Hydrodynamical forces acting on particles in a two-dimensional flow near a solid wall

The hydrodynamical forces acting on a single particle and on a random rigid array of particles suspended in a two-dimensional shear flow of Newtonian fluid near a rigid wall were studied numerically in the flow regime where the relevant Reynolds numbers are of the order of unity. The simulations were done with conventional finite volume method for single-particle cases and with lattice-Boltzmann method for many-particle cases. A set of comparison cases was solved with both methods in order to check the accuracy of the lattice-Boltzmann method. For the single-particle case analytic formulae for the longitudinal drag force and for the transverse lift force were found. A modification to Darcy's law is proposed which takes into account the increase of the drag force near a moving wall. In the flow conditions studied here, the lift force acting on the particle array was found to be repulsive close to the wall, but becomes weakly attractive as the distance from the wall is increased.