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Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach
R Folch1, J Casademunt, A Hernández-Machado
1Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain.
Summary
We developed a phase-field model for fluid dynamics in Hele-Shaw cells, accurately capturing interface behavior and corrections for varying fluid viscosities. This model shows slower convergence with higher viscosity contrasts.
Area of Science:
- Fluid Dynamics
- Computational Physics
Background:
- Hele-Shaw cells are crucial for studying fluid interfaces.
- Modeling immiscible fluid dynamics with viscosity contrast presents challenges.
Purpose of the Study:
- To present a phase-field model for two immiscible fluids in a Hele-Shaw cell.
- To analyze the model's accuracy and convergence, especially with arbitrary viscosity contrasts.
Main Methods:
- Developed a phase-field model for interface dynamics.
- Employed asymptotic matching techniques to validate against Hele-Shaw equations.
- Calculated first-order interface thickness corrections and their impact on dispersion relations.
Main Results:
- The phase-field model correctly reproduces Hele-Shaw equations in the sharp-interface limit.
- Quantified corrections to Hele-Shaw equations and their effect on linear dispersion.
- Observed slower convergence for higher viscosity contrasts.
Conclusions:
- The phase-field model provides accurate Hele-Shaw dynamics with quantifiable corrections.
- Interface thickness control is key for model accuracy and convergence.
- High viscosity contrasts necessitate careful consideration for model convergence.