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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Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow
TL;DR: A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded and global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem.
Journal ArticleDOI
An adaptive remeshing strategy for viscoelastic fluid flow simulations
TL;DR: In this article, a general adaptive finite element solution procedure is proposed for the solution of two-dimensional viscoelastic fluid flow problems, which can be applied to a large variety of problems.
Journal ArticleDOI
On predicting abrupt contraction flows with differential and algebraic viscoelastic models
TL;DR: In this article, the algebraic extra-stress model (AESM) derived from the differential constitutive equation for an Oldroyd-B fluid is extended to a Phan-Thien-Tanner fluid.
Journal ArticleDOI
Viscoelastic multi-mode simulations of wire-coating
TL;DR: In this article, a multi-mode Phan-Thien/Tanner constitutive equation is used to model the viscoelastic stresses that arise in a tube-tooling wire-coating problem.
Journal ArticleDOI
Bubble Deformation and Growth Inside Viscoelastic Filaments Undergoing Very Large Extensions
TL;DR: In this article, the axisymmetric extensional flow of a viscoelastic liquid filament that contains one or three initially spherical bubbles along its axis of symmetry is studied.
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.