相关论文: Steady-state fingering patterns for a periodic Mus…
The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth…
Viscous flows in a quasi-two-dimensional Hele-Shaw geometry can lead to an interfacial instability when one fluid, of viscosity $\eta_{in}$ displaces another of higher viscosity, $\eta_{out}$. Recent studies have shown that there is a delay…
New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves 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 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…
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…
We study self-similar viscous fingering for the case of divergent flow within a wedge-shaped Hele-Shaw cell. Previous authors have conjectured the existence of a countably-infinite number of selected solutions, each distinguished by a…
The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1],…
In this paper we consider the evolution of two fluid phases in a porous medium. The fluids are separated from each other and also the wetting phase from air by interfaces which evolve in time. We reduce the problem to an abstract evolution…
A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form ``fingered'' patterns upon increasing the number of electrons. We construct explicit examples of these…
The linear stability of miscible displacement for radial source flow at infinite P\'eclet number in a Hele-Shaw cell is calculated theoretically. The axisymmetric self-similar flow is shown to be unstable to viscous fingering if the…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
The well-studied selection problems involving Saffman-Taylor fingers or Taylor-Saffman bubbles in a Hele-Shaw channel are prototype examples of pattern selection. Exact solutions to the corresponding zero-surface-tension problems exist for…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
The onset of viscous fingering in the presence of a non monotonic viscosity profile is investigated theoretically for two immiscible fluids. Classical fluid dynamics predicts that no unstable behavior may be observed when a viscous fluid…
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…
The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model.…
In this paper, we establish the global well-posedness of the one-phase Muskat problem with surface tension for small initial data. This problem describes the motion of the interface separating a wet region from a dry region within a porous…
When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves, Dauchot, and Bouchaud, 2013). These fingers occur without…
During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an…