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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
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Edge fracture in cone-plate and parallel plate flows
Matti Keentok,Shicheng Xue +1 more
TL;DR: In this article, a study of the theoretical, experimental and computational aspects of edge fracture in second-order liquids is undertaken, which is approximately extended to cover the Criminale-Ericksen-Filbey (CEF) model.
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A taylor-petrov-galerkin algorithm for viscoelastic flow
TL;DR: In this paper, a viscoelastic flow is solved using a generalised Taylor-Galerkin/pressure correction scheme that incorporates consistent Petrov and Galerkin streamline upwinding within the discretisation of the constitutive equations.
Journal ArticleDOI
Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels
TL;DR: In this paper, the stability of steady planar stagnation flows of a dilute polyethylene oxide (PEO) solution using T-shaped microchannels was investigated, where the stagnation point is located on a free streamline, whereas in the absence of a recirculating cavity the stagnation points at the separating streamline is pinned at the confining wall of the microchannel.
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Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan-Thien-Tanner model.
TL;DR: The electro-osmotic flow of a viscoelastic fluid between parallel plates is investigated analytically and equations for the critical shear rates and maximum electrical potential that can be applied to maintain a steady fully developed flow are derived and discussed.
Journal ArticleDOI
Numerical-simulation of Highly Viscoelastic Flows Through An Abrupt Contraction
TL;DR: In this paper, a new mixed algorithm for calculating viscoelastic flow is proposed, where the coupling between velocity and stress components is solved by means of multiple bilinear stress sub-elements embedded in the Lagrangian element for the velocity field while streamline upwinding is used for solving the advection dominated constitutive equations.
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.