THE DEVELOPMENT OF POISEUILLE FLOW OF A PSEUDOPLASTIC FLUID

摘要

We consider here the two-dimensional steady flow of a liquid down a semi-infinite straight channel, a much-studied problem of obvious practical and theoretical interest. Far from the entrance, the flow is parallel to the walls and the determination of the velocity distribution is a simple matter, whatever the constitutive model. We consider here the region sufficiently far downstream that the flow is almost parallel, so that the equations can be linearized about the parallel-flow solution. We then look for the approach to fully-developed flow by way of decaying eigenmodes. This was done for the Newtonian liquid by Wilson. In that paper both large and small Reynolds numbers were considered; here we consider only low Reynolds number. This is reasonable in view of the generally large viscosity of the liquids.