Two-phase convex-type corner flows

Abstract

The flow of an inviscid incompressible fluid, with imbedded identical spherical particles, around an arbitrary corner is treated by the method of small perturbations. Application is made to convex flows only and the approximate effects of separation are also considered. The assumption of arbitrary initial particle density k0 leads to a complex system of equations, which appears to have no simple solution in general, and is not considered. For small k0 the particle density distribution is governed by a first-order partial differential equation which, when solved by the method of characteristics, yields ordinary differential equations, whose solutions are simple and analytic for unseparated flow and numerical only when separation is considered. In the former flow, spiral type curves partially encircling the plate tip, and then trailing downstream, delineate the particle-free zones, and it is found that the particle density increases monotonically in the downstream direction on all particle streamlines. In the separated flow, the most noteworthy effect is the disappearance of the infinite velocity at the origin and the consequent considerable reduction in the magnitude of the perturbation.