Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
1997-08-05
Physics
Condensed Matter
Soft Condensed Matter
36 pages, 5 figures, Latex, added references, to appear in Physica D (1998)
Scientific paper
10.1016/S0167-2789(98)00097-9
The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.
Miranda Jose A.
Widom Michael
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