Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell

Details Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell

1997-11-25

arxiv.org/abs/cond-mat/9711270v2

Physics

Condensed Matter

Soft Condensed Matter

42 pages, 5 figures, added references, minor changes, to appear in Int. J. Mod. Phys. B (1998)

Scientific paper

We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.

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