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Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study.
Gabriel D Carvalho1, José A Miranda1, Hermes Gadêlha2
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
Elastic interfaces in Hele-Shaw cells can become unstable, forming finger patterns. Tuning interface rigidity controls finger width, revealing the importance of curvature effects in fluid dynamics.
Area of Science:
- Fluid dynamics
- Soft matter physics
- Interface science
Background:
- Viscous fingering is a classic instability in Hele-Shaw cells.
- Elastic interfaces with bending rigidity introduce new dynamics.
- Understanding these dynamics is crucial for predicting pattern formation.
Purpose of the Study:
- Investigate how interface elasticity influences pattern morphology in viscous fingering.
- Analyze the role of nonlinear effects and curvature-dependent rigidity.
- Determine how to control finger width through elasticity.
Main Methods:
- Employed a second-order mode-coupling approach.
- Studied a conventionally stable configuration with equal fluid viscosities.
- Focused on weakly nonlinear regimes.
Main Results:
- Nonlinear effects are crucial for inducing instabilities and determining pattern shape.
- Interface elasticity can lead to sizable interfacial instabilities.
- The rigidity fraction parameter controls the emergence of narrow or wide fingers.
- Observed a curvature weakening effect favoring finger development in low-rigidity regions.
Conclusions:
- Interface elasticity significantly alters viscous fingering patterns.
- Tuning rigidity offers a method to control pattern morphology.
- Curvature effects play a vital role in elastic interface instabilities.
