Rheology of concentrated disperse systems II. A model for non-newtonian shear viscosity in steady flows

TLDR: In this article, a structural intrinsic viscosity model for non-Newtonian shear viscosities is presented, which depends on volume concentration φ and shear rate φ.

Abstract: A relative viscosity — volume concentration relationship,η r =η r (φ) deduced from an energy principle, which operates in newtonian range, is phenomenologically extended to the description of non-newtonian behaviour. Such an extension is performed, using a structural intrinsic viscosity $$\tilde k$$ , which depends on volume concentrationφ and shear rate $$\dot \gamma $$ . At constant $$\dot \gamma $$ , some new results concerningk(φ) are given, leading to determination of the thickness of a surfactant layer onto particle surface, and allowing good agreement to the semi-empirical viscosity relation given byThomas. At constantφ, a rate equation governs the evolution of $$\tilde k$$ as a structural parameter. In steady conditions ( $$\dot \gamma $$ = const.), an equilibrium value $$\tilde k(\dot \gamma _r )$$ is reached, $$\dot \gamma _r $$ being a relative shear rate, depending on the overall time relaxation of the structure. A non-newtonian shear viscosity for steady flows is then obtained, depending on $$(\dot \gamma _r )^p $$ . For systems of non-spherical particles, an empirical determination ofp givesp ≈ 0.5.