Thermogravitational Thermal Diffusion in Liquids. III. Velocities, Gradients, and Fluxes in a Narrow Cylindrical Annulus

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Abstract
The velocities, gradients, and fluxes in a binary liquid system in a narrow, cylindrically symmetrical annulus subjected to a horizontal temperature difference are obtained by a self‐consistent application of the locally linear macroscopic transport equations. In the case of thermogravitational thermal diffusion, the expression for the vertical composition gradient is identical in form to the expression previously found by the authors [J. Chem. Phys. 37, 2842 (1962)] by a less rigorous procedure. The nine independent partial differential equations are solved for nine independent pointwise steady‐state properties. These are, in the order in which they are obtained formally, vertical barycentric velocity, radial barycentric velocity, pressure, composition, radial diffusion flux, vertical diffusion flux, temperature, radial heat flux, and vertical heat flux. Final equations are infinite series which may be truncated according to the experimental system of interest. Formulas are derived for three experimental cases: binary mixture subjected to zero temperature gradient, pure fluid, and binary mixture subjected to nonzero temperature gradient.