RAYLEIGH SIMILARITY SOLUTIONS AND BOUNDARY-LAYER FLOW FOR CONCENTRATED SUSPENSIONS

We have investigated a series of transient problems in the flows of co ncentrated suspensions to test the effects of particle migration on th e evolution of concentration and velocity profiles. First, we report a similarity solution to a Rayleigh problem, where the boundary of the infinite half space is given a velocity proportional to the square roo t of time. Next, the classical Rayleigh problem, where the boundary is impulsively started initially at a constant velocity, is examined. Th e structure of the kinematics resembles that obtained in the first pro blem, but the concentration does not have a similarity form. and tends asymptotically to a uniform profile at large time. Finally, we solve the flow of a suspension past a semi-infinite plate, and discuss its c onnection to the Rayleigh problem. In all three cases, our calculation s reveal Newtonian kinematics in the practical limit of a/L much less than 1, where a is the particle size, and L is a viscous diffusion len gth scale. In addition we see vastly different time and length scales in the evolution of the velocity and the concentration profiles. The v elocity develops faster in time (by O(a/L)(2)), and extends further in space (by O(L/a)) than the concentration profile.