Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation

In this paper we study the lift-off to equilibrium of a single circular particle in Newtonian and viscoelastic fluids by direct numerical simulation. A particle heavier than the fluid is driven forward on the bottom of a channel by a plane Poiseuille flow. After a certain critical Reynolds number, the particle rises from the wall to an equilibrium height at which the buoyant weight just balances the upward thrust from the hydrodynamic force. The aim of the calculation is the determination of the critical lift-off condition and the evolution of the height, velocity and angular velocity of the particle as a function of the pressure gradient and material and geometric parameters. The critical Reynolds number for lift-off is found to be larger for a heavier particle whereas it is lower for a particle in a viscoelastic fluid. A correlation for the critical shear Reynolds number for lift-off is obtained. The equilibrium height increases with the Reynolds number, the fluid elasticity and the slip angular velocity of the particle. Simulations of single particle lift-off at higher Reynolds numbers in a Newtonian fluid by Choi & Joseph (2001) but reported here show multiple steady states and hysteresis loops. This is shown here to be due to the presence of two turning points of the equilibrium solution.