Perturbation method in gas-assisted power-law fluid displacement in a circular tube and a rectangular channel

In this paper the two dimensional flow of a power-law fluid is studied anal ytically using a singular perturbation method in order to determine the res idual liquid film thickness of power-law fluids on the wall of a circular t ube or a rectangular channel when displaced by another immiscible fluid. In ner and enter expansions are developed in terms of a small parameter C-A(1/ 3) (modified capillary number). A differential equation for the shape of ga s bubble is solved numerically in order to determine the inner solution. Th e method of matched asymptotic expansions is used to match the inner and ou ter solutions. This approach indicated that the residual liquid film thickn ess of non-Newtonian fluids increases with decreasing power-law index. (C) 1999 Elsevier Science S.A. All rights reserved.