The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. Assuming the existence of sufficiently smooth solutions we will show that the one-sided Mullins-Sekerka flow does not preserve convexity. Introduction The Mullins-Sekerka flow is a nonlocal generalization of the mean curvature flow arising from physics [10,...

It is shown that surface tension effects on the free boundary have a regularizing effect for Hele-Shaw models, which implies existence and uniqueness of classical solutions for general initial domains.

This thesis discusses the radial version of the Hele-Shaw problem. Different from the channel version, traveling-wave solutions do not exist in this version. Under algebraic potentials, in the case that the droplets expand, in finite time, cusps will appear on the boundary and classical solutions may not exist afterwards. Physicists have suggested that for (2p+ 1, 2)-cusps, that near cusp singu...

2014 The covering surfaces of a Hele-Shaw cell may be roughened mechanically, or modified by random chemical patches which change the wetting properties. We discuss first the quasi-static injection of a single fluid (with a finite contact angle 03B8e) in an imperfect cell. The shape of the injected region depends critically on a dimensionless number i (ratio of the boundary energy 03C4 over the...

A model for the aerobic and anaerobic growth of Escherichia coli (HB101 K12 pGLO) depending on the concentration of oxygen and DOC as substrate has been developed based on laboratory batch experiments. Using inverse modelling to obtain optimal sets of parameters, it could be shown that a model based on a modified double Contois kinetic can predict cell densities, organic carbon utilisation, oxy...

We perform direct numerical simulations of a non-magnetic drop immersed in immiscible ferrofluids in a confined Hele-Shaw cell under an azimuthal field by a diffuse-interface method. The interface is unstable in such a condition because of the inward attraction of the ferrofluids induced by the magnetic field gradient. We focus on the fingering onset and pattern influenced by the coupling visco...