2.10.1. Governing equations
Some assumptions are introduced to derive the governing equations of the
IEC theory (Gu, 2015; Yamamoto et al., 1983a, 1983b). 1. Plug flow with
axial dispersion in the column. 2. Total and species material balances
for the liquid phase. 3. Isothermal condition throughout the column. 4.
The ion components are in dilute concentration, and then the effect of
adsorption on the total mass balance is negligible. Thus, superficial
velocity and volumetric flow rate remain constant. 5. Ideal mixing
happens in the aqueous phase. Further, the overall molar volume is
constant according to the dilute concentration of ionic components. 6.
Total exchange capacity of the resin inside the bed is constant.7. Kinetic model was used to specify the overall mass transfer of ionic
components between the bulk liquid and adsorbed phase. Additionally, the
mass transfer should be overcome in mass transfer resistance within the
boundary layer surrounding the particle, as well as mass transfer
resistance within the resin particle. The second resistance usually
controls the overall mass transfer rate. Therefore, a lumped mass
transfer rate was employed along with solid-film resistance.
Generally, the model describing the IEX column includes material and
momentum transport in the bulk liquid (mobile phase), mass transfer from
the bulk liquid to the adsorbent (stationary phase), and mass transfer
resistances which influence this transport.
2.10.2. General
mass balance equation for IEX
The following equation is introduced for the general mass balance
equation for describing the behavior of the exchanged counter-ion in the
bulk liquid phase, i.e. each ionic species in the liquid phase enters
into the ion-exchange column (Mehay & Gu, 2014).