Related papers: Two-Phase Flow in Rotating Hele-Shaw Cells with Co…
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…
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set. Our contributions are twofold. First, we establish…
Tissue fluidity regulates many critical biological processes, including embryonic development, wound healing, and cancer metastasis. In confluent epithelia, where cell packing fraction is effectively fixed, the prevailing paradigm…
We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in…
The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid He-3 is magnetically stabilized. With uniform rotation we create a state with…
The Saffman-Taylor instability occurs when { a} Stokes fluid is displaced by a less viscous one { in} a Hele-Shaw cell. { This model is useful to study the secondary oil recovery from a pororus medum.} Since 1960, { polymer solutions} were…
We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…
Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are…
We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of…
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…
This paper investigates the connection between the chemotaxis--Navier--Stokes system with porous medium type nonlinear diffusion and the Hele--Shaw problem in $\mathbb{R}^d$ ($d\geq2$). First, we prove the global-in-time existence of weak…
A classical topic in the mathematical theory of hydrodynamics is to study the evolution of the free surface separating air from an incompressible perfect fluid. The goal of this survey is to examine this problem for two important sets of…
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.
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…
The present paper studies the structure of the set of stationary solutions to the incompressible Euler equations on the rotating unit sphere that are near two basic zonal flows: the zonal Rossby-Haurwitz solution of degree 2 and the zonal…
We study a system of equations governing liquid and gas flow in porous media. The gas phase is homogeneous while the liquid phase is composed of a liquid component and dissolved gas component. It is assumed that the gas component is weakly…
In disordered porous media, two-phase flow of immiscible fluids (biphasic flow) is organized in patterns that sometimes exhibit fractal geometries over a range of length scales, depending on the capillary, gravitational and viscous forces…
We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two…
We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is…
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…