Pattern formation in non-Newtonian Hele-Shaw flow

Petri Fast, L. Kondic, Michael J. Shelley, Peter Palffy-Muhoray

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1191-1212
Number of pages22
JournalPhysics of Fluids
Volume13
Issue number5
DOIs
StatePublished - May 2001

Fingerprint

Shear thinning
Liquid Crystals
shear thinning
Fluids
Liquid crystals
Boundary value problems
Solidification
Taylor instability
fluids
viscoelasticity
Computer simulation
Liquids
Air
boundary value problems
solidification
emerging
bubbles
liquid crystals
retarding
formulations

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Fast, P., Kondic, L., Shelley, M. J., & Palffy-Muhoray, P. (2001). Pattern formation in non-Newtonian Hele-Shaw flow. Physics of Fluids, 13(5), 1191-1212. https://doi.org/10.1063/1.1359417

Pattern formation in non-Newtonian Hele-Shaw flow. / Fast, Petri; Kondic, L.; Shelley, Michael J.; Palffy-Muhoray, Peter.

In: Physics of Fluids, Vol. 13, No. 5, 05.2001, p. 1191-1212.

Research output: Contribution to journalArticle

Fast, P, Kondic, L, Shelley, MJ & Palffy-Muhoray, P 2001, 'Pattern formation in non-Newtonian Hele-Shaw flow', Physics of Fluids, vol. 13, no. 5, pp. 1191-1212. https://doi.org/10.1063/1.1359417
Fast P, Kondic L, Shelley MJ, Palffy-Muhoray P. Pattern formation in non-Newtonian Hele-Shaw flow. Physics of Fluids. 2001 May;13(5):1191-1212. https://doi.org/10.1063/1.1359417
Fast, Petri ; Kondic, L. ; Shelley, Michael J. ; Palffy-Muhoray, Peter. / Pattern formation in non-Newtonian Hele-Shaw flow. In: Physics of Fluids. 2001 ; Vol. 13, No. 5. pp. 1191-1212.
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