Mass transport in a layer of power-law fluid forced by periodic surface pressure

Abstract

An asymptotic theory is presented for the mass transport in a thin layer of non-Newtonian fluid which is forced by periodic pressure on the free surface. The fluid is supposed to be pseudoplastic or shear thinning, and a power-law model is adopted to describe the stress and shear rate relationship. Based on the assumptions of shallowness and small deformations, a perturbation analysis is carried out to the second order to yield equations of motion in terms of the Lagrangian variables. These equations are non-linear because of the power law for the shear rate. Therefore, unlike the Newtonian case, the mass transport velocity cannot be found simply by first time-averaging the second-order differential equation, which instead must be solved in full before the steady component is separated from the complete solution. Numerical results, which are generated with finite differences, are examined in particular for the dependence of the fluid motion (first-order particle displacements and second-order mass transport velocity) on the pressure forcing as a function of the flow index.