Abstract:

We study patterns formed by the viscous fingering instability in a porous media. When the displacing fluid preferentially wets the medium, the finger width is much larger than the pore size and, when normalized by the square root of the permeability, is found to scale with capillary number as Ca^−1/2. While traditional theories based on Hele-Shaw geometry give this dependence for the most unstable wavelength, they are unable to explain the magnitude of the finger. We consider here the effect of a velocity dependent capillary pressure in addition to the more conventional static term, and suggest that it may control the scaling of the finger width on Ca. We demonstrate the existence of this dynamic capillary pressure, which offers new insight into the basic physics of the motion of a fluid interface in porous media.

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