Related papers: Doubly-periodic array of bubbles in a Hele-Shaw ce…
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a…
The evolution of a two-phase Hele-Shaw problem, a Muskat problem, under assumption of a negligible surface tension is considered. We use the Schwarz function approach and allow the sinks and sources to be line distributions with disjoint…
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…
The first stages of finger formation in a Hele-Shaw cell with lifting plates are investigated by means of linear stability analysis. The equation of motion for the pressure field (growth law) results to be that of the directional…
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 consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…
The dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell are studied experimentally, theoretically and by phase-field simulations of the H-S equations. As the central, denser fluid is centrifuged, it forms…
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 consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can exhibit bubbling along a sequence of times -- the solution…
Using a recently derived filament model, the stability of fluid filaments in Hele-Shaw cells, driven by a constant pressure gradient, is studied. It is found that thin circular filaments grow if their initial radius exceeds a dimensionless…
In this paper, we propose a method of fundamental solutions for the problem of two-dimensional potential flow in a doubly-periodic domain. The solution involves a doubly-periodic function, to which it is difficult to give an approximation…
We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap $H$. We do observe an instability of the initially homogeneous…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find…
A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
Blob-filaments (or simply 'blobs') are coherent structures formed by turbulence and sustained by nonlinear processes in the edge and scrape-off layer (SOL) of tokamaks and other magnetically confined plasmas. The dynamics of these…
We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, and…
We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analogue of…
We consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. The model is derived by taking the incompressible limit of porous medium type equations, and the boundary instability of this model was recently studied…