FORCED-CONVECTION AND SEDIMENTATION PAST A FLAT-PLATE

The steady laminar flow of a well-mixed suspension of monodisperse sol id spheres, convected steadily past a horizontal flat plate and sedime nting under the action of gravity, is examined. It is shown that, in t he limit as Re-->infinity and epsilon-->0, where Re is the bulk Reynol ds number and epsilon is the ratio of the particle radius alpha to the characteristic length scale L, the analysis for determining the parti cle concentration profile has several aspects in common with that of o btaining the temperature profile in forced-convection heat transfer fr om a wall to a fluid stream moving at high Reynolds and Prandtl number s. Specifically, it is found that the particle concentration remains u niform throughout the O(Re--1/2) thick Blasius boundary layer except f or two O(epsilon(2/3)) thin regions on either side of the plate, where the concentration profile becomes nonuniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the lea ding edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the fre e stream by an amount proportional to X(5/6), With X measuring the dis tance along the plate, and decreases in a similar fashion along the un derside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier (Nir and Acrivos 1990), here the concentration profile remains continuous ever ywhere. For values of X beyond the region near the leading edge, the p article concentration profile is obtained through the numerical soluti on of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle c oncentration along the top side of the plate attains its maximum value phi(m) and that, beyond this point, a stagnant sediment layer will fo rm that grows steadily in time. This critical value of X is computed a s a function of phi(s), the particle volume fraction in the free strea m. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along t he underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be u sed to describe particle migration in other shear flows, as, for examp le, in the case of crossflow microfiltration.