相关论文: Systematic weakly nonlinear analysis of interfacia…
The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the…
The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which…
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 one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from…
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…
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.…
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…
Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
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…
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.…
In this paper, the interaction between two immiscible fluids with a finite mobility ratio is investigated numerically within a Hele-Shaw cell. Fingering instabilities initiated at the interface between a low viscosity fluid and a high…
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…
Traditional mathematical models of Hele--Shaw flow consider the injection (or withdrawal) of an air bubble into (or from) an infinite body of viscous fluid. The most commonly studied feature of such a model is how the Saffman-Taylor…
We present a theoretical and numerical study on the (in)stability of the interface between two immiscible liquids, i.e., viscous fingering, in angled Hele-Shaw cells across a range of capillary numbers ($Ca$). We consider two types of…
A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in…
Two dimensional free surface flows in Hele-Shaw configurations are a fertile ground for exploring nonlinear physics. Since Saffman and Taylor's work on linear instability of fluid--fluid interfaces, significant effort has been expended to…
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it…
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…
When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…