An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Inversion of particle-stabilized emulsions of partially miscible liquids by mild drying of modified silica particles

Using a system of modified silica particles and mixtures of water and 2,6-lutidine to form particle-stabilized emulsions, we show that subtle alterations to the hydration of the particle surface can cause major shifts in emulsion structure. We use fluorescence confocal microscopy, solid state nuclear magnetic resonance (NMR) and thermo-gravimetric analysis (TGA) to explore this sensitivity, along with other shifts caused by modifications to the silica surface chemistry. The silica particles are prepared by a variant of the St?ber procedure and are modified by the inclusion of 3-(aminopropyl)triethoxysilane and the dye fluorescein isothiocyanate. Treatment prior to emulsification consists of gently drying the particles under carefully controlled conditions. In mixtures of water and 2,6-lutidine of critical composition, the particles stabilize droplet emulsions and bijels. Decreasing particle hydration yields an inversion of the emulsions from lutidine-in-water (L/W) to water-in-lutidine (W/L), with bijels forming around inversion. So dependent is the emulsion behavior on particle hydration that microscopic differences in drying within a particle sample can cause differences in the wetting behavior of that sample, which helps to stabilize multiple emulsions. The formation of bijels at emulsion inversion is also crucially dependent on the surface modification of the silica.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.