Inertial effects in the Saffman-Taylor instability

Details Inertial effects in the Saffman-Taylor instability Inertial effects in the Saffman-Taylor instability

2005-06-22

arxiv.org/abs/cond-mat/0506568v1

Physics

Condensed Matter

Soft Condensed Matter

14 pages, 8 figures, submitted to J. Fluid Mech

Scientific paper

For the Saffman-Taylor instability, the inertia of the fluid may become important for large Reynolds numbers Re. We investigate the effects of inertia on the width of the viscous fingers experimentally. We find that, due to inertia, the finger width can increase with increasing speed, contrary to what happens at small Re. We find that inertial effects need to be considered above a critical Weber number We. In this case it can be shown that the finger width is governed by a balance between viscous forces and inertia. This allows us to define a modified control parameter 1/B', which takes the corrections due to inertia into account; rescaling the experimental data with 1/B', they all collapse onto the universal curve for the classical Saffman-Taylor instability. Subsequently, we try and rationalize our observations. Numerical simulations taking into account a modification of Darcy law to include inertia, are found to only qualitatively reproduce the experimental findings, pointing to the importance of three-dimensional effects.

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