Influence of inertia on viscous fingering patterns: rectangular and radial flows
Eduardo O Dias1, José A Miranda
1Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.
Summary
Inertia stabilizes Saffman-Taylor instability in Hele-Shaw flows, widening fingers in rectangular setups and enhancing tip splitting in radial flows. This research clarifies the role of inertia in fluid dynamics.
Area of Science:
- Fluid Dynamics
- Instability Phenomena
Background:
- Saffman-Taylor instability is crucial in fluid dynamics.
- Inertial effects are increasingly recognized as significant factors influencing this instability.
Purpose of the Study:
- To investigate the impact of inertia on viscosity-driven fingering patterns in Hele-Shaw flows.
- To analyze stability and morphology changes due to inertial effects.
Main Methods:
- Perturbative-mode-coupling method applied to analyze fingering patterns.
- Consideration of both rectangular and radial Hele-Shaw flow geometries.
- Analytical solutions derived for the rectangular configuration.
Main Results:
- Inertia exhibits a stabilizing effect during the linear stage of instability.
- Inertia promotes finger widening in the weakly nonlinear regime for rectangular flows.
- Inertia induces enhanced finger tip splitting at the onset of nonlinearities in radial flows.
Conclusions:
- Analytical findings for rectangular Hele-Shaw flows align with experimental observations.
- Inertia plays a critical role in shaping fingering patterns, particularly at nonlinear stages.
- The study provides insights into inertia's influence on complex fluid instabilities.
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