Pattern formation in non-Newtonian Hele-Shaw flow

Document Type

Article

Publication Date

1-1-2001

Abstract

We study theoretically the Saffman-Taylor instability of an air bubble expanding into a non-Newtonian fluid in a Hele-Shaw cell, with the motivation of understanding suppression of tip-splitting and the formation of dendritic structures observed in the flow of complex fluids, such as polymeric liquids or liquid crystals. A standard visco-elastic flow model is simplified in the case of flow in a thin gap, and it is found that there is a distinguished limit where shear thinning and normal stress differences are apparent, but elastic response is negligible. This observation allows formulation of a generalized Darcy's law, where the pressure satisfies a nonlinear elliptic boundary value problem. Numerical simulation shows that shear-thinning alone modifies considerably the pattern formation and can produce fingers whose tip-splitting is suppressed, in agreement with experimental results. These fingers grow in an oscillating fashion, shedding "side-branches" from their tips, closely resembling solidification patterns. A careful analysis of the parametric dependencies of the system provides an understanding of the conditions required to suppress tip-splitting, and an interpretation of experimental observations, such as emerging length-scales. © 2001 American Institute of Physics.

Identifier

0035340114 (Scopus)

Publication Title

Physics of Fluids

External Full Text Location

https://doi.org/10.1063/1.1359417

ISSN

10706631

First Page

1191

Last Page

1212

Issue

5

Volume

13

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