Non-linear flow properties of viscoelastic surfactant solutions

Abstract

This paper gives a quantitative description of the viscoelastic properties of aqueous solutions of entangled rod-shaped micelles. The experimental data are compared with the theoretical predictions of a special constitutive equation which is based on the concept of deformation-dependent tensorial mobility. In the regime of small deformations, shear stresses or shear rates, the dynamic features of the viscoelastic solutions are characterized by the equations of a simple Maxwell material. These phenomena are linked to the average lifetime of the micellar aggregates and the rheological properties are controlled by kinetic processes. At these conditions one observes simple scaling laws and linear relations between all theological quantities. At elevated values of shear stresses or deformations, however, this simple model fails and non-linear properties as normal stresses, stress overshoots or shear-thinning properties occur. All these phenomena can be described by a constitutive equation which was first proposed by H. Giesekus. The experimental results are in fairly good agreement with the theoretical predictions, and this model holds for a certain, well defined value of the mobility factor α. This parameter describes the anisotropic character of the particle motion. In transient and steady-state flow experiments we always observed α = 0.5. Especially at these conditions, the empirically observed Cox-Merz rule, the Yamamoto relation and both Gleißle mirror relations are automatically derived from the Giesekus model. The phenomena discussed in this paper are of general importance, and can be equally observed in different materials, such as polymers or proteins. The viscoelastic surfactant solutions can, therefore, be used as simple model systems for studies of fundamental principles of flow.