Thermal diffusion column theory

Because the complete theoretical description of the operation of a thermal diffusion column is quite intricate, a simplified theory due to Jones and Furry (J12) is summarized here a more extensive discussion along with a survey of column operation from the phenomenological standpoint is given by Grew and Ibbs (Gil). 

Their separation performance was characterized by two parameters. F is In ypjyp, the overall separation between top and bottom when equilibrium is attained at total reflux. 0 is a parameter that was inferred from the rate at which product composition at total reflux approached equilibrium. The theory of the time dependent separation performance of a thermal diffusion column developed by Cohen [C6] and others shows that 0 is given by... 

G. Vasaru, Thermal Diffusion Column Theory and Practice VEB Deutscher Verlag, Berlin (1969). 

The Clusius-Dickel column is shown schematically in Figure 2. A wire is mounted at the axis of a cylinder. The wire is heated electrically and the outer wall is cooled. This sets up a radial thermal gradient which leads to a thermal diffusion separation in the x direction. As a result of the radial temperature gradient, a convection current is established in the gas, which causes the gas adjacent to the hot wire to move up the tube with respect to the gas near the cold wall. The countercurrent flow leads to a multiplication of the elementary separation factor. For gas consisting of elastic spheres, the light molecules will then concentrate at the top of the column, while the heavy molecules concentrate at the bottom. The transport theory of the column has been developed in detail (3, iS, 18) and will not be presented here. In a later section we shall discuss the general aspects of the multiplication of elementary separation processes by countercurrent flow. 

The resulting temperature gradient establishes thermal diffusion in the radial direction and the consequent mass gradient causes convection. Molecules near the center move up the tube with respect to gas near the cold wall. The countercurrent flow thus established leads to multiplication of the elementary separation factor. The theory of such columns has been developed in detail, but will not be reviewed here (Jones and Furry 1946 London 1961). 

Recently Desmet and Deridder transformed the effective medium theory (EMT), which applied thermal and electrical conductivity, to determine longitudinal diffusion in chromatography (71). EMT equations can be applied for fully porous, porous shell, spherical, and cylindrical particles. The theory considers the column as a binary medium, which consists of an interstitial void with a volumetric fraction Se and particles with a volumetrical fraction of 1- e. ... 

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