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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Nonlinear property of the visco-elastic-plastic material in the impact problem
TL;DR: In this article, a numerical investigation on the non-Newtonian flow problem is conducted, in order to shed further light on the mathematical and virtual test methods in the auto-crash safety analysis.
Journal Article
Melt spinning dynamics of Phan-Thien Tanner fluids
TL;DR: In this paper, the draw resonance criterion based on the traveling times of various kinematic waves in the spinline has been confirmed, the reason why the spin line cooling is stabilizing is analyzed, and the effect of fluid viscoelasticity on spinline stability is summarized.
Book ChapterDOI
Chapter 5 Mathematical Analysis of Viscoelastic Fluids
TL;DR: In this paper, the authors focus on the equations arising from the modeling of viscoelastic polymeric liquids, such as the questions of existence, stability, and development of singularities.
Journal ArticleDOI
Stresses of PTT, Giesekus, and Oldroyd-B fluids in a Newtonian velocity field near the stick-slip singularity
TL;DR: In this paper, the authors characterise the stress singularity of the Oldroyd-B, Phan-Thien-Tanner (PTT), and Giesekus viscoelastic models in steady planar stick-slip flows.
Journal ArticleDOI
An ultraweak DPG method for viscoelastic fluids
Brendan Keith,Philipp Knechtges,Nathan V. Roberts,Stefanie Elgeti,Marek Behr,Leszek Demkowicz +5 more
TL;DR: A vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method is explored and an intrinsic a posteriori error indicator is developed which is used for adaptive mesh generation.
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.