Viscous Fingering Pattern Characterization in a Radial Hele-Shaw Cell with Anisotropy and Defects
Abstract
We examine the viscous fingering patterns formed by forcing nitrogen gas into the center of a horizontal, radial Hele-Shaw cell filled with paraffin oil. The lower plate of the cell has anisotropy in the form of a rectangular lattice. We examine the often-observed transition(Jordi Ignes-Mullol and J. V. Maher, Phys. Rev. E 53), 3788 (1996). from isotropic, tip-splitting viscous fingers to anisotropic, side-branching, needle-like fingers by varying the Hele-Shaw cell gap and the gas injection rate. By adding defects to the lattice, we see increased branching in the pattern morphologies. We use plates having different amounts of lattice defects (from 0 - 10%). The ratio of the perimeter squared to the area of the pattern at the end of a run shows a power-law-like dependence on the areal growth rate of the pattern (and hence, on the gas injection rate). This ratio clearly reveals increased pattern ramification at larger injection rates and for smaller gaps. The approximate power-law exponent depends little on the density of defects and on the gap spacing. The transition from viscous fingering to side branching and dendritic fingering is shifted to larger flow rate by increasing the defect density.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 1998
- Bibcode:
- 1998APS..MAR.A2906D