lateral force induced by the particle sedimentation and the shear flow of the carrier phase. A characteristic longitudinal length scale is determined, on which the particles migrate across the slot through a distance of the order of the slot half-width. The evolution of the particle number concentration and velocity fields along the channel is studied using the full Lagrangian method. Depending on the particle inertia parameter, different particle migration regimes (with and without crossing of the channel central plane by the particles) are detected. A critical value of the particle inertia parameter corresponding to the change in migration regime is found analytically. The possibility of intersection of the particle trajectories and the formation of singularities in the particle number concentration is demonstrated.