Abstract
On the basis of the reptation theory, this paper discusses the shear-rate-associated transition of a polymer-fluid structure formed by topological polymer-chain crosslinks to a new steady-state condition. Structure-characterizing ratio z of the current number of polymer chain Kuhn segments between effective along-chain crosslinks to the steady-state value of this number is introduced. The recurrence equation z n + 1 ∼ Wi · z n (1 − z n ) + z n is calculated to describe the transition through period-doubling bifurcations from the steady-state condition (z → 1) to the chaotic behavior of z values with an increase in the Weissenberg number (Wi). This transition should cause flow instability and the development of the so-called elastic turbulence of polymer fluids at low Reynolds numbers. Specific examples are used to show that the suggested scenario can be confirmed both qualitatively and quantitatively with the published experimental data on the development of elastic turbulence of polymer fluids.
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Original Russian Text © S.V. Vasil’chenko, 2015, published in Vysokomolekulyarnye Soedineniya. Ser. A, 2015, Vol. 57, No. 4, pp. 368–372.
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Vasil’chenko, S.V. Scenario of the development of elastic turbulence of polymer fluids. Polym. Sci. Ser. A 57, 489–493 (2015). https://doi.org/10.1134/S0965545X15040148
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DOI: https://doi.org/10.1134/S0965545X15040148