Frans_M_Everaerts_Isotachophoresis_378342.pdf

44 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
B
t t t t t t t ! t
Concentration r-I separation Boundary
boundary boundaries l‘. e. -A I
< r n < .......... ern i rn < rn
AP-l A2 Al A1
Fig.4.3. Zone boundaries formed when an electric current is passed across a zone boundary as shown
in Fig.4.2.
from the mixture, viz., that anionic species with the highest effective mobility of the
anionic species that remain.
The last boundary created is the boundary A,. . . JAl . . . (r- I). The last zone boundary is
the original boundary Al.. .,-/Al . . .r, where an adaptation in concentrations according
to Ohm’s law takes place. This concentration boundary can be considered as stationary
[6]. Two types of boundaries have to be distinguished, viz., the concentration and the
separation boundaries. For the concentration boundary, the number of anionic species
is identical on both sides of the boundary, whereas for the separation boundaries one
particular ionic species is present on one side of the boundary only. In general, rt 1
boundaries will be present if an electric field is passed across the original boundary as
shown in Fig.4.2, considering the separation of anionic species, viz., one concentration
boundary (the original boundary), r-1 separation boundaries and the boundary
between the single electrolyte and the zone containing the anionic species with the
highest effective mobility in the anionic mixture (see Fig.4.3).
The velocity of the boundary A,/A, is equal to the velocity of the anionic species
A, and 4,. The velocities of the separation boundaries are equal to the velocities of the
ionic species with the lowest effective mobilities in those zones (see section 4.2.3).
These anionic species are not present in the preceding zones.
For the derivation of the general equations, the following assumptions are made: the
electric current is constant; the cross-section of the tube is constant; the influence of
diffusion, hydrostatic flow and electroendosmosis is neglected. The activity coefficients
and the influence of the radial temperature differences can be neglected.
Further, only those boundaries that are formed between the original zone boundary
and the anode are considered. The general equations describing electrophoretic processes
are: the equilibrium equations; the electroneutrality equation; the mass balances for all
ionic species; and the modified Ohm’s law. These equations are considered in more detail
in sections 4.2.1-4.2.5.
0