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Rheological Chaos in a Scalar Shear-Thickening Model | | M.E. Cates
; D.A. Head
; A. Ajdari
; | | Date: |
7 Apr 2002 | | Journal: | Phys. Rev. E 66, 025202(R) (2002). | | Subject: | Soft Condensed Matter | cond-mat.soft | | 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 dotgamma and relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(sigma_1) and a linear decay at rate lambdasigma_2. Here sigma_{1,2}(t) = au_{1,2}^{-1}int_0^tsigma(t’)exp[-(t-t’)/ au_{1,2}] {
m d}t’ are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when au_2> au_1 and 0>R’(sigma)>-lambda so that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of 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 au_1 o 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows. | | Source: | arXiv, cond-mat/0204162 | | Services: | Forum | Review | PDF | Favorites | |
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