The Mathematical Institute, University of Oxford, Eprints Archive

Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study

Carvalho, G D and Miranda, J A and Gadelha, H (2013) Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study. Physical Review E, 88 (5). 053006.

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Abstract

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1796
Deposited By: Sara Jolliffe
Deposited On:21 Feb 2014 08:46
Last Modified:29 May 2015 19:29

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