Competition between anisotropic viscous fingers
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
a e-mail: Piotr.Szymczak@fuw.edu.pl
Received: 30 June 2014
Revised: 21 July 2014
Published online: 22 September 2014
We consider viscous fingers created by injection of low viscosity fluid into the network of capillaries initially filled with a more viscous fluid (motor oil). Due to the anisotropy of the system and its geometry, such a setup promotes the formation of long-and-thin fingers which then grow and compete for the available flow, interacting through the pressure field. The interaction between the fingers is analyzed using the branched growth formalism of Halsey and Leibig (Phys. Rev. A 46, 7723, 1992) using a number of simple, analytically tractable models. It is shown that as soon as the fingers are allowed to capture the flow from one another, the fixed point appears in the phase space, corresponding to the asymptotic state in which the growth of one of the fingers in hindered by the other. The properties of phase space flows in such systems are shown to be remarkably insensitive to the details of the dynamics.
© EDP Sciences, Springer-Verlag, 2014