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

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

1999-03-10

arxiv.org/abs/cond-mat/9903171v2

Phys. Rev. E, 60, pp. 1724-1733 (1999)

Physics

Condensed Matter

Soft Condensed Matter

17 pages in revtex. changes: 1 reference added

Scientific paper

10.1103/PhysRevE.60.1724

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 detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

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