相关论文: On a Generalized Two-Fluid Hele-Shaw Flow

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…

Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele-Shaw cells create intriguing patterns.We propose a simple numerical method for Hele-Shaw type problems by the method of fundamental…

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…

We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…

Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem is well-posed.

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that nonlocal relation between current and electric field due to momentum-conserving inter-particle collisions…

This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…

Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…

Let the interface between two immiscible fluids in a Hele-Shaw cell have, at t=0, a wedge shape. As a wedge is scale-free, the fluid relaxation dynamics are self-similar. We find the dynamic exponent of this self-similar flow and show that…

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…

The classical approach to visualizing a flow, in terms of its streamlines, motivates a topological/soft-analytic argument for constrained variational equations. In its full generality, that argument provides an explicit formula for…

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples…

We introduce and investigate a generalization of the Hele-Shaw flow with injection where several droplets compete for space as they try to expand due to internal pressure while still preserving their topology. Droplets are described by…

The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic…

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 present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…

In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult…

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

With the Lattice Boltzmann method (using the BGK approximation) we investigate the dynamics of Hele-Shaw flow under conditions corresponding to various experimental systems. We discuss the onset of the instability (dispersion relation), the…

Time-dependent injection strategies are commonly employed to control the number of viscous fingers emerging at the interface separating two fluids during radial displacement in Hele-Shaw flows. Here we demonstrate theoretically that such a…