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: