Dynamic Model for Unidirectional Progressive Freeze-Concentration of Aqueous Methylene Blue Solution

We studied the transient distribution behavior of methylene blue (MB) during unidirectional progressive freeze concentration (PFC) using an aqueous MB solution agitated by a planar blade. The transient changes in the height of the ice layer and the concentration of aqueous MB were measured at agitation rates that were varied from 50 to 500 rpm. To describe the agitation-dependent inclusion behavior of MB during ice-layer growth, a dynamic model incorporating a time-dependent effective solute distribution coefficient, Keff, was proposed. The model was developed to represent the transient evolution of dendritic ice structures and their influence on solute trapping and subsequent solute exclusion during ice growth. Fitting the model to the experimental results revealed the relationships between the agitation rate and the kinetic parameters, including the intrinsic distribution coefficient, mass-transfer coefficient, and time constant of Keff. The heat input to the solution was mostly independent of the agitation rate over the range examined. The calculated results reproduced the transient changes in both aqueous MB concentration and ice-layer height with good agreement, particularly during the initial stage of ice formation, where a temporary decrease in liquid-phase MB concentration and both positive and negative feedback behavior were observed.