In polymer processing, it is established that the flow causes the polymer chains to stretch and store the energy, by changing their quiescent state free energy. Koscher et al.  presented in 2002 an experimental work concerning the flow induced crystallization. They made the assumption that the polymer melt elasticity, quantified by the first normal stress difference, is the driving force of flow-induced extra nucleation. In their work, a constant shear stress is considered, and the first normal stress difference agrees with the use of the trace of the stress tensor. The stored energy due to the flow “Δ Ge” is commonly called elastic free energy and associated to the change in conformational tensor due to flow. By extending the Marrucci theory , several studies link this Δ Ge to the trace of the deviatoric stress tensor (first invariant). In this paper, a numerical model able to simulate polymer crystallization is developed. It is based on the assumption that flow induced extra nucleation is linked to the trace of the deviatoric stress tensor. Thus a viscoelastic constitutive equation, the multimode Upper Convected Maxwell (UCM) model, is used to express the viscoelastic extra-stress tensor τVE, and a damping function is introduced in order to take into account the nonlinear viscoelasticity of the material. In Koscher’s work , the integral formulation of the Upper Convected Maxwell (UCM) model is used too, but without any damping function, i.e. they assume that the polymer behaves as linear viscoelastic. As an application, a 2D isothermal flow configuration between two plates is simulated. A comparison between the proposed model and the Koscher’s one is then performed, and interesting resultes are pesented: without introducing a damping function, the two models give similar results in the same configurations, but the introduction of a damping function leads to important discrepancies between the two models, seeming that the assumption of a linear viscoelastic behavior is not realistic when the fluid strain and/or stresses are greater than a given values.
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Simulation of Polymer Crystallization: Role of the Visco-Elasticity
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Boutaous, M, Zinet, M, El Otmani, R, & Bourgin, P. "Simulation of Polymer Crystallization: Role of the Visco-Elasticity." Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C. Montreal, Quebec, Canada. August 1–5, 2010. pp. 1393-1400. ASME. https://doi.org/10.1115/FEDSM-ICNMM2010-30209
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