chapter  5
10 Pages


Axial dispersion of a solute in a column is also responsible for

the dispersion of a solute in a chromatographic column as well as

intraparticle diffusion (Chap. 4). In the usual case, the axial

dispersion in an ion-exchange chromatographic column can be

treated in a way similar to that in a gel chromatographic column

or in a column packed with nonporous packing materials. Ac-

cording to the mass balance model I given in Sec. 2. 1. 3, the

mass balance equation in a column with porous gels is given by

Eq. (5.1) (the effect of mass transfer across the mobile/gel

phase interface is ignored) with appropriate initial and boundary


ac at



Equation (5.1) is rearranged in nondimensional form as

12H aC*1 Fe ad* d*=l


where t* = tU/dp C* = C/Cref (Cref is any fixed concentration) Pe = dpu/DL

z* = z/dp Pe = dpu/D

d* = d/dp = 2r/dp

The Peclet number Pe dpu/DL indicates the degree of axial

dispersion in a column. The higher the Pe number, the smaller

is the dispersion of a solute in a column. For a column with

nonporous packing materials, the third terms on the right-hand

side of Eqs. (5.1) and (5.2) are eliminated. In this case the

dispersion of a solute (second central moment 112) in a column

is expressed as

2 Peu


where Z = length of a column. On the other hand, \.I 2 is given

by Eq. (5.4) according to the plate theory (see Secs. 2. 1.5

and 2.1.6) (Martin and Synge, 1941).