where \(\text{MTC}_{\text{sk}}\) shows the solid film mass transfer
coefficient (MTC), \(w_{k}^{*}\) indicates the ion loading in
equilibrium with liquid phase ion concentration\(\left(c_{k}\right),\) and \(w_{k}\) is the ion loading on resin.
The Yamamoto isotherm (Yamamoto et al., 1988), which can successfully
express the equilibrium of several combinations of protein and
ion-exchange resin adsorbent, was employed in this regard.