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

Gabriel D. Carvalho, José A. Miranda, Hermes Gadêlha

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12 Scopus citations

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. © 2013 American Physical Society.
Original languageEnglish (US)
JournalPhysical Review E
Volume88
Issue number5
DOIs
StatePublished - Nov 11 2013
Externally publishedYes

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