Related papers: Selection of the Taylor-Saffman Bubble does not Re…
We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $\lambda_1$ and…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
The displacement of a viscous liquid by air in the narrow gap between two parallel plates - a Hele-Shaw channel - is an exemplar of complex pattern formation. Typically, bubbles or fingers of air propagate steadily at low values of the…
We demonstrate experimentally the existence of a purely elastic fingering instability which arises when air penetrates into an elastomer confined in a Hele-Shaw cell. Fingers appear sequentially and propagate within the bulk of the material…
We consider the Hele-Shaw flow that arises from injection of two-dimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic…
We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and…
A circular Hele-Shaw cell bounded by a volumetrically confined elastic solid can act as a fluidic fuse: during radially outward fluid flow, the solid deforms in response to the viscous pressure field such that the gap expands near the inlet…
We investigate the dynamics of relaxation, by surface tension, of a family of curved interfaces between an inviscid and viscous fluids in a Hele-Shaw cell. At t=0 the interface is assumed to be of the form |y|=A x^m, where A>0, m \geq 0,…
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…
A two-phase Hele-Show problem with a time-dependent gap describes the evolution of the interface, which separates two fluids sandwiched between two plates. The fluids have different viscosities. In addition to the change in the gap width of…
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
A mathematical model for tissue growth is considered. This model describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that such cell population model converges at the incompressible limit…
We present an anomalous experimental observation on the rising speed of air bubbles in a Hele-Shaw cell containing a suspension of spherical, neutrally-buoyant, non-Brownian particles. Strikingly, bubbles rise faster in suspensions as…
In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…
In Hele-Shaw cells, pressure-driven viscous fluid motion between two closely-spaced plates gives rise to a two-dimensional potential flow with zero circulation. Here, we show how the introduction of electromagnetic effects enables the…
When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation…
A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out.…
We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time…
Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal…
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…