Viscous fluid fingering on a negatively curved surface
Rodolfo Brandão1, José A Miranda1
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Summary
Researchers studied viscous fingering on a hyperbolic plane, finding negative curvature influences pattern formation. A control strategy was developed to minimize this fluid instability growth.
Area of Science:
- Fluid dynamics
- Non-Euclidean geometry
- Pattern formation
Background:
- Viscous fingering in Hele-Shaw cells is a well-established fluid mechanics phenomenon.
- Previous studies have primarily focused on flat, Euclidean surfaces.
Purpose of the Study:
- To investigate viscous fingering dynamics on a hyperbolic plane (H(2)) with negative Gaussian curvature.
- To analyze the impact of negative curvature on fingertip splitting and finger competition.
- To explore a time-dependent control strategy for mitigating viscous fingering.
Main Methods:
- Application of a perturbative mode-coupling formalism.
- Mathematical analysis of fluid instabilities on curved surfaces.
- Development and simulation of a dynamic injection rate control strategy.
Main Results:
- Negative Gaussian curvature significantly influences the pattern formation mechanisms of viscous fingering.
- The study identifies key changes in fingertip splitting and finger competition due to curvature.
- A time-dependent control of injection rate effectively minimizes viscous fingering growth on the hyperbolic plane.
Conclusions:
- Surface curvature is a critical factor in viscous fingering dynamics.
- Understanding these effects on non-Euclidean surfaces advances fluid mechanics.
- The proposed control strategy offers a method for managing fluid instabilities in curved geometries.
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