Dissipative structures in shear-thickening complex fluids

The main objective of this work is to demonstrate that non-local terms of the structure variable and shear-stress is a sufficient condition to predict multiple bands in rheologically complex fluids, i.e., shear-thickening fluids. Here, shear bands are considered as dissipative structures arising from spatial instabilities (Turing patterns) rather than the classical mechanical instability. In the present analysis, a monotonic relation between shear-stress and shear-rate holds. The formation of banded patterns is discussed for shear-thickening fluids with a model that consist of an upper-convected Maxwell-type constitutive equation coupled to an evolution equation for the structure variable, in which both non-local terms of the stress and of the structure variable are included (non-local Bautista-Manero-Puig model). The Turing mechanism is used to predict a critical point for primary instabilities (stable bands), while the amplitude formalism is used to predict secondary instabilities and marginal curves.