Forces acting on near-wall spherical particles in shear flows of diluted gases

In the present paper, we studied the forces on a spherical particle of radius R moving in the vicinity of the plane wall in a shear flow of free molecular regime. We consider that the distance ratio between the plane wall and the particle (L) and the particle radius (R) is large (e.g., L/R > 5), and the gas molecular mean free path (λ) is much higher than the particle size (λ/R ≫1). An analytical formula for the forces is obtained based on gas kinetic theory and certain simplifying assumptions, and is verified by using Direct Simulation Monte Carlo Method. It is found that the forces acting on the particle can be affected by the momentum accommodation coefficients (σ) of the wall and particle surfaces, the wall/gas temperature ratios (T_w/T), and the velocity gradient (G) of the gas flow. In the cases of specular reflections (σ = 0), the near-wall effect can be neglected. With the increase of the momentum accommodation coefficients, the near-wall effect can be enhanced. When near-wall particles move in the direction parallel to the plane wall, there is a lift force which is perpendicular to the wall due to the near-wall effect and the shear flow. For T_w/T < 1, the lift force for the near-wall particles is in the direction against the wall. While for T_w/T > 1, the force is in the direction away from the plane wall. The findings presented in this paper can provide theoretical guidance for the application of near-wall particles in shear flows.