Constitutive modeling of dispersive mixtures

A rheological model for the stress in liquid–liquid systems is developed based on unifying the theory of the present phenomenological models and by applying a description of the dispersed phase microstructure to remove most of the adjustable parameters present in the rheological models. However, this introduces new parameters in the model for the microstructure. The main features of the model are: (a) the stress related to the viscosity difference is not purely viscous, (b) a closure approximation is used for the stress contribution due to the interfacial stress, and (c) the stress relaxation time depends on the droplet deformation. Especially the latter is of importance to get the description of some characteristic rheological behavior of dispersive mixtures right. The interfacial area, the droplet stretch ratio, and the rate of change of the interfacial area show up explicitly in the equation for the stress evolution. The description of the spatial evolution of the dispersed phase microstructure is accomplished by coupling preexisting models of coalescence and breakup yielding a description of the evolution of the microstructure. Model predictions are compared with experimental results from literature [Vinckier et al. (1997); Vinckier (1998)]. It is shown that, by incorporating a structure dependent relaxation time, remarkably good agreement between the model and experiment is obtained, even for very different experimental conditions. Moreover, the complex rheological phenomena observed can now be understood in terms of the evolution of the microstructure.