Isogeometric analysis of thermal diffusion in binary blends

In modern technical applications diverse multiphase mixtures are used to meet demanding mechanical, chemical and electrical requirements. Consequently multicomponent systems such as biological tissues in medical science, metallic alloys or polymer solutions occupy a crucial role in everyday life. Therefore the material specific modulation of these systems and their application became a subject of recent studies. In this contribution we will study the impact of thermal diffusion (Ludwig–Soret effect) on the microstructural evolution of the binary polymer blend consisting of poly(dimethylsiloxane) and poly(ethyl-methylsiloxane). This polymer blend has a wide range of applications such as coating implementations and cosmetics manufacturing. For this reason we focus on diffusion induced phase separation and coarsening in the presence of a local non-uniform temperature field. In order to capture the microstructural evolution we apply a Cahn–Hilliard phase-field model, which is here extended by an additional thermal diffusivity. The diffusion equation under consideration constitutes a partial differential equation involving spatial derivatives of fourth order. Thus, the variational formulation of the problem requires approximation functions which are piecewise smooth and globally C1-continuous. In this paper we employ the innovative isogeometric concept of finite element analysis in order to fulfill this demanding continuity requirement. A concluding comparison of experimental observations and numerical simulations of phase separation in the presence of local temperature fields of a critical PDMS/PEMS polymer blend will illustrate the flexibility and versatility of our approach.