Lateral migration of a small spherical buoyant particle in a wall-bounded linear shear flow

Abstract

Lateral migration velocities of solid spherical particles suspended in a linear wall-bounded shear flow are measured for Reynolds number, Re<2 (Re=2RU/ν, where R is the particle radius, U is the local slip velocity between the particle and the fluid, and ν is the kinematic viscosity of the suspending fluid). The velocity parallel to the wall and the distance between the particle and the wall are measured as a function of time, allowing the lateral migration velocity and the slip velocity of the particle to be determined. The measured velocities are compared to the theoretical predictions of McLaughlin [“The lift on a small sphere in wall-bounded linear shear flows,” J. Fluid Mech. 246, 249 (1993)] and Magnaudet et al. [J. Fluid Mech. 476, 115 (2003)] corresponding to the situation where the wall lies in the Oseen region and in the Stokes region of the flow disturbance produced by the particle, respectively. A good agreement is observed in both regimes with the corresponding prediction. The measurements are used to build an empirical fit capable of predicting the migration velocity whatever the distance between the particle and the wall.