s (in alphabetical order) Michael Dallaston (Imperial College London) ”Interfacial Hele-Shaw flows that develop corner singularities” It is well known that the evolution of a receding free boundary in one-phase Hele-Shaw flow (such as an expanding air bubble surrounded by viscous fluid) is ill-posed and generically forms cusps. The interfacial velocity at the cusp points is unbounded. Imposing ...

Rights: © 2013 Wiley-Blackwell. This is the post print version of the following article: Repo, Päivikki & Benick, Jan & Gastrow, Guillaume von & Vähänissi, Ville & Heinz, Friedemann D. & Schön, Jonas & Schubert, Martin C. & Savin, Hele. 2013. Passivation of black silicon boron emitters with atomic layer deposited aluminum oxide. Physica Status Solidi RRL. Volume 7, Issue 11. 950-954. DOI: 10.10...

Some known models in phase separation theory (Hele-Shaw, nonlocal mean curvature motion) and their approximated phase field models (Cahn–Hilliard, nonlocal Allen-Cahn) are used to generate planar curve evolution without shrinkage, with application to shape recovery. This turns out to be a level set approach to an area preserving geometric flow, in the spirit of Sapiro and Tannenbaum [36]. We di...

We study numerically and experimentally the dynamics and control of viscous fingering patterns in a circular Hele-Shaw cell. The nonlocality and nonlinearity of the system, especially interactions among developing fingers, make the emergent pattern difficult to predict and control. By controlling the injection rate of the less viscous fluid, we can precisely suppress the evolving interfacial in...

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 amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface...

We consider two-dimensional Hele-Shaw corner flows without effect of the surface tension and with an interface extending to the infinity along one of the walls. Explicit solutions that present a ”long-pin” deformations of the trivial solution are got. Making use of the Polubarinova-Galin approach we derive parametric equations for the moving interface in terms of univalent mappings of a canonic...

We consider a zero-surface-tension two-dimensional Hele-Shaw flow in an infinite wedge. There exists a self-similar interface evolution in this wedge, an analogue of the famous Saffman-Taylor finger in a channel, exact shape of which has been given by Kadanoff. One of the main features of this evolution is its infinite time of existence and stability for the Hadamard ill-posed problem. We deriv...

An upper bound on the growth rate of disturbances in three-layer Hele-Shaw flows with the middle layer having a smooth viscous profile is obtained using a weak formulation of the disturbance equations. A recently reported approach for the derivation of this bound is tedious, cumbersome, and requires numerical analysis. In contrast, the present approach is very simple, elegant, and requires no n...