Kinetic model for a sol-gel transition: application of the modified Bailey criterion

Precise a priori prediction of time required to achieve colloidal sol-gel transition is a challenging task. This is because not much system-specific theoretical work has been carried out on kinetics of colloidal gelation, where the physical bond formation is strongly affected by the surface characteristics of the colloidal particles. Under such situation, drawing analogies from apparently dissimilar phenomena that share the same physical foundation can prove helpful. Interestingly the physical processes such as the fracture dynamics in a material leading to failure, as represented by the Bailey criterion of durability, and sol-gel transition are known to satisfy the Markovian criterion, suggesting equivalent mathematical formalism. Such equivalence leads to a simple mathematical formalism given by the modified Bailey criterion which is identical in construction to the criterion in fracture dynamics. In this work, we assess the modified Bailey criterion of durability to predict the time required to attain the sol-gel transition in a colloidal dispersion under non-isothermal conditions. The model parameters are derived from the gelation experiments on colloidal clay dispersion conducted under the isothermal conditions. Interestingly, the prediction of the time to attain the sol-gel transition under non-isothermal condition from the modified Bailey criterion matches the experimental observation with remarkable accuracy, thereby validating an independent methodology to obtain vital knowledge on colloidal sol-gel transition. This work, therefore, validates the mathematical formalism of one Markovian process (fracture dynamics) by carrying out experiments on another Markovian process (sol-gel transition), which are otherwise distinctly different from each other. Such correspondence highlights the profound similarity in the microstructural changes occurring in the two distinct systems.