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We examine the simplest relevant molecular model for large-amplitude shear (LAOS) flow of a polymeric liquid: the suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response. We include a detailed comparison of these predictions with the corresponding results for the simplest relevant continuum model: the corotational Maxwell model. We find that the responses of both models are qualitatively similar. The rigid dumbbell model relies entirely on the dumbbell orientation to explain the viscoelastic response of the polymeric liquid, including the higher harmonics in large-amplitude oscillatory shear flow. Our analysis employs the general method of Bird and Armstrong ["Time-dependent flows of dilute solutions of rodlike macromolecules," J. Chem. Phys. 56, 3680 (1972)] for analyzing the behavior of the rigid dumbbell model in any unsteady shear flow. We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the "paren functions," we use these for evaluating the shear stress for LAOS flow.We find the shapes of the shear stress versus shear rate loops predicted to be reasonable. [ABSTRACT FROM AUTHOR]

Studies teh diffusion-stress relations in polymer mixtures. Linearization of the time-evolution equation of the singlet distribution function; Derivation of the Maxwell-Stefan equations for the mass flux.

For a macromolecule modeled as a Rouse chain in dilute solution, we give the exact nonequilibrium expression for the joint probability density for the configuration of any number of links of the chain, expressed in terms of the connector vector coordinates. From this expression we get the probability density for a single link and the joint probability density for two links. For these two functions we give the associated diffusion equations. We also give the length-independent probability density for the orientation of a single link. Finally we illustrate the application of these results in steady shear flow. [ABSTRACT FROM AUTHOR]

Derives an expression for the thermal conductivity of a dilute polymer solution, with the polymers represented as arbitrary bead-spring models. Use of the Curtiss-Bird phase-space kinetic theory of polymers; General expression specialized to Rouse bead-spring chains; Momentum-space averages; Configuration-space distribution function for polymer chains.

Shows how a Fokker-Planck equation in the phase of a single polymer molecule in a multicomponent mixture is obtained from the Liouville equation in the phase space of a mixture of polymeric fluids. Generalization of the Schieber-Ottinger equation for a dilute solution of a single polymer species.

In this paper we examine molecular stretching in the inception of uniaxial elongational flow of dilute polymer solutions. The polymer molecules are modeled as bead–spring chains with finitely extensible nonlinear elastic springs, and we use the Peterlin approximation. This work is distinguished from earlier work because we model the macromolecules with chains instead of dumbbells, and we examine the time dependence of three average quantities describing the chain conformation in unsteady flows: root-mean-square end-to-end distance, root-mean-square extensions of the individual links, and mean moment of inertia about the axis of elongation. We observe a gradual transition from the coiled equilibrium state of the chain to the stretched state after the inception of strong uniaxial elongational flow, and we describe the nature of this transition which takes place in roughly four stages: I equilibrium coil; II deformed coil; III spring stretched (‘‘locally unraveled’’); and IV unfolded chain. Inclusion of hydrodynamic interaction changes the macromolecular response quantitatively but not qualitatively. [ABSTRACT FROM AUTHOR]

According to a known heuristic argument, a given polymeric liquid will be expected to exhibit a positive or negative Weissenberg effect (i.e., will move up or down a rotating vertical rod immersed in it, under conditions where contact angle and centrifugal force effects are negligible) if the value of R:=1+2(σ/N1)dN2/dσ is positive or negative, where σ, N1, and N2 denote the shear stress and first and second normal stress differences in steady shear flow. The value of this heuristic treatment lies in its applicability to finite shear rate ranges for which an exact calculation is not available. The treatment includes (and generalizes) a known exact low-shear-rate limiting condition β0<0.25 for rod climbing, where β0 denotes the low-shear-rate limiting value of β:=-N2/N1. Using published experimental data for N1(σ) and N2(σ) to evaluate R, we find that positive Weissenberg effects are predicted for polyisobutylene and some polystyrene solutions (even when β=0.6), in agreement with observation, but that negative effects are predicted for other polystyrene solutions, in disagreement with observation. We cannot explain this disagreement. We also use the Curtiss–Bird kinetic theory for monodisperse polymers to evaluate R for various values of the ‘‘link tension coefficient’’ ε. Over ranges of shear rate experimentally accessible for molten polymers, we find that R>0 provided that ε>1/8. When ε=0, however, we find that R<0 for most low-to-moderate shear rates; it follows that, according to the present heuristic argument, the Doi–Edwards theory (ε=0) for monodisperse polymers predicts negative Weissenberg effects for a significant range of shear rates, in disagreement with all known measurements for molten polymers. Using the Curtiss–Bird theory for polydisperse polymers having a log-normal distribution with Mw=2Mn, we find R values greater than those found... [ABSTRACT FROM AUTHOR]

Comments on a study which considered kinetic theory derivations of constitutive equations for polymeric liquids, with special reference to the 'nonlinear regime far removed from equilibrium. Information on evolution equations derived from kinetic equations; Arguments on constitutive equations; Discussion on network theory for polymeric liquids.