Thermophoresis in binary blends

Various types of temperature sensitive binary blends are employed in modern technical applications, e.g., polymer solutions in adhesives, lubricants or in coating implementations. In this paper we deduce and thoroughly investigate a model of segregation of such blends in the presence of a locally non-uniform temperature field.Capturing the microstructural evolution requires a phase-field model of Cahn-Hilliard type extended by contributions originated from thermal diffusion (Soret-effect). A consistent derivation of such a model starting from the second law of thermodynamics is presented here. The resulting diffusion equation constitutes a partial differential equation involving spatial derivatives of fourth order. Consequently, the variational formulation of the problem mandates approximation functions which are at least piecewise smooth and globally C1-continuous. In order to fulfill these requirements a spline-based finite element scheme is provided.Numerical simulations of phase separation subjected to local non-uniform temperature gradients within a binary polymer blend consisting of poly(dimethylsiloxane) and poly(ethyl-methylsiloxane) will illustrate the quality and versatility of the presented approach.

► We deduce a thermodynamically consistent model for thermal diffusion in binary blends.
► The arising diffusion model is discretized with a robust numerical scheme.
► Computational studies of a PDMS/PEMS blend show the flexibility and reliability of our diffusion model.