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Published on: October 5, 2018
Coriolis effects on rotating Hele-Shaw flows: a conformal-mapping approach.
José A Miranda1, Hermes Gadêlha, Alan T Dorsey
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil. jme@df.ufpe.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
The Coriolis force influences fluid interface dynamics in rotating Hele-Shaw cells, affecting cusp formation and pattern rotation. It opposes centrifugal effects, altering instability development.
Area of Science:
- Fluid Dynamics
- Mathematical Physics
Background:
- Studying fluid-fluid interface dynamics in radial Hele-Shaw cells is crucial for understanding complex flow phenomena.
- Zero surface tension simplifies interface behavior, allowing focus on inertial and rotational effects.
Purpose of the Study:
- To investigate the impact of Coriolis force on fluid interface dynamics in a rotating Hele-Shaw cell with injection.
- To analyze the formation and evolution of singularities, specifically cusp singularities, under these conditions.
Main Methods:
- Utilized a conformal-mapping approach to model the fluid-fluid interface.
- Employed Richardson's harmonic moments method to derive conformal maps representing time evolution.
- Analyzed exact solutions for inviscid, negligible density fluids, considering Coriolis force effects.
Main Results:
- Coriolis force significantly impacts the timing of cusp formation and introduces rotational phase drift to evolving patterns.
- The force's effect on cusp breakdown depends on the relative viscosity and density of the fluids.
- No finger bending events were observed in the exact solutions, even with Coriolis effects.
Conclusions:
- The Coriolis force is a key factor in determining singularity development and pattern evolution in rotating Hele-Shaw flows.
- Its interplay with centrifugal forces dictates the stability of the fluid interface.
- Further research could explore scenarios with non-negligible fluid densities and viscosities.
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