Delayed onset and the transition to late time growth in viscous fingering

Abstract

The characteristic heavily branched patterns that result from viscous fingering instability are due to highly nonlinear growth of the fingers at late time. Here, the existence of an onset length scale associated with the transition between linear and nonlinear growth is revealed. Remarkably, by measuring this onset point, features of the patterns that form well into the nonlinear regime can be predicted. Existing theoretical work is not sufficient to understand this length scale, especially for miscible fluids where the fluid structure within the small scale of the gap becomes important.

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