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

the open chemical engineering journal

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