Journal ArticleDOI
A new constitutive equation derived from network theory
Nhan Phan Thien,Roger I. Tanner +1 more
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In this paper, a constitutive equation is derived from a Lodge-Yamamoto type of network theory for polymeric fluids, where the network junctions are not assumed to move strictly as points of the continuum but allowed a certain "effective slip".Abstract:
A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.read more
Citations
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Maximum-Likelihood Parameter Estimation for the Thin-Shell Quasi-Newtonian Model for a Laboratory Blown Film Extruder
TL;DR: In this paper, the Pearson and Petrie thin-film extrusion model incorporates a quasi-Newtonian constitutive relation for the effect of temperature and crystallization on the viscosity of the polymer and a spatial variation of the heat transfer coefficient that is qualitatively consistent with turbulent flow simulations.
Journal ArticleDOI
Constitutive equations for non-affine polymer networks with slippage of chains
TL;DR: In this paper, a model for isothermal three-dimensional deformation of polymers with finite strains is derived, where a polymer fluid is treated as a permanent network of chains bridged by junctions (entanglements).
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A Theoretical Study on Transitional Shear Flow Behavior of the Compressible and Isothermal Thermoplastic Polymer
Dong-Lei Liu,Feng Zhou,Kun Fang +2 more
TL;DR: In this paper, a dynamic end-to-end (ETE) vector was presented to describe the polymer chain's instantaneous morphology based on the spring-bead theory, which is simplified as the generalized Newton's law.
References
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Journal ArticleDOI
The Visco-elastic Properties of Network Structure I. General Formalism
TL;DR: In this article, the authors derived the stress-strain-time (S − S − T )relation at each instance of macroscopic observations by using the statistical mechanical considerations of equilibrium states.
Journal ArticleDOI
Constitutive equations from molecular network theories for polymer solutions
TL;DR: In this article, constitutive equations based on the network models of Yamamoto, Lodge, and Kaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum.
Journal ArticleDOI
Anisotropic Fluid Theory: A Different Approach to the Dumbbell Theory of Dilute Polymer Solutions
R. J. Gordon,W. R. Schowalter +1 more
TL;DR: In this paper, the authors used the continuum theory of anisotropic fluids, as developed by Ericksen and others, to formulate an expression for the time derivative of the end-to-end vector of a linear macromolecule when used in conjunction with the equation describing the distribution function for a dilute solution of dumbbell elements.