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Nov 1993

Volume 37, Issue 6, pp. 961-1251


Orientation of long bodies falling in a viscoelastic liquid

Daniel D. Joseph and Yaoqi Joe Liu

J. Rheol. 37, 961 (1993); http://dx.doi.org/10.1122/1.550380 (23 pages) | Cited 1 time

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New experiments on the orientations of a cylinder settling in viscoelastic and pseudoplastic fluids are described in an attempt to identify the main mechanisms which control the orientation of the cylinder as it falls.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.60.Bc Linear viscoelasticity
83.85.Cg Rheological measurements—rheometry
83.85.Jn Viscosity measurements

Rheological characterization of director tumbling induced in a flow‐aligning nematic solvent by dissolution of a side‐chain liquid‐crystal polymer

Dong‐Feng Gu, A. M. Jamieson, and S. Q. Wang

J. Rheol. 37, 985 (1993); http://dx.doi.org/10.1122/1.550381 (17 pages) | Cited 4 times

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We present rheological evidence which demonstrates that dissolution of a side‐chain liquid‐crystal polymer with a methyl methacrylate backbone (MSHMA) in a flow‐aligning low molar mass nematogen (LMMN) pentylcyanobiphenyl (5CB) produces a director‐tumbling response. For comparison, we also provide the rheological behavior of pure octylcyanobiphenyl (8CB), a LMMN which exhibits director tumbling. 8CB and the MSHMA/5CB mixture each show a similar pattern of shear stress oscillations, both in flow startup and flow reversal, characteristic of director tumbling, whereas pure 5CB has no oscillation response. Our results indicate that addition of a side‐chain liquid‐crystal polymer to a shear‐aligning nematic solvent changes the sign of the Leslie viscosity coefficient α3 from negative (shear‐aligning) to positive (director‐tumbling). This is consistent with a theoretical discussion of Brochard (1979), provided that the polymer has an oblate configuration.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
83.10.Gr Constitutive relations
83.60.Bc Linear viscoelasticity
83.85.Cg Rheological measurements—rheometry

Internal viscosity dumbbell model with a Gaussian approximation

Jay D. Schieber

J. Rheol. 37, 1003 (1993); http://dx.doi.org/10.1122/1.550406 (25 pages) | Cited 3 times

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A noninertial Hookean dumbbell with internal viscosity (or internal friction) is studied in transient and steady shear flows by use of a Gaussian closure on the second moment equation of the configuration of the dumbbell. The model predicts shear thinning for the viscosity and first normal stress coefficients for all values of the relative internal viscosity parameter ϵ. A second Newtonian region is observed for the viscosity. Qualitative, but not quantitative, agreement is found with optically determined orientation angles of polymer coils in steady shear flows for dilute polymer solutions. The model greatly overestimates the amount of relative stretching of the polymer coil in steady shear flow. In startup flows, large, but finite, values of ϵ show shear stress overshoot at high shear rates, and oscillatory behavior at the highest shear rates studied. Transient negative values of the first normal stress difference are also predicted. The maximum in stress is attained at much lower values of strain than for the predictions at small ϵ. The oscillations are shown to be caused primarily by oscillations in the orientation of the polymer coil, rather than by oscillations in the size of the polymer coil. Instantaneous jumps in the shear stress at t=0 are observed in agreement with Manke and Williams. Cessation of shear flows shows a jump in stress in agreement with data on xanthan gum. The decay upon cessation is nonexponential, but does follow the Lodge–Meissner relation. The width of the polymer coil is predicted to go through a maximum during this decay. Also, the addition of internal viscosity to the dumbbell satisfactorally gives a positive asymptotic value for η′−ηs (in‐phase complex viscosity minus solvent contribution) in small amplitude oscillatory shear flow.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.10.Kn Reptation and tube theories
83.10.Mj Molecular dynamics, Brownian dynamics
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Numerical simulation of planar entry flow for a polyisobutylene solution using an integral constitutive equation

E. Mitsoulis

J. Rheol. 37, 1029 (1993); http://dx.doi.org/10.1122/1.550407 (12 pages)

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Numerical simulations have been undertaken for the entry flow through a 4:1 planar contraction of a well‐characterized shear‐thinning polymer solution (polyisobutylene in tetradecane) used previously in an experimental study. The fluid has been modeled using an integral constitutive equation of the K‐BKZ type with a spectrum of four relaxation times. Numerical values for the constants appearing in the equation have been obtained from fitting linear viscoelastic material functions as well as shear and elongational viscosity data and normal stresses as measured in shear. The numerical solutions for the range of experimental Deborah and Reynolds numbers show a stagnant small corner vortex that slightly decreases with increasing flow rate. The velocity and stress fields are compared with the experimental ones, showing a good general agreement. The constitutive equation overpredicts, however, the maximum centerline birefringence values by as much as 40% for the highest De. The behavior of shear stress and first normal stress difference near the re‐entrant corner are also illustrated.  
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
47.11.-j Computational methods in fluid dynamics
83.10.Rs Computer simulation of molecular and particle dynamics
83.60.Bc Linear viscoelasticity

Elongational flow of polyethylenes in isothermal melt spinning

Pascale Revenu, Jacques Guillet, and Christian Carrot

J. Rheol. 37, 1041 (1993); http://dx.doi.org/10.1122/1.550408 (16 pages)

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The elongational behavior of two polyethylenes with different structures, namely, a low‐density polyethylene and a linear low‐density polyethylene, has been investigated by isothermal melt spinning. The length along the spinline has been rescaled according to time. The evolution of the calculated elongational viscosity versus time has been compared to the transient elongational viscosities measured after imposition of a constant extension rate. The data demonstrate that these two situations, which are in many ways similar, give nearly the same results. Consequently, the viscosity which can be obtained from a fiber spinning experiment is a transient elongational viscosity. Differences in the elongational behavior between the long branched and the linear polyethylene are presented such as displayed in the spinning experiment. The strong influence on practical parameters such as melt strength or breaking stretch ratio is demonstrated.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Jf Extensional flow and combined shear and extension

Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics

Martin Kröger, Werner Loose, and Siegfried Hess

J. Rheol. 37, 1057 (1993); http://dx.doi.org/10.1122/1.550409 (23 pages) | Cited 52 times

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Results of nonequilibrium molecular dynamics computer simulations of a planar Couette flow are presented for the multibead anharmonic‐spring model. The finitely extensible nonlinear elastic force law is used to connect the up to 100 beads of a chain molecule. Rheological data (shear viscosity, normal pressure differences) are discussed and compared with quantities describing the chain conformation (e.g., alignment tensor, static structure factor). This renders possible a test of the theoretical approaches which connect these quantities. In agreement with recent experiments, the static strucure factor exhibits characteristic elliptical distortions of the polymer coil whose magnitude depends on the distance from the gyration center. In our simulations the zero‐shear‐rate viscosity is found to scale linearly with the number of beads N up to chains with N=60. A weak upturn of the viscosity per bead for N=100 is found which may indicate the onset of the reptation regime.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
47.11.-j Computational methods in fluid dynamics
83.10.Rs Computer simulation of molecular and particle dynamics
83.50.Ax Steady shear flows, viscometric flow

A filament stretching device for measurement of extensional viscosity

V. Tirtaatmadja and T. Sridhar

J. Rheol. 37, 1081 (1993); http://dx.doi.org/10.1122/1.550372 (22 pages) | Cited 34 times

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A filament stretching device for measuring the extensional viscosity of low‐viscosity liquids is presented. The fluid sample is held between two disks which move apart at an increasing velocity so that the extension rate, based on the filament midpoint diameter, is constant. The device was used to measure the extensional stress growth coefficients of three ideal elastic solutions, including the model fluid M1 and a shear‐thinning model fluid A1. The results indicate that all solutions containing high molecular weight polymer exhibit significant strain hardening as the fluid is extended. For the ideal elastic fluids, steady state in extensional stress was observed at strain above 4.5 and the steady Trouton ratio obtained for the fluids range from 2 to 5×103. For the fluid M1 the extensional viscosities obtained are higher than the apparent extensional viscosity obtained by other methods. This is the first time that the steady extensional viscosity has been measured for polymer solutions. The results obtained enable one to evaluate the numerous constitutive equations that have been proposed for polymer solutions.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.Jf Extensional flow and combined shear and extension
83.85.Jn Viscosity measurements

The use of line spectra in the estimation of the zero‐shear‐rate steady‐state fluidity and of the steady‐state compliance

I. Emri and N. W. Tschoegl

J. Rheol. 37, 1103 (1993); http://dx.doi.org/10.1122/1.550373 (14 pages) | Cited 1 time

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Determination of the retardation line spectra from data on both the storage and the loss compliances of a rheodictic material may yield an acceptable estimate of the zero‐shear‐rate stead‐state fluidity (the reciprocal of the zero‐shear‐rate steady‐state viscosity), even when the loss compliance data do not extend sufficiently far into the flow region to determine it from the loss asymptote. The same calculations also furnish an estimate of the difference between the steady‐state and the glassy compliance. The zero‐shear‐rate steady‐state viscosity can be obtained from the storage and loss moduli by first converting them to the compliances. This route is preferable to the traditional ways of estimating it via summation or integration, because those routes yield an acceptable value for the viscosity only when the experimental window is ‘‘pseudoinfinite,’’ i.e., it spans a sufficiently large portion of the frequency scale to approach effectively the ‘‘infinite’’ window extending on the logarithmic frequency scale from minus to plus infinity.
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36.20.-r Macromolecules and polymer molecules
83.50.Ax Steady shear flows, viscometric flow

Simple shearing flow of three‐dimensional foams and highly concentrated emulsions with planar films

Douglas A. Reinelt

J. Rheol. 37, 1117 (1993); http://dx.doi.org/10.1122/1.550463 (23 pages) | Cited 4 times

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Simple shearing flow of a ‘‘dry,’’ perfectly ordered, three‐dimensional foam composed of planar films is considered. The undeformed spatially periodic cell structure is formed by regular tetrakaidecahedra, which have six square surfaces and eight regular hexagonal surfaces. The elastic–plastic response of the foam is modeled by assuming that all surfaces remain planar and that the angle between connected surfaces does not change during elastic deformation. An explicit expression for the stress tensor that is valid up to the elastic limit is determined. Past the elastic limit, the foam structure and macroscopic stress are piecewise continuous functions of strain. Discontinuities in structure and stress are associated with topological (T1) changes in the film network structure that occur when the area of an individual film vanishes. These T1 changes, which reduce surface energy and result in the switching of cell neighbors, are essential mechanisms for yield behavior in foam flow. The foam structure is determined for all values of shear strain by choosing initial cell orientations that lead to periodic behavior with strain. The shear stress evaluated from a strain energy method differs from that obtained by volume averaging the local surface tension forces; this inconsistency arises because a foam with planar films cannot satisfy the equilibrium requirement that three films meet at equal angles of 120°.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Ax Steady shear flows, viscometric flow
83.60.La Viscoplasticity; yield stress

Analysis of isothermal spinning of liquid‐crystalline polymers

Suresh Ramalingam and R. C. Armstrong

J. Rheol. 37, 1141 (1993); http://dx.doi.org/10.1122/1.550374 (29 pages) | Cited 5 times

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In this paper we use the constitutive equation of Bhave et al. (1993) for rod‐like, liquid‐crystalline polymer solutions to analyze the isothermal, steady‐state spinning of these liquids in order to understand the evolution of microstructure, predict the velocity and normal stress distributions in the filament, and examine the effect of different upstream microstructural conditions. Our analysis shows that in contrast to fiber spinning models of isotropic liquids, the velocity, structure, and stress profiles are sensitive to the choice of initial conditions. In addition we have investigated the impact of the closure approximation used in the constitutive equation of Bhave et al. on the fiber spinning problem by solving the equation for the distribution function directly; only slight changes are seen in the velocity and stress profiles. An apparent elongational viscosity defined as the ratio of normal stress difference to strain rate at the takeup compares very well with the true elongational viscosity η̄ for the model, thereby suggesting that fiber spinning flows can be used to determine η̄ for liquid‐crystalline polymer solutions. Model predictions of the velocity and stress agree well with data obtained by Prilutski (1984) for HPC/acetic acid solutions. Finally, we present a linear stability analysis of the spinning problem to show the impact of viscoelasticity, inertia, gravity, and surface tension on the onset of draw resonance instabilities. The neutral stability curves obtained for dominant viscoelastic forces reflect trends in the apparent elongational viscosity. Model predictions are in qualitative agreement with the draw resonance data reported by Prilutski.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.50.-v Deformation and flow
83.50.Jf Extensional flow and combined shear and extension

Jet swelling of concentrated silicone oil‐in‐water emulsions

D. H. Fruman, J. L. Zakin, F. Li, and A. Makria

J. Rheol. 37, 1171 (1993); http://dx.doi.org/10.1122/1.550375 (10 pages)

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Jet swelling is shown to exist when a concentrated oil‐in‐water emulsion is ejected from a capillary tube into a stagnant fluid. The jet swells up to ten times the diameter of the capillary tube depending on the shear rate in the tube and the density difference between the ejected and the stagnant fluid. The relative jet swelling increases with silicone oil concentration, decreases in silicone oil viscosity, decreases in tube diameter, and decreases in tube length. The diameter ratio (jet/tube) grows as the 1/3 power of the wall shear stress in the capillary tube. The analogy between the swelling behavior of these emulsions and that observed in dilute and semidilute polymer solutions is discussed.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.50.Lh Slip boundary effects (interfacial and free surface flows)
47.27.wg Turbulent jets
47.50.-d Non-Newtonian fluid flows

Compatible pseudospectral approximations for incompressible flow in an undulating tube

Robert G. Owens and Timothy N. Phillips

J. Rheol. 37, 1181 (1993); http://dx.doi.org/10.1122/1.550376 (19 pages)

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The flow of an Oldroyd‐B fluid through an undulating tube is considered. The effect of elasticity and inertia on flow resistance is investigated numerically using a time‐splitting technique. This technique can be used to solve both steady and transient viscoelastic flows. A pseudospectral method based on mixed Fourier–Chebyshev expansions is used to represent the flow variables in space. An approximation space for pressure is constructed which is compatible with that for the velocity. This is achieved by removing the spurious modes using a singular value decomposition. A projection method ensures that mass is conserved identically at the collocation points. Numerical results are presented in such a way as to highlight the inertial and elastic effects. To this end two sets of results are given: the first, inertialess viscoelastic flow; the second, flow at nonzero Reynolds number holding the Weissenberg number constant. The two cases are shown to have quite opposite effects upon the flow rate and resistance.
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83.60.Df Nonlinear viscoelasticity
02.70.Hm Spectral methods
83.50.Ax Steady shear flows, viscometric flow
83.10.Gr Constitutive relations

Rheological differences among liquid‐crystalline polymers. I. The first and second normal stress differences of PBG solutions

S.‐G. Baek, J. J. Magda, and R. G. Larson

J. Rheol. 37, 1201 (1993); http://dx.doi.org/10.1122/1.550377 (24 pages) | Cited 7 times

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In this paper and its sequel, we attempt to understand the rheological differences between lyotropic and thermotropic liquid‐crystalline polymers by contrasting the rheology of three different liquid‐crystalline polymers at concentrations ranging from moderate (12%–30%) to highly concentrated (30%–50%) to densely packed (50%–100%). This first paper presents the steady‐state first and second normal stress differences N1 and N2 as functions of the shear rate γ̇ for solutions of poly(γ‐benzyl‐glutamate) with molecular weight 238 000, in the solvent metacresol, at concentrations C ranging from 12.5% to 40% by weight. Predictions of N1 and N2 for this range of concentration are obtained from the Doi molecular theory for rod‐like nematics, using both an approximate, and a nearly exact, method for solving the Doi equation. The predictions of N1, and to a lesser extent N2, agree qualitatively with measured values for all concentrations. In particular, the range of shear rates over which N1 is negative shifts upward with increasing concentration: if we define γ̇max as the shear rate for which N1 reaches a positive maximum value N1max, then we find that theory agrees with experiment in that both γ̇max and N1max increase monotonically with concentration C. These increases occur because the strength of the nematic interaction increases with C, which implies that for high concentrations, N1 becomes negative only at high‐shear rates.
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83.80.Xz Liquid crystals: nematic, cholesteric, smectic, discotic, etc.
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.85.Cg Rheological measurements—rheometry
83.85.Lq Normal stress difference measurements

Dynamic rheological behavior of flocculated fumed silica suspensions

Saad A. Khan and Nancy J. Zoeller

J. Rheol. 37, 1225 (1993); http://dx.doi.org/10.1122/1.550378 (11 pages) | Cited 8 times

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Fumed silica suspensions in low molecular weight solvents are used in many photonic and microelectronic applications. The rheology of these thixotropic systems plays a major role in the effectiveness of their usage. In this study, we use dynamic rheological measurements to examine the particle–particle and particle–solvent interactions of fumed silica with hydrophilic and hydrophobic surface groups dispersed in both polar and nonpolar solvents, polypropylene glycol and mineral oil, respectively. We find the mineral oil‐based suspensions to have a frequency‐independent elastic modulus (G′) for all solids concentration, whereas the polypropylene glycol‐based systems exhibit a ‘‘sol–gel’’ transition to a frequency‐independent G′ at high concentrations. The results are explained in terms of different solvent particle mechanisms present in the two systems. The behavior of the mineral oil suspensions are dominated by particle–particle interactions through hydrogen bonds, resulting in a gel structure. The polypropylene glycol systems, on the other hand, are dominated by the interactions of the polar solvent with the fumed silica thereby preventing the formation of a 3D gel network. Static light‐scattering experiments are used to probe the microstructure of both suspensions. We find the presence of a gel‐like network in mineral oil but not in polypropylene glycol, corroborating the rheological results. In addition, both rheology and light‐scattering data for the mineral oil suspensions are consistent with the prediction of a diffusion‐limited cluster–cluster aggregation model.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
83.85.Ei Optical methods; rheo-optics
83.60.Pq Time-dependent structure (thixotropy, rheopexy)

Evaluation of unsteady Couette‐flow measurement under the influence of fluid inertia

D. Aschoff and P. Schümmer

J. Rheol. 37, 1237 (1993); http://dx.doi.org/10.1122/1.550379 (15 pages) | Cited 1 time

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The use of modern viscometers ensures that the inertia of the measuring device in unsteady rheometry is taken into account. This is made possible by appropriate viscometer design, or by considering the transmission function during the recording of data. On the other hand the inertia of the fluid in general is neglected in the evaluation of experiments. This leads to errors in the determination of material functions for liquids with low‐shear viscosities, such as dilute polymer solutions. For shear oscillatory experiments evaluation methods are presented for cylindrical and plane Couette flow which yield the complex viscosity of linear viscoelasticity taking into account fluid inertia. For cessation or inception of steady‐shear flow one has to assume a specific constitutive equation for linear viscoelastic liquids in order to develop a correct evaluation method. Relations are presented for Maxwell and Jeffreys fluids. For more complicated models a numerical evaluation method is outlined.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.85.Jn Viscosity measurements
83.60.Bc Linear viscoelasticity
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