Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell
Abstract
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.
Cite
@article{arxiv.cond-mat/0201589,
title = {Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell},
author = {Jose A. Miranda},
journal= {arXiv preprint arXiv:cond-mat/0201589},
year = {2016}
}
Comments
14 pages, 3 ps figures, Revtex