Forces on a finite-sized particle located close to a wall in a linear shear flow

Abstract

To understand and better model the hydrodynamic force acting on a finite-sized particle moving in a wall-bounded linear shear flow, here we consider the two limiting cases of (a) a rigid stationary spherical particle in a linear wall-bounded shear flow and (b) a rigid spherical particle in rectilinear motion parallel to a wall in a quiescent ambient flow. In the present computations, the particle Reynolds number ranges from 2 to 250 at separation distances to the wall from nearly sitting on the wall to far away from the wall. First we characterize the structure of the wake for a stationary particle in a linear shear flow and compare with those for a particle moving parallel to a wall in a quiescent ambient [see L. Zeng, S. Balachandar, and P. Fischer, J. Fluid Mech. 536, 1 (2005)]. For both these cases we present drag and lift results and obtain composite drag and lift correlations that are valid for a wide range of Re and distance from the wall. These correlations have been developed to be consistent with all available low Reynolds number theories and approach the appropriate uniform flow results at large distance from the wall. Particular attention is paid to the case of particle in contact with the wall and the computational results are compared with those from experiments.