title: Rheological chaos in a scalar shear-thickening model.
abstract: We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress sigma is driven at a constant shear rate gamma; and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma(1)) and a linear decay at rate lambda sigma(2). Here sigma(1,2)(t)= tau(-1)(1,2) integral (t)(0)sigma(t')exp[-(t-t')/tau(1,2)]dt' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when tau(2)>tau(1) and 0>R'(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of the material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case tau(1)-->0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.
authors.affiliation: Department of Physics and Astronomy, JCMB King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, Scotland.
authors.forename: M E
authors.initials: ME
authors.lastname: Cates
authors.forename: D A
authors.initials: DA
authors.lastname: Head
authors.forename: A
authors.initials: A
authors.lastname: Ajdari