Computational Model to Characterize the Rheokinetic Response of the Gelling Process

Abstract

The approach toward the sol-gel transition may be described by a basic structural parameter that evolves to the percolation value under static conditions. In this framework, two asymptotic responses are well identified for the gelling process of macromolecular solutions. One involves the initial sol viscosity that may be associated with the equilibrium viscosity value when the structural parameter is null (the microstructure is fully broken). The other is the percolation zero shear rate viscosity and corresponds to the maximum value of the structural parameter. Under flow, thixotropic
theories allow one to convert directly experimental data obtained as shear stress versus time for a given shear rate into the time evolution of the structural parameter. Consequently rheometric experimental data available places the search for a kinetic model of the structural parameter. Here, an expression for this model is investigated computationally, which involves both the rates of structure
breakdown and buildup, where the sizes of floccules are governed by the value of the shear rate. The rate equation thus obtained may be then applied, in principle, to any arbitrary rate of deformation history. Numerical results of the rheokinetic model proposed in this work fit well experimental
rheometric data obtained in shear flow for the sol evolution of gelatin solutions.