Inertial effects in the Saffman-Taylor instability

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dc.creatorChevalier, C.
dc.creatorAmar, M. Ben
dc.creatorBonn, D.
dc.creatorLindner, A.
dc.date2005-06-22
dc.date.accessioned2026-07-07T03:05:45Z
dc.date.available2026-07-07T03:05:45Z
dc.descriptionFor 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.
dc.description14 pages, 8 figures, submitted to J. Fluid Mech
dc.identifierhttps://arxiv.org/abs/cond-mat/0506568
dc.identifierhttp://arxiv.org/abs/cond-mat/0506568
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/26563
dc.subjectSoft Condensed Matter
dc.titleInertial effects in the Saffman-Taylor instability
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