It is pointed out that the two-parameter family of solutions for the Saffman-Taylor problem recently studied by Magdaleno and Casademunt [Phys. Rev. E 60, R5013 (1999)] does not correspond to two fingers moving in a Hele-Shaw cell with the channel geometry, as was implied in their paper. It is thus clarified that their solution, while correctly describing a periodic array of axisymmetric finger...

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hel...

Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele–Shaw cells intriguing patterns. We propose a simple numerical method for type problems by the of fundamental solutions. The solutions is one mesh-free solvers potential problems, which provides highly accurate approximate solution despite its simplicity. Moreover, satisfies volume-preserving property...

In this second part of the series, we focus on approximating the Hele-Shaw problem via the Cahn-Hilliard equation ut + ∆(ε∆u − εf(u)) = 0 as ε ↘ 0. The primary goal of this paper is to establish the convergence of the solution of the fully discrete mixed finite element scheme proposed in [21] to the solution of the Hele-Shaw (Mullins-Sekerka) problem, provided that the HeleShaw (Mullins-Sekerka...

We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a nonuniform, azimuthal magnetic field, appl...

The lifting Hele-Shaw cell flow is a variation of the celebrated radial viscous fingering problem for which the upper cell plate is lifted uniformly at a specified rate. This procedure causes the formation of intricate interfacial patterns. Most theoretical studies determine the total number of emerging fingers by maximizing the linear growth rate, but this generates discrepancies between theor...

We present an experimental study of a new surfactant-driven fingering phenomenon in a Hele-Shaw cell. First, the threshold of instability is examined and compared with the linear theory. Second, the nonlinear evolution of fingering is quantified, and steady and unsteady patterns are distinguished. A wide range of dynamical behaviour is observed from drifting and merging fingers to cusp formatio...

J. C. LAIDLAW AND L. YOUNG I953 Folin, 0. (1905). J. biol. Chem. 1, 131. Hele, T. S. (1924). Biochem. J. 18, 110. Hele, T. S. (1931). Biochem. J. 25, 1736. Laidlaw, J. C. (1947). Thesis, University of Toronto. Laidlaw, J. C. & Young, L. (1948). Biochem. J. 42, Proc. 1. Lawrie, N. R. (1931). Biochem. J. 25, 1037. Manson, L. A. & Young, L. (1950). Biochem. J. 47, 170. Rhode, H. (1923). Hoppe-Seyl...

Forced displacement of oil by polymer flooding in oil reservoir is one of the effective methods of enhanced (tertiary) oil recovery. A classical model of this process within Hele-Shaw approximation involves three-layer fluid in a Hele-Shaw cell having a variable viscosity fluid in the intermediate layer between oil and water. The goal here is to find an optimal viscosity profile of the intermed...