Near-wall dynamics of a neutrally buoyant spherical particle in an axisymmetric stagnation point flow

Abstract

The motion of a neutrally buoyant spherical particle along the axis of an axisymmetric stagnation point flow at a rigid and smooth flat wall (Hiemenz–Homann flow) is investigated in the presence of low-to-moderate inertia effects. The particle dynamics is elucidated using numerical simulation. At distances large compared to the characteristic thickness of the boundary layer \delta=(\nu/B)^{1/2}, with \nu the kinematic viscosity and B the strain rate of the carrying flow, the particle decelerates as it approaches the wall, due to the ambient pressure increase toward the stagnation point. In this part of the path, its velocity is nearly identical to that of the local undisturbed fluid at the position of its centre. Relative motion between the particle and fluid increases as the wall–particle gap reduces, due to wall-induced hydrodynamic interaction forces. Two distinct evolutions of the net force on the particle are observed, depending on the relative particle size, a/\delta=Re^{1/2}, where a is the particle radius and Re=2Ba^2/\nu is the Reynolds number. For a/\delta=2, the force decays monotonically to zero, while it undergoes a sharp rise before returning to zero for larger particles. In the latter case, the particle retains a sufficient velocity even for very small gap widths such that, under usual roughness levels, a rebounding collision would occur. The stress profiles at the particle surface are investigated to separate the various contributions to the hydrodynamic force. Theoretical predictions for near-wall viscous and inertial forces available in the creeping-flow and low-but-finite Reynolds-number limits, respectively, are used to pinpoint the origin of the dominant inertia effect that controls the particle dynamics when the particle gets very close to the wall.