The characterization and understanding of rock deformation processes due to fluid flow is a challenging problem with numerous applications. The signature of this problem can be found in Earth Science and Physics, notably with applications in natural hazard understanding, mitigation or forecast (e.g., earthquakes, landslides with hydrological control, volcanic eruptions), or in industrial applic...

In this note, we discuss the quantum Hele-Shaw flow, a random measure process in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et al. This process arises in the theory of electronic droplets confined to a plane under a strong magnetic field, as well as in the theory of random normal matrices. We extend a result of Elbau and Felder [6] to general external field potentia...

We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of a Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a co...

It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class of initial data. As a consequence, we give a rigorous proof of the fact that homogeneous Hele-Shaw flows with positive surface tension are volume preserving and area shrinking.

Complete synchronization between two Hele-Shaw cells is examined. The two dynamical systems are chaotic in time and spatially extended in two dimensions. It is shown that a large number of connectors are needed to achieve synchronization. In particular, we have studied how the number of connectors influences the dynamical regime that is set inside the Hele-Shaw cells.

Preface One of the most influential works in Fluid Dynamics at the edge of the 19-th century was a short paper [130] written by Henry Selby Hele-Shaw (1854–1941). There Hele-Shaw first described his famous cell that became a subject of deep investigation only more than 50 years later. A Hele-Shaw cell is a device for investigating two-dimensional flow of a viscous fluid in a narrow gap between ...

Electrowetting has recently been explored as a mechanism for moving small amounts of fluids in confined spaces. We propose a diffuse interface model for drop motion, due to electrowetting, in a Hele-Shaw geometry. In the limit of small interface thickness, asymptotic analysis shows the model is equivalent to Hele-Shaw flow with a voltagemodified Young-Laplace boundary condition on the free surf...

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-co...