Effects of shear on particle motion near a surface—application to resuspension

Abstract

The objective of the present work is to describe the effects of shear on small particle motion close to a horizontal surface. These effects can then be combined with those of turbulence for a complete description of particle dynamics near a stationary wall, yielding the conditions required for particle resuspension. The equations of motion are derived from the existing analytical expressions for the hydrodynamic forces of lift and drag acting on a small particle near a wall. In particular, the present solution utilizes the recent expression for the lift force of Cherukat and McLaughlin, obtained for a particle the center of which is located less than ten diameters from the wall. The equations are linearized using asymptotic expansion and solved analytically. It is shown that the shear-induced lift near a surface may be represented by two components. The first component depends on the relative particle velocity, while the second is due to the solid surface. In order to assess the accuracy of the linearized analytical solution, the full equations of particle motion are solved numerically by the Runge–Kutta method. The results show, in general, good agreement with the simplified linearized model. The linearized analysis makes it possible to determine whether particle motion for given flow conditions is stable or not. The condition of instability is derived in terms of particle size, flow shear rate, fluid viscosity, fluid and particle densities, and the distance from the wall. Unstable particle motion means that the particle escapes very rapidly from the surface into the main flow. It is shown both analytically and numerically that unstable particle motion depends on its initial velocity and distance from the wall. This result is important for the study of particle resuspension from surfaces in turbulent flows, where the particle moves inside the viscous sublayer and is subject to both shear and turbulent effects.