Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a set and rules for the free boundary are given related to the classical Hele-Shaw model of fluid dynamics. Following the lines of previous papers where the mat...

In enhanced oil recovery by chemical flooding within tertiary oil recovery, it is often necessary to choose optimal viscous profiles of the injected displacing fluids that reduce growth rates of hydrodynamic instabilities the most thereby substantially reducing the well-known fingering problem and improving oil recovery. Within the three-layer Hele–Shaw model, we show in this paper that selecti...

Bubbles freely rising in a fluid at rest can display variety of complex paths and shapes. We investigate experimentally their behavior the inertial regimes obtained for Hele-Shaw cell, where additional lateral walls are introduced to modify cell width, thus coupling between bubbles' velocity shape. Scaling laws characterizing different motion provided.

This article is devoted to the investigation of Marangoni-driven pattern formation at the interface between two immiscible fluids filling a Hele-Shaw cell, each of them containing a reactant of an exothermic neutralization reaction. In such a system, convective patterns arise when one reactant diffuses through the interface to react with the other chemical species in one of the fluids. A chemo-...

The relative immobility of foam in porous media suppresses the formation of fingers during oil displacement leading to a more stable displacement which is desired in various processes such as Enhanced Oil Recovery (EOR) or soil remediation practices. Various parameters may influence the efficiency of foam-assisted oil displacement such as properties of oil, the permeability and heterogeneity of...

The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularization on the interface is not provided by surface tension but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, ...

We apply the J-integral to free-boundary flows in a channel geometry such as viscous fingering or blob injection in Hele-Shaw cells, void propagation in electromigration, and injection of air bubbles into inviscid liquids. The theory of that and related conservation integrals, developed in elasticity, is outlined in a way that is applicable to fluid mechanics problems. Depending on the boundary...

In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data. 0. Introduction. Consider a c...