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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Extrudate swell of a high-density polyethylene melt: II. Modeling using integral and differential constitutive equations
TL;DR: In this paper, the extrudate swell phenomenon of a high-molecular-weight HDPE is modeled using the following viscoelastic constitutive equations: the multi-mode Kaye-Bernstein-Kearsley-Zapas (K-BKZ) integral model with the Wagner and the Papanastasiou-Scriven-Macosko (PSM) damping functions, and multimode Phan-Thien-Tanner (PTT), Giesekus and Double Convected Pom-Pom (
Journal ArticleDOI
Nonlinear fluid dynamics description of non-Newtonian fluids
TL;DR: In this paper, a generalized hydrodynamic description of viscoelasticity is presented, which replaces the (often neglected) strain diffusion by a relaxation of the strain as a minimal ingredient, and can be used to get a nonlinear dynamic equation for the stress tensor.
Journal ArticleDOI
2-D Numerical Simulation of Differential Viscoelastic Fluids in a Single-Screw Continuous Mixer: Application of Viscoelastic Finite Element Methods
TL;DR: In this paper, a single-screw, continuous mixer with kneading paddles was used to simulate viscous mixing flows with a singlemode Phan-Thien Tanner nonlinear, viscoelastic fluid model.
Journal ArticleDOI
Evaluation of a transient network model for telechelic associative polymers
TL;DR: In this paper, experimental results for such experiments are compared with the predictions of a transient network model, i.e., the Vaccaro-Marrucci model, which has only a single adjustable parameter to describe nonlinear behaviour.
Journal ArticleDOI
A new finite element formulation for viscoelastic flows: Circumventing simultaneously the LBB condition and the high-Weissenberg number problem
TL;DR: In this paper, the authors proposed a new, fully consistent and highly stable finite element formulation for the simulation of viscoelastic flows, which has implemented equal order interpolants for all variables and a combination of classical finite element stabilization techniques (PSPG/DEVSS-TG/SUPG) with the log-conformation representation of the constitutive equation that has allowed to obtain numerically stable solutions at high Weissenberg numbers.
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.