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Capillary and geometrically driven fingering instability in nonflat Hele-Shaw cells
Rodolfo Brandão1, José A Miranda1
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901 Brazil.
Physical Review. E
|April 19, 2017
Summary
Viscous fingering instability, typically seen in flat Hele-Shaw cells, can now occur in reverse and viscosity-matched flows within nonflat cells, even at low capillary numbers. This new instability is driven by cell geometry and capillary effects.
Area of Science:
- Fluid dynamics
- Complex systems
Background:
- Viscous fingering instability typically occurs in flat Hele-Shaw cells when a less viscous fluid displaces a more viscous one.
- Under standard conditions, reverse flow (more viscous displacing less viscous) and viscosity-matched flows are stable, exhibiting no fingering.
Purpose of the Study:
- To investigate fluid flow instabilities in nonflat Hele-Shaw cells.
- To determine if geometric confinement can induce instability in traditionally stable flow regimes.
Main Methods:
- Theoretical analysis of fluid dynamics in a nonflat Hele-Shaw cell geometry.
- Investigation of linear stability and nonlinear pattern formation dynamics.
Main Results:
- Demonstrated that both reverse and viscosity-matched flows can become unstable in specific nonflat Hele-Shaw cells.
- Showed this instability can occur even at low capillary numbers, contrary to classical understanding.
- Identified combined capillary effects and cell geometry as the driving forces for this novel fingering instability.
Conclusions:
- Hele-Shaw cell geometry significantly influences fluid flow stability.
- Nonflat geometries can induce viscous fingering in previously stable flow configurations.
- Geometric confinement is a critical factor in controlling fingering patterns in confined fluid flows.