Modeling of nons-tationary thermodiffusion flows in viscous electroconductive liquid

Background. The study of thermoelectric phenomena plays an important role in condensed-matter physics, also due to broad prospects of using such kinds of phenomena for creating energy converters. The analysis of crisscross phenomena of transfer under the action of three thermodynamic forces is also of interest. The crisscross phenomena of a new class were previously predicted, experimentally discovered, and studied in detail. They occur in viscous electroconductive environment under the action of three thermodynamic forces when there is a transfer of mass (of particles), heat (the presence of temperature gradient) and an electric charge, and are called thermoelectrokinetic phenomena. The aim of the paper is to construct a mathematical model of the thermoelectrokinetic effect during an experiment with a linear heat source moving along the stationary electrolyte solution within the framework of phenomenological thermodynamics of irreversible processes; to conduct a computing experiment on the basis of the model and to obtain quantitative evaluation of magnitude of thermoelectrokinetic EMF. Materials and methods. The model is based on equations of balance of heat and matter, which in this case are nonlinear and non-stationary differential equations of partial derivatives. The authors suggested an algorithm of calculating thermoelectrokinetic EMF of the constructed model by the method of finite differences. It was implemented in the package of applied mathematics Scilab. Results. Time dependences of the spatial distribution of temperature and of the concentration of aqueous solution of chlorine hydride were obtained as a result of the computational experiment. The calculation reproduces the main qualitative feature of the temperature field of the electrolyte - its asymmetry, which is the cause of the difference in the concentration of ions formed along the moving heat source. The authors quantitatively evaluated the EMF's magnitude that was stipulated by the generated concentration gradient and by the formula of isothermal diffusion. Conclusions. The design quantity of the thermoelectrokinetic EMF agrees well with the previously obtained experimental results. It proves the validity of the proposed mathematical model which can be used as a theoretical basis for the analysis of such crisscross phenomena.