Related papers: Toward the zero surface tension limit: The granula…
Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the channel and moving jointly with an assembly…
We study a diffuse interface model describing the motion of two viscous fluids driven by the surface tension in a Hele-Shaw cell. The full system consists of the Cahn-Hilliard equation coupled with the Darcy's law. We address the physically…
We investigate the viscous fingering instability that arises when air is injected from the end of an oil-filled, compliant channel. We show that induced axial and transverse depth gradients foster novel pattern formation. Moreover, the…
When particles settle through a stable temperature or salinity gradient they can drive an instability known as sedimentary fingering convection. This phenomenon is thought to occur beneath sediment-rich river plumes in lakes and oceans, in…
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of…
We investigate, both experimentally and theoretically, the fow and structure of a slurry when sheared between 2 horizontal plates. The slurry, otherwise called a "wet granular material", is made of non-Brownian particles immersed in a…
The behaviour of a viscous drop squeezed between two horizontal planes is treated by both theory and experiment. When the squeezing force F is constant and surface tension is neglected, the theory predicts ultimate growth of the radius a~…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
We present a theoretical and numerical study on the (in)stability of the interface between two immiscible liquids, i.e., viscous fingering, in angled Hele-Shaw cells across a range of capillary numbers ($Ca$). We consider two types of…
We investigate the convective instability resulting from the dissolution of carbon dioxide (CO$_{2}$) into water in a heterogeneous Hele-Shaw cell utilizing both experimental and numerical approaches. Experiments are conducted in a…
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…
In this paper we study the effects of dynamic wetting on the immiscible displacement of a high viscosity fluid subject to the radial injection of a less viscous fluid in a Hele-Shaw cell. The displaced fluid can leave behind a trailing film…
We address pattern selection problems in nonlinear interface dynamics by maximizing the entropy of the most probable (classical) scenario associated with the processes. This variational principle we applied to well-known selection problems…
The results from a series of well characterised, unstable, miscible displacement experiments in a Hele Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform…
We present here a detailed numerical study of the dynamical behaviour of `soft' uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the…
We consider the process of convective dissolution in homogeneous and isotropic porous media. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is…
We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions…
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…