The hydrodynamic force and torque on a bounded sphere in Poiseuille flow

The lattice Boltzmann (LB) method is used to study the hydrodynamic force and torque acting on a sphere held stationary between parallel plates in pressure-driven flow. This and associated flow configurations are explored in this paper. LB results are in excellent agreement with existing theory and numerical results for simple pressure-driven flow between parallel plates, for flow through a periodic medium of spheres [Zick AA, Homsy GM. Stokes flow through periodic arrays of spheres. Journal of Fluid Mechanics 1982; 115: 13], and for the force and torque acting on a sphere held fixed at the quarter vertical position in a pressure-driven flow between parallel plates. In the latter case, LB calculations reveal a screening effect caused by neighboring periodic images of the test sphere. It is shown that the test sphere is hydrodynamically decoupled from its periodic images when separated by approximately 30 sphere radii. LB results for force and torque as a function of sphere height and flow cell height are also reported. Copyright © 2001 John Wiley & Sons, Ltd.