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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Comprehensive physical visualisation of the chain conformation and solution property of carboxymethylated konjac glucomannan: Comparison of charged and uncharged polyelectrolytes
TL;DR: In this paper, a comprehensive molecular characterization and delineation of solution property of a series of charged and uncharged carboxymethylated konjac glucomannan (CMKGM) with different molecular weights (Mw, 1.57×−105−7.33, DS, 0.19−1.63) by using various rheological models and solution scaling theory is presented.
Journal ArticleDOI
On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows
TL;DR: In this article , the authors compare the response of the simplified linear form of the Phan-Thien-Tanner model (sPTT) with the finitely extensible nonlinear elastic (FENE-P) dumbbell model.
Journal ArticleDOI
Rheology of acrylonitrile–butadiene–styrene polymer melts and viscoelastic constitutive models
TL;DR: In this paper, a commercial grade acrylonitrileitrile-butadiene-styrene (ABS) polymer melt is presented and the authors compare the performance of two constitutive models (Phan-Thien and Tanner (PTT) and two Kaye-Bernstein-Kearsley-Zapas (K-BKZ) type single integral models (Wagner and Papanastasiou-Scriven-Macosko (PSM) for the prediction of residual stresses.
Journal ArticleDOI
Numerical Approximation of the Spectra of Phan-Thien Tanner Liquids
TL;DR: The linear stability of the linear Phan-Thien Tanner (PTT) fluid model is investigated for plane Poiseuille flow and it is demonstrated that the linear extensional and elasticity parameters considered are considered.
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Fluid structure-interaction in a deformable microchannel conveying a viscoelastic fluid
L. Ramos-Arzola,Oscar Bautista +1 more
Abstract: We theoretically analyze the interaction between a viscoelastic fluid flow, whose constitutive equation is the simplified Phan–Thien–Tanner model, and a deformable slender shallow microchannel. The microchannel top wall displacement is analyzed considering two cases: a) as a thin plate, using the Kirchhoff–Love theory, and b) as a thick plate, based on the Reissner–Mindlin theory. The mathematical model is nondimensionalized, and dimensionless parameters related to problem physics arise that control the fluid–structure interaction. The governing equations that describe the hydrodynamic field are simplified using the lubrication theory, and the displacement of the top wall is analyzed for each plate theory, relating the hydrodynamic pressure and the volumetric flow rate. These equations are implicit in the pressure and are solved numerically. The effect of dimensionless parameters on the pressure drop-volumetric flow rate relationship is analyzed, showing that for a viscoelastic fluid flowing through deformable channels, the volumetric flow rate is higher than the case of a Newtonian fluid under the same pressure. Our results are compared against those published in the specialized literature, showing an excellent agreement.
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.
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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.
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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.