The transient separation of multicomponent mixtures in a cylindrical thermogravitational column

This work deals with the transient separation of a multicomponent mixture in a cylindrical thermogravitational column. The model describing the evolution of separation in vertical direction is derived and solved analytically. It is assumed that the profiles of velocity and temperature in radial direction are established and the forgotten effect as well as vertical diffusion in the column are ignored. The dependence of separation and characteristic transient time on the ratio of inner and outer cylinders radii δ is obtained. The transient time tends to diffusion time along the column height when δ approaches zero, while it reduces to the transient time for a flat-plate column when δ approaches unity. The analytical results are compared with two-dimensional numerical simulation for binary and ternary mixtures, and a good agreement is observed. It is concluded that for typical liquid mixtures, the decrease of radii ratio between inner and outer cylinders results in a slight increase of separation and in a significant increase of transient time.