A reversible surface reaction model with an effectiveness factor and its application to sorption kinetics of cupric ions on corncob particles

A novel reversible surface reaction model with an effectiveness factor was developed. To avoid uncertainty of nonlinear regression, an experimental procedure was designed to determine the following four constants in the model: the effectiveness factor, the maximum sorption capacity, and the intrinsic forward and backward rates. In this procedure first the intrinsic forward and backward rate constants for copper sorption were estimated to be 1.082 l/(mmol min) and 0.472 min−1 based on the elimination of the effect of the intraparticle and external mass transfers, and then the other two constants, the effectiveness factor and the maximum sorption capacity, were regressed as a function of the corncob particle size. Their values increased with decreasing the particle size. The simple external mass transfer model can describe only the solute change in solution for an initial 5 min period of time, which suggests that sorption of copper on corncob particles is controlled first by the external mass transfer, and then by the intraparticle mass transfer. The external mass transfer coefficients increased with increasing the modified Reynolds number, and then reached a maximum at higher values of the number. Studying the effects of the agitation speed and size of corncob particle on the kinetics of cupric ions sorption, it was found that the uptake of cupric ions on corncob particles increased with decreasing particle size and with increasing the agitation speed.