Related papers: Fingering instabilities of a reactive micellar int…
We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general. It includes…
We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the…
The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the…
Viscous fingers in the lifting Hele-Shaw cell form a hierarchical pattern due to competition between growing fingers in a converging geometry. If the defending fluid is visco-plastic, a permanent three-dimensional pattern is formed, which…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
We analyze experimental data on double diffusive convection in an electrochemical cell in the finger regime. All fingers in the experiments are bounded on at least one end by a solid wall. The properties of these fingers are compared with…
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples…
The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, $\lambda_c$, which…
Adding swimming bacteria to a liquid causes its effective shear viscosity to decrease, eventually reaching a regime of zero viscosity. We examined whether this property leads to viscous finger-like displacement fronts like those observed…
We identify a fundamental morphological instability of mobile dislocations in crystals and related line defects. A positive gradient in the local driving force along the direction of defect motion destabilizes long-wavelength vibrational…
We present in this paper an experimental study of the invasion activity during unstable drainage in a 2D random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (non-wetting) displacing…
A thin water film on a cleaved mica substrate undergoes a first order phase transition between two values of film thickness. By inducing a finite evaporation rate of the water, the interface between the two phases develops a fingering…
The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw…
We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a…
Two dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid--fluid interfaces, significant effort has been expended to…
We show that unstable fingering patterns of two dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the KdV hierarchy. In this framework, the fingering instability is linked to a known…
Viscous fingers have been produced in the lifting Hele-Shaw cell, with concentric circular grooves etched onto the lower plate. The invading fluid (air) enters the defending newtonian fluid - olive oil as fingers proceeding radially inwards…
We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the…
Two laboratory scale experiments of dry and under-water avalanches of non-cohesive granular materials are investigated. We trigger solitary waves and study the conditions under which the front is transversally stable. We show the existence…
The temporal evolution of a water-sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the different modes appearing in the developing…