where \(w_{k}\) is ion loading on resin, \(c_{b}\) shows counter ion
concentration in liquid phase, \(c_{k}\) indicates ion concentration in
liquid phase and \(\alpha_{1k},\ \beta_{2k}\) and \(\gamma_{3k}\) are
considered as the isotherm parameters which are related to equilibrium
constants, stoichiometric coefficient in mass action equilibrium, and
possible changes in the ionic strength of the elution buffer.
Ultimately, in Eq. (1), the total charge of both liquid and resin must
be kept neutral in which the number of counter-ions released from the
resin and inflowing the liquid phase are determined by the amount of
ions exchanged from the liquid phase (Ernest, Whitley, Ma, & Wang,
1997) as follows: