Near-wall dynamics of a neutrally-buoyant particle in Hiemenz flow

We perform a DNS based on an Immersed Boundary Method to study neutrally buoyant spherical particle motion on the axis of an axisymmetric stagnation point flow at a wall (Hiemenz flow). We seek to find conditions leading to solid collision with the wall. Depending on the ratio between particle inertia and viscous boundary layer thickness, the force exerted on the particle exhibits two distinct behaviors. Far from the wall, the slip Reynolds number is vanishingly small, implying that the particle behaves essentially as a tracer, but its finite size implies an ambient inertial force nearly identical to the force that would decelerate the equivalent volume of fluid. Near the wall, the slip Reynolds number increases as the particle approaches the wall, and several forces besides the ambient inertial force play a role. We investigate the stress profile on the particle surface to identify the origin of these forces : ambient force due to finite size and non-uniform flow, lubrication due to squeeze film, and added-mass due to acceleration of particle and fluid. Using the DNS results, we build a model which may be used with under-resolved simulation and show that its results agree satisfactorily with well-resolved simulation.