By Vladimir V. Rachinskii
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Additional resources for The General Theory of Sorption Dynamics and Chromatography
O 0 ~ Z (n) dn + ~ z (N) dN = O. 67) This expression permits us to give an unambiguous determination of the integration constant C in equations (UL58) and (Ill. 62). 64) into (Ill. 67), we obtain 710 N. S %0 (n) dn + S %0 (N) dN C =. 45). Geometrically it corresponds to a family of asymptotes, each of which gives the graph of the motion of a set concentration point n (Fig. 11). All the asymptotes in Fig. 11 possess the same slope. The slope of the straight lines is numerically equal to the rate of motion of the stationary front v.
If DO = O. then according to the Wilson law. the front of the substance is propagated in the column at a velocity v with a straight break. and the coordinate of this break =vt. Thus. the coordinate =vt of a front with a break when D* = 0 coincides with the beginning of the reading of z = 0 in the new coordinate system. moving at a velocity v together with the blurred stationary front at DO ¢ O. This comparison of the two solutions shows that the coordinate =vt. or z = O. which is the same. possesses the character of a Singular point.
Hence a single way remains-the experimental establishment of these relationships by model experiments. ), the rate of flow, concentration, etc. -and experimentally determining the criterion of similarity Fo, the empirical dependence of the criterion Fo on various experimental parameters can be established according to the sorption dynamiCS. Usually all these determining parameters are also grouped in the form of dimensionless criteria of similarity, for example. the Reynolds number Re =ud/l1, where d is the grain diameter, the P~clet number Pe = ud/ Dm.
The General Theory of Sorption Dynamics and Chromatography by Vladimir V. Rachinskii