Inertial effects on viscous fingering in the complex plane

Andong He, Andrew Belmonte

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We present a nonlinear unsteady Darcy's equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension we derive a generalized Polubarinova-Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.

Original languageEnglish (US)
Pages (from-to)436-445
Number of pages10
JournalJournal of Fluid Mechanics
Volume668
DOIs
StatePublished - Feb 10 2011

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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