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

C. Escobar1, F. Méndez*, 1, E. Luna2
1 Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510, Mexico
2 Recuperación de Hidrocarburos, Instituto Mexicano del Petróleo, 07730, Mexico

© 2008 Escobar et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510, Mexico; E-mail:


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 between both fluids. In order to obtain the residual film thickness, m , we used a singular perturbation technique: the matching 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.

Keywords: Gas-assisted power-law fluid displacement, gas bubble dynamics, matched asymptotic, lubrication theory.