J. Phys. II France
Volume 7, Numéro 7, July 1997
Page(s) 967 - 972
DOI: 10.1051/jp2:1997105
J. Phys. II France 7 (1997) 967-972

Fingering in 2D Parallel Viscous Flow

N. Rakotomalala, D. Salin and P. Watzky

Laboratoire Fluides, Automatique et Systèmes Thermiques URA 871, Bâtiment 502, Campus Universitaire, 91405 Orsay Cedex, France

(Received 15 July 1996, revised 16 October 1996, received in final form 30 April 1997, accepted 14 May 1997)

We study the displacement of miscible fluids of different viscosities (viscosity ratio M) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above $M \sim 10$, the interface becomes a well-defined finger, the reduced width of which tends to $\lambda_{\infty}= 0.56$ at large M. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.

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