Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach.

@article{Folch1999PhasefieldMF,
  title={Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach.},
  author={Roger Folch and Jaume Casademunt and A Hernandez-Machado and Laureano Ram{\'i}rez-Piscina},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1999},
  volume={60 2 Pt B},
  pages={1724-33}
}
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in… CONTINUE READING

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