Frans_M_Everaerts_Isotachophoresis_378342.pdf

50 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
Fig.4.5. Migration paths for the different ionic species over a separation boundary S. For furthe1
explanation, see text.
the points S1 and M (at time t = 1). The distance SoSl is equal to EUriiAp u. The ion
present at point P (at time t = 0) migrates in the zone U, so the distance PS1 is equal to
EUfiAu-l, U and the ion present at point So (at time t = 0) migrates in the (U- 1)th zone,
so the distance SoM is equal to EU-l~Au-l, The amount of ions between P and So
(at time t=O) is
oc~u-l, U (psI-sO sl) = ocAu-l, U(EUriiAu-l, U-EUriiA, U)
where 0 is the cross-sectional area of the narrow-bore tube and ci is the total
U-l’U
concentration of the anionic species A,, in the Uth zone.
The amount of the anionic species A,, between the points S1 and M (at time
t= 1) will be
The amount of the anionic species between P and So (at time r = 0) reaches the
separation boundary within one unit of time and the amount between S1 and M passes
the separation boundary within one unit of time. These amounts must be identical for
a stationary state, so we can write for the mass balance of the anionic species A,, :
‘kU-,,U (EUmAu-,,TEUfiAu,U)= c~~-,,U-i (EU-l fiAu-l,U-l-EUfiAu,U)
The general expression for the mass balance of an anionic species is
‘A,., U WEUfiAu, U) = A,., U-1 (EU-l fiA,., U-l-EUmAu, U) (4.19)
In a similar manner, the following expression for the counter ions can be derived:
‘B, t U- 1 (EU-l ‘B , U-1 -k EU fiAu, U) = ‘i, U (EUfiB, U -k EUriiAu, U)
(4.18)
(4.20)