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Finger competition dynamics in rotating Hele-Shaw cells
Hermes Gadêlha1, José A Miranda
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
Interfacial instabilities in rotating Hele-Shaw cells are analyzed. Viscosity contrast, surface tension, and gap spacing significantly influence finger competition dynamics, with vanishing viscosity contrast suppressing competition.
Area of Science:
- Fluid dynamics
- Nonlinear phenomena
Background:
- Hele-Shaw cells are crucial for studying fluid-fluid interfaces.
- Interfacial instabilities drive pattern formation in various physical systems.
Purpose of the Study:
- To analytically investigate interfacial instabilities in rotating Hele-Shaw cells.
- To understand the role of dimensionless parameters (viscosity contrast, surface tension, gap spacing) in finger competition dynamics.
Main Methods:
- A mode-coupling approach was employed.
- A modified pressure jump boundary condition accounted for normal stresses.
- A differential equation for early nonlinear interface evolution was derived.
Main Results:
- Finger competition dynamics are linked to viscosity contrast (A), surface tension (B), and gap spacing (b) via subharmonic perturbations.
- Vanishing viscosity contrast (A=0) suppresses finger competition irrespective of B and b.
- Positive A enhances outward finger competition, while negative A enhances inward finger competition.
Conclusions:
- The study provides analytical insights into finger competition in Hele-Shaw cells across a range of parameters.
- Pattern morphology is sensitive to viscosity contrast, with significant modifications observed for -1 ≤ A ≤ 1.
- The interplay of A, B, and b dictates diverse finger competition behaviors.