Study of sol–gel transition in calcium alginate system by population balance model

The growth of calcium alginate (Ca-alginate) clusters and its sol–gel transition phenomena were simulated with a population balance model. The classical statistical concept proposed by Flory–Stockmayer has been adopted and incorporated by the factor of cyclic structures formation into the model. Ca-alginate gelation was described as a random cross-linking of multifunctional monochains. The resulting discretized kinetic equations were solved numerically by parallel computation. After demonstrating the accuracy of this model, the effect of the cyclic structure, the reaction rate constants and the physical properties of the reactants (i.e., alginate and gelling agent of Ca2+ ions) were examined. The present work clarifies the mechanisms for forming ionotropic Ca-alginate gels and presents the concentration ranges where the transition between the sol state and the gel state occurs. The model allows for the estimation of the relative magnitude of stepwise reaction rate constants and the prediction of the sol–gel transition boundary. Finally, a reasonable agreement was obtained between the experimental results and model predictions.