Viscosity Flow Curves of Agar and the Bounded Ripening Growth Model of the Gelation Onset

The gelation kinetics of agar aqueous solutions were studied by means of the viscosity flow curves using a coaxial Couette cylinder viscometer. The viscosity curves show an unusual sigmoidal trend or an exponential decay to a viscous steady state. An original theory of gelation kinetics was developed considering the coarsening of increasingly larger and more stable clusters due to Ostwald ripening and the breakup of clusters that were too large due to the instability of rotating large particles induced by the shear rate. The developed Bounded Ripening Growth model takes into account the trend of the viscosity curves by means of an autocatalytic process with negative feedback on aggregation according to the logistic kinetic equation, in which the constants $k_1(\gamma )$ and $k_{-}(\nu )$ are governed by the surface tension and shear rate, respectively. A dimensionless equation based on the difference between the Weber number and the ratio of the inverse kinetic constant to forward constant, accounts for the behavior of the dispersed phase in equilibrium conditions or far from the hydrostatic equilibrium.