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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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Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method
TL;DR: In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them.
Book
Non-Newtonian Fluid Mechanics
TL;DR: In this paper, the authors present a set of formal formulas for special curvilinear coordinates for continuous fluid flow and show that they can be used to describe the normal stress functions of normal stress differences.
Journal ArticleDOI
Finite-element Analysis of Die Swell of a Highly Elastic Fluid
Marcel Crochet,Roland Keunings +1 more
TL;DR: In this article, a mixed finite element method is applied to the die swell calculation of ana Oldroyd fluid B. The use of large entry lengths together with the presence of the retardation time in the constitutive equations allow us to reach values of the recoverable shear as high as four for the flow emerging from slit and circular dies, with swelling ratios of the order of 2.
Journal ArticleDOI
Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications
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A constitutive analysis of uniaxial elongational flow data of low-density polyethylene melt
TL;DR: In this article, the uniaxial elongational flow data of a well-characterized LDPE melt were analyzed in terms of a single integral constitutive equation, which has already been successfully used to described shear flow experiments of the same polymer melt.
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.