Constitutive modeling of dispersive mixtures

A rheological model for the stress in liquid-liquid systems is developed ba sed on unifying the theory of the present phenomenological models and by ap plying a description of the dispersed phase microstructure to remove most o f the adjustable parameters present in the theological models. However, thi s introduces new parameters in the model for the microstructure. The main f eatures of the model are: (a) the stress related to the viscosity differenc e 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 import ance 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 e quation fur the stress evolution. The description of the spatial evolution of the dispersed phase microstructure is accomplished by coupling preexisti ng models of coalescence and breakup yielding a description of the evolutio n of the microstructure. Mode! predictions are compared with experimental r esults from literature [Vinckier et al. (1997); Vinckier (1998)]. It is sho wn 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 pheno mena observed can now be understood in terms of the evolution of the p micr ostructure. (C) 2001 The Society of Rheology.