Determination of the Thickness of a Power-Law Fluid Driven by the Penetration of a Long Gas Bubble in a Rectangular Channel Using a Singular Perturbation Method

摘要

In the present work an analytical and numerical study is presented in order to determine the residual fluid filmthickness of a power-law fluid on the walls of a rectangular horizontal channel when it is displaced by another immisciblefluid of negligible viscosity. The mathematical model describes the motion of the displaced fluid and the interface betweenboth fluids. In order to obtain the residual film thickness, m , we used a singular perturbation technique: the matchingasymptotic method; in the limit of small capillary number, Ca . The main results indicated that the residual filmthickness of the non-Newtonian fluid decreases for decreasing values of the power-law index, which is in qualitativeagreement with experimental results.