Related papers: Scaling Relations of Viscous Fingers in Anisotropi…
We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and…
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 finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically-tractable hydrodynamic instability…
We studied dendritic side-branching mechanism in the experiment of anisotropic viscous fingering. We measured the time dependence of growth speed of side-branch and the envelop of side-branches. We found that the speed of side-branch gets…
Viscous fingering (VF) is an interfacial instability that occurs in a narrow confinement or porous medium when a less-viscous fluid pushes a more viscous one, producing finger-like patterns. Controlling the VF instability is essential to…
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…
We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate boundary integral method where a coupled integral equation system is formulated.…
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],…
We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of…
Viscous fingering and wormhole growth are complex nonlinear unstable phenomena. We view both as the result of competition for water in which the capacity of an instability to grow depends on its ability to carry water. We derive empirical…
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…
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 growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities -…
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…
Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute…
We introduce applied shear as a method to control viscous fingering by smoothing the interface between miscible fluids. In the viscous fingering instability, a less viscous fluid displaces a more viscous one through the formation of…
The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a…
The process of one fluid pushing another is universally common while involving complex interfacial instabilities. Particularly, occurring in a myriad of natural and industrial processes, wavy fingering patterns frequently emerge when a less…
A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation…
We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale…