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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/18762
Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach
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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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FOLCH MANZANARES, Roger, et al. Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach. Physical Review E. 1999. Vol. E60, num. 1734-1740. ISSN 1063-651X. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/18762