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تسجيل مستخدم جديدRheological Chaos in a Scalar Shear-Thickening Model
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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) = tau_{1,2}^{-1}int_0^tsigma(t)exp[-(t-t)/tau_{1,2}] {rm d}t 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 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_1to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.
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