Modeling of the ion exchange in pulp suspensions by Gibbs energy minimization

The ion exchange processes, which occur when two compartments of aqueous solutions separated by a semipermeable interface are placed in aqueous electrolyte solutions, were modeled using the multiphase Gibbs energy-minimization method. The Gibbs energy-minimization technique was applied for the ion-exchange system consisting of pulp fibers and the surrounding aqueous bulk solution. In such a system, the anionic acid groups inside the fibers cause an uneven distribution of ionic species between the solution within the fiber walls and the solution external to the fibers. The method was tested with four cation concentrations, which are naturally present in the fibers and whose partitioning between the fiber phase and the external solution phase has been described earlier. Although the Donnan distribution constant is not explicitly calculated in the Gibbs energy-minimization model, the results are consistent with the Donnan equilibrium theory. With the Gibbs energy-minimization multiphase model, the formation of solid precipitates can also be calculated.