Droplet motion with contact-line friction: long-time asymptotics in complete wetting

We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the...

Self-similar solutions to the porous medium equation

The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...

Zener solutions for particle growth in multi-component alloys

In this paper the Zener theory on precipitate growth in supersaturated alloys for planar, cylindrical and spherical geometries is extended to multi-component alloys. The obtained solutions can be used to check the results from numerical simulations under simplified conditions. Further, the multi-component solutions are used to derive the quasi...

Solution of vector Stefan problems with cross-diffusion

A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusant phase. To facilitate the analysis we use a...

Mathematical models for particle dissolution in metallic alloys

This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in...

A mathematical model for the dissolution of stoichiometric particles in multi-component alloys

A general model for the dissolution of stoichiometric particles in multi-component alloys is proposed and analysed. We introduce the concept of mass-conserving solutions and give a self-similar solution for the resulting Stefan-problem. Furthermore, we show that particle dissolution in multi-component alloys can under certain circumstances be...

A model for a viscous preflush prior to gelation in a porous medium

In this paper we propose and analyse a simplified mathematical model on the effect of a fully miscible preflush on gel-placement in an oil reservoir. The approach is based on a segregated flow model even if the two phases are fully miscible. For the rate of a constant injection rate condition, fully implicit solutions can be constructed....

Some mathematical aspects of particle dissolution and cross-diffusion in multi-component alloys

A general model for the dissolution of stoichiometric particles, taking into account the influences of cross-diffusion, in multi-component alloys is proposed and analyzed using a diagonalisation argument. We give a self-similar solution for the resulting Stefanproblem and state when the solutions are mass-conserving. We also give criteria for...