Numerical study of particle migration in tube and plane Poiseuille flows

The lateral migration of a single spherical particle in tube Poiseuille flow is simulated by ALE scheme, along with the study of the movement of a circular particle in plane Poiseuille flow with consistent dimensionless parameters. These particles are rigid and neutrally buoyant. A lift law L = CUs (Omega(s) - Omega(se),) analogous to L = rho U Gamma is validated in both two dimensions and three dimensions here; U-s and Omega(s) are slip velocity and angular slip velocity, Omega(se) is the angular slip velocity at equilibrium. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulas predict the change of sign of the lift force which is necessary in the Segre-Silberberg effect. Correlation formulas are compared between tube and plane Poiseuille flows by fixing the dimensionless size of particle and the Reynolds number. Our work provides a valuable reference for a better understanding of the migration of particle in Poiseuille flows and the Segre-Silberberg effect.