\section{Introduction}

Thermal diffusion, also known as the Soret effect or Ludwig-Soret effect, is an intriguing phenomenon that has interested researchers for over a hundred years since it was first described by Carl Friedrich Wilhelm Ludwig in the mid 19th century.\cite{soret_intro} The phenomenon is that a mixture with an imposed temperature gradient will develop a concentration gradient. This a consequence of the well known result from irreversible thermodynamics, that there are cross-coupling coefficients between fluxes and driving forces.\cite{irrev_bok} The inverse effect - a heat flux resulting from an imposed gradient in chemical potential is known as the Dufour effect. 

Onsager showed that the coefficient matrix that describes coupling of fluxes and forces is symmetrical, introducing the famous Onsager reciprocal relations.\cite{onsager} These relations imply that the coefficient coupling a thermal gradient to a mass flux is equal to the coefficient that couples a chemical potential gradient to a heat flux. This means that if one is capable of modelling the Soret coefficient, the same model can be used to predict the Dufour effect.

As modern science progresses, engineering applications also require ever increasing modelling capabilities. Nano-scale precision is commonly used in the production and development of modern technology, both in the texturing of surfaces and structuring of pores in nano-porous materials.\cite{stat_term_bok} At this scale small variations in concentration and temperature lead to enormous gradients. In the design of battery electrodes and electrolytes, transport properties are of major importance, and during operation a temperature gradient arises in the battery due to the electrode reactions and internal resistance.\cite{elkjem_bok} Further development in these fields therefore warrants precise descriptions of the coupling of heat and mass transfer.

Modern material applications on the macro scale require materials that can perform reliably when subjected to temperature gradients.\cite{irrev_bok} This includes the materials used in reactors, both chemical and nuclear, as well as materials in pipes and containers containing fluids far from ambient temperature, and the coatings used on said materials. The effects of thermal diffusion on these materials can be relevant even with small temperature gradients, and can become highly significant in environments with large temperature gradients. To further progress the development of materials subjected to extreme conditions, increased precision in the modelling and prediction of diffusive behaviour is required. Among prominent examples of conditions in which thermal diffusion is of significant importance is in the storage of nuclear waste.\cite{radioactive_waste} Temperature gradients resulting from the activity of the partially active waste can lead to migration of radioactive materials and thereby contamination of the environment.

In the field of Biochemical engineering, precise control of heat- and oxygen flow is required.\cite{bio} This is also a major hurdle in the up-scaling of bio-reactors. Specifically, the transfer of oxygen into the reactor solution at a rate high enough to keep a high concentration of microorganisms alive is challenging. More precise modelling of how the thermal gradients in the reactor and the mass transfer of oxygen interact may be of use in overcoming this challenge.

In short, the list of possible future applications of a reliable model for thermal diffusion is long.\cite{applications_soret} The current lack of such a model therefore warrants further study into the fundamentals of developing a model for the Soret effect.

\input{intro/models}
\input{intro/scope}
