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Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate

L. Fraštia, U. Thiele, L. M. Pismen (2010)

Mathematical Modelling of Natural Phenomena

We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem...

Numerical analysis of a Stokes interface problem based on formulation using the characteristic function

Yoshiki Sugitani (2017)

Applications of Mathematics

Numerical analysis of a model Stokes interface problem with the homogeneous Dirichlet boundary condition is considered. The interface condition is interpreted as an additional singular force field to the Stokes equations using the characteristic function. The finite element method is applied after introducing a regularization of the singular source term. Consequently, the error is divided into the regularization and discretization parts which are studied separately. As a result, error estimates...

The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model

Shin-Ichiro Ei, Tohru Tsujikawa (2009)


Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in 2 and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates...

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