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Controlling fingering instabilities in nonflat Hele-Shaw geometries
Luciano dos Reis1, José A Miranda
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
Controlling viscous fingering in Hele-Shaw cells is challenging. This study develops injection rate strategies to suppress pattern splitting and achieve robust n-fold symmetry in curved environments.
Area of Science:
- Fluid dynamics
- Interfacial phenomena
- Pattern formation
Background:
- Viscous fingering in Hele-Shaw cells typically produces complex, ramified patterns.
- Fingertip splitting in these systems leads to unpredictable and uncontrollable interfacial structures.
- Nonflat geometries like conical and spherical cells introduce further complexity.
Purpose of the Study:
- To develop methods for controlling interfacial patterns in nonflat Hele-Shaw cells.
- To suppress the development of bifurcated shapes during injection-driven flow.
- To achieve robust n-fold symmetry in interfacial structures.
Main Methods:
- Calculation of time-dependent injection rates tailored for curved confined environments.
- Application of a weakly nonlinear approach for analytical insights.
- Analysis of geometric and topological influences on fingering control.
Main Results:
- Derived injection rate expressions effectively suppress fingertip splitting.
- Demonstrated achievement of stable, n-fold symmetric interfacial patterns.
- Identified key geometric and topological factors influencing control efficiency.
Conclusions:
- Controlled injection strategies can dictate interfacial pattern formation in nonflat Hele-Shaw cells.
- Robust n-fold symmetry is attainable by suppressing bifurcations.
- The findings offer a pathway to predictable and controllable fluid interfaces in complex geometries.
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