Thermodiffusion and thermo-osmosis in thin membranes with slit pores

Waste heat sources are potentially useful for component separation in fluid mixtures. To better understand how thermal driving forces can contribute to separation, we have investigated the Soret balances of forces for thermodiffusion and thermo-osmosis. A set of two-component fluid isotope mixtures with mass ratio $m_2/m_1$ has been investigated in membranes with molecular-sized pores. Numerical support generated by molecular dynamics simulations is achieved for two models; one for the Soret coefficient, $S=a_m(m_2-m_1)/(m_2+m_1)+b_{\epsilon }({\epsilon }_{2\text{m}}-1)$ , and one for the thermo-osmotic coefficient, $D_p=a(\Delta H/\Delta T)+b$ , where ${\epsilon }_{2\text{m}}$ is a parameter for the fluid-membrane interactions, $\Delta$ refers to a difference across the membrane, H is the bulk fluid enthalpy, and T is the temperature. In these formulas $a_m,b_{\epsilon },a,b$ are system-specific constants. The results apply to Lennard-Jones/spline isotope mixtures of mass ratios $0.1<(m_2/m_1)<10$ , with thermally insulating membrane materials, and component-specific fluid-pore interactions. The results give information about how the Soret balances depend on membrane properties, which potentially can be used to tailor membranes for efficient separation.