An integral equation for immiscible fluid isplacement in a two-dimensional porous medium or Hele-Shaw cell

Two dimensional Leidenfrost Droplets in a Hele Shaw Cell

Porous Medium Equation to Hele-shaw Flow with General Initial Density

In this paper we study the “stiff pressure limit” of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced in [PQV], describes the growth of a tumor zone with a restriction on the maximal cell density. In a general context, this extends previous results of Gil–Quirós [GQ1] and Kim [K] who res...

Selection Principle of Optimal Profiles for Immiscible Multi-Fluid Hele-Shaw Flows and Stabilization

In this paper, we discuss a previously unknown selection principle of optimal viscous configurations for immiscible multi-fluid Hele-Shaw flows that have emerged from numerical experiments on threeand four-layer flows. Moreover, numerical investigation on four-layer flows shows evidence of four-layer systems which are almost completely stabilizing. Simple physical mechanisms that explain both o...

Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell.

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast, c=(mu(1)-mu(2))/(mu(1)+mu(2)), in a model porous medium defined as a Hele-Shaw cell with random gap b(0)+delta b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, nonconserved, and power-law corr...

Two-dimensional Stokes and Hele-Shaw flows with free surfaces

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...