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Finger tip behavior in small gap gradient Hele-Shaw flows.

Eduardo O Dias1, José A Miranda

  • 1Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

In Hele-Shaw cells, a slight gap gradient alters finger tip behavior, causing widening or narrowing based on gradient sign. This study analytically predicts these phenomena in early nonlinear dynamics.

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Area of Science:

  • Fluid dynamics
  • Pattern formation

Background:

  • Finger splitting and narrowing are uncommon in early flow stages of parallel-plate Hele-Shaw cells.
  • Previous experiments show gap gradients significantly influence finger tip behavior.

Purpose of the Study:

  • To analytically investigate the effect of nonparallel plates on finger tip dynamics in Hele-Shaw cells.
  • To predict finger tip splitting and narrowing phenomena using a theoretical approach.

Main Methods:

  • Perturbative mode coupling theory was employed to analyze the nonparallel-plate situation.
  • The study focused on early nonlinear stages of fluid dynamics.

Main Results:

  • The sign of the gap gradient dictates finger tip behavior: positive gradients lead to wider fingers, negative gradients to narrower fingers.
  • Analytical predictions align with experimental observations of finger tip phenomena.

Conclusions:

  • The theoretical framework successfully predicts finger tip splitting and narrowing in Hele-Shaw cells with a gap gradient.
  • Gap gradient is a key factor controlling pattern formation at the finger tip in early nonlinear dynamics.