BEHAVIOR OF SPHERICAL SOLID PARTICLES RELEASED IN A LAMINAR BOUNDARY LAYER ALONG A FLAT PLATE

The behavior of a very small solid spherical particle initially at rest on the surface of a flat plate in a laminar boundary layer along the plate is investigated. The Stokes drag is the only force considered to be acting on the particle. The fluid Reynolds number Ref is assumed to be large, and the particle Reynolds number Re is assumed to be small. The equations describing the motion of the particle are two simultaneous, second order, nonlinear, ordinary differential equations with one parameter. A complete digital computer solution and analytic limiting solutions for large and small values of a dimensionless time τ have been obtained. The numerical and the analytic solutions are in close agreement. The results presented are the velocity, trajectory, and time history of the particle and the force acting on the particle. These results show that the particle comes into equilibrium with the fluid very quickly with respect to the spatial coordinates, rising only several radii from the surface in its entire flight. © 1969 Martinus Nijhoff.