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Viscosity contrast effects on fingering formation in rotating Hele-Shaw flows
José A Miranda1, Enrique Alvarez-Lacalle
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil. jme@df.ufpe.br
Numerical simulations reveal how viscosity contrast shapes fluid fingers in rotating Hele-Shaw cells. The study details finger morphology, length distribution, and pinch-off singularities, especially when the inner fluid is less viscous.
Area of Science:
- Fluid dynamics
- Complex fluid interfaces
Background:
- Hele-Shaw cells are crucial for studying fluid dynamics.
- Understanding interfacial instabilities is key in various scientific fields.
Purpose of the Study:
- To numerically investigate finger morphologies at fluid interfaces in a rotating Hele-Shaw cell.
- To analyze the impact of viscosity contrast on fingering patterns and their evolution.
Main Methods:
- Numerical simulations of immiscible fluid flow in a rotating Hele-Shaw cell.
- Systematic analysis across the full range of viscosity contrasts.
- Weakly nonlinear analysis for pattern development validation.
Main Results:
- Viscosity contrast magnitude and sign significantly influence finger shape and length distribution.
- Less viscous inner fluids lead to distinct pinch-off singularities, disconnecting full fingers.
- Finger competition dynamics are accurately predicted by early-stage interfacial evolution analysis.
Conclusions:
- The study elucidates the complex interplay between viscosity contrast and fingering phenomena.
- Numerical and analytical findings offer insights into interfacial pattern formation and dynamics.
- Results highlight the critical role of viscosity in determining fluid behavior at interfaces.
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