Laminar flow of power-law fluids through narrow three-dimensional channels of varying gap

Abstract

Experimental results are presented for the flow of non-Newtonian aqueous polymer solutions in narrow three-dimensional channels of varying gap. The fluids are assumed to obey the power-law rheological model. Experimental streamline flow patterns were photographed and compared directly with numerical solutions of approximate equations of motion derived by Pearson on the basis of lubrication theory. Streamlines were found to remain locally two-dimensional, indicating the absence of significant elastic and normal force effects. By means of a perturbation scheme it is shown that the narrow channel approximation will begin to break down when the local channel angle becomes of the order of 10°. Effects near channel boundaries are taken into account by using a boundary layer approach, in which the solution for a power-law fluid in the flow field is matched at the boundaries with the solution for a power-law fluid in a rectangular duct. The case of unsteady flow is also considered.