On the theory of oscillating flows in complex liquids

Experiments with highly concentrated suspensions and other complex liquids frequently demonstrate nonmonotonic N- or S-shaped dependences of viscous stress σ on shear rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma $$\end{document} and strong oscillations of the shear rate at a constant flow-inducing external stress, as well as oscillations of the viscous stress at a constant average shear rate. A phenomenological mathematical model is proposed for oscillating flows according to which oscillations arise when an applied stress (or the average shear rate, depending on the design of an experiment) is in the descending region of the σ-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot \gamma $$\end{document} dependence and a complex liquid exhibits pronounced viscoelastic properties.