Near-wall and inertial forces on a neutrally buoyant particle in a wall-bounded stagnation-point flow

A suitable form of the reciprocal theorem is employed to predict the hydrodynamic forces acting on a small neutrally buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation-point flow. To this end, a simple analytical model of the undisturbed velocity field is established, reproducing the gradual transition of the actual flow from a pure linear straining flow in the bulk to a parabolic flow at the wall. The particle Reynolds number is considered small but finite and the particle is assumed to stand close enough to the wall for the latter to be in the inner region of the disturbance. Predictions including finite inertial effects are successfully compared with results provided by fully-resolved numerical simulations for the position-dependent slip velocity between the particle and the ambient fluid. Comparison with predictions based on the creeping-flow approximation reveals that finite-inertia effects due to particle–wall interactions and to the relative acceleration between the particle and fluid substantially modify the way the slip velocity varies with the distance to the wall.