Frans_M_Everaerts_Isotachophoresis_378342.pdf

48 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
Substitution of eqns. 4.7 and 4.9 into 4.13 for both the sample ionic species and
counter ions gives
r= 1
4.2.3. Mass balances for all ionic species
-+
(4.14)
In the stationary state (N.B., the ‘steady state’ is not meant here), if all zone boundaries
are formed and migrate, some ionic species will migrate more rapidly and others more
slowly than a particular zone boundary, and ionic species will therefore pass continuously
those zone boundaries that have a lower velocity. For the ionic species that pass zone
boundaries, mass balances can be formulated.
In order to decide which ionic species will pass zone boundaries and their amounts,
we shall consider the velocities of the zone boundaries. The velocity of the concentration
boundary can be neglected, so that for constant effective mobilities the ratios of the
concentrations on the two sides of the concentration boundary are identical for all ionic
species (see eqn. 4.18).
The velocity of a separation boundary, S, is equal to the migration velocity of the
ionic species with the lowest effective mobility in that zone (see Fig.4.4).
The velocity of the zone boundary (U--l)/(U-2) is equal to the migration velocity
of the (U-1)th anionic species, which is not present in the preceding zone U-2.
Similarly, the velocity of the zone boundary U/(U-1) is equal to the velocity of the
anionic species A,. If the electric field strengths in the zones are E,, Eup1 and E,-,,
respectively, the migration velocities of those boundaries are E,-l mA and E, MAu,
U- 1
respectively. In these terms, the quantities indicated with a bar (m) do not apply to ions,
but to the equilibrium mixtures of all forms of the constituent; consequently, FI
represents the effective mobilities of the ionic species. As the boundary velocity is
determined by the llth ionic species, the subscript r in M is replaced with U. For the
effective mobility, Tiselius 1161 pointed out that a substance which consists of several
forms with different mobilities in equilibrium with each other will generally migrate as a
A,