Goddard Chris, Hess Ortwin, Balanov Alexander G, Hess Siegfried
Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, GU2 7XH, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026311. doi: 10.1103/PhysRevE.77.026311. Epub 2008 Feb 29.
A generalized model for the behavior of the stress tensor in non-Newtonian fluids is investigated for spatially homogeneous plane Couette flow, showing a variety of nonlinear responses and deterministic chaos. Mapping of chaotic solutions is achieved through the largest Lyapunov exponent for the two main parameters: The shear rate and the temperature and/or density. Bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found. Suggested mechanisms for stability loss in these complex fluids include Hopf, saddle-node, and period-doubling bifurcations.
