On two-dimensional laminar flows of a particulate suspension in the presence of gravity field

Three simple two-dimensional streaming motions of a mixture of solid particles with a continuous carrier fluid, or gas, in the presence of the gravity field are considered. These include flow of a mixture over an infinite stationary rigid plane perpendicular to the direction of the gravity field, flow near an oscillating rigid plane and flow in a mixture induced by a suddenly accelerated plane. The nature of the boundary conditions at the interface between a layer of sediment settling on the rigid boundary and the mixture above it suggests an introduction of the independent variables that enable simple analytical expressions for the solutions of the first two flows and a numerical solution by means of a Laplace transform in the last case.