Contents

Mechanisms for Viscosity Reduction of Polymer Blends; Blends of Fluoroelastomer and High-Density Polyethylene

Chi-Ming Chan and Jiyun Feng

Negative ER Effect and Electrical Properties of a Teflon/Silicone Oil Suspension

C. W. Wu and H. Conrad

The Effect of Die Materials and Pressure-Dependent Slip on the Extrusion of Linear Low-Density Polyethylene

Timothy J. Person and Morton M. Denn

Characterization of the Rheological Properties of a Fast-Curing Epoxy-Molding Compound

Sejin Han, K. K. Wang, C. A. Hieber, and C. Cohen

Thermodynamic Approach to Rheological Modeling and Simulations at the Configuration Space Level of Description

R.J.J. Jongschaap, A.I.M. Denneman, and W. Conrads

Solution Rheology of a Hydrophobically-Modified Alkali-Soluble Associative Polymer

Robert J. English, Harpreet S. Gulati, Richard D. Jenkins, and Saad A. Khan

Exploiting Accurate Spinline Measurements for Elongational Material Characterization

V.V. Ramanan, V. Gauri, K.W. Koelling, S.E. Bechtel, and M.G. Forest

The Elastic Stress in 'Film Fluids'

R. G. Larson

On the Non-Linear Rheology of a Worm-Like Micellar System in the Presence of Sodium Salicylate Salt

A. Aït-Ali and R. Makhloufi

Measurements of Velocity Profile Development in the Spinning Flows of Liquid Crystalline Polymer Solutions

N. Mori, Y. Hamaguchi, and K. Nakamura

A Smoluchowski Theory with Simple Approximations for Hydrodynamic Interactions in Concentrated Dispersions

R. A. Lionberger and W. B Russel

Oscillatory Shear of a Confined Fiber Suspension

Richard L. Schiek and Eric S. G. Shaqfeh

Electrorheological Effect in Immiscible Polymer Blends

Kozo Tajiri, Keiichi Ohta, Hiroshi Orihara, Yoshihiro Ishibashi, Masao Doi, and Akio Inoue

Full Tensor Optical Rheometry of Polymer Fluids

Sokratis G. Kalogrianitis and Jan W. van Egmond.

The Rheology of Charge Stabilized Silica Suspensions

M. E. Fagan and C. F. Zukoski

Viscoelastic Properties of Colloidal Gels

C. J. Rueb and C. F. Zukoski

Mechanisms for Viscosity Reduction of Polymer Blends;
Blends of Fluoroelastomer and High-Density Polyethylene

Chi-Ming Chan and Jiyun Feng
Department of Chemical Engineering
The Hong Kong University of Science and Technology
Clear Water Bay, Hong Kong

Abstract

The rheological behavior of fluoroelastomer/HDPE blends was investigated in detail. A capillary rheometer was used to determine the apparent viscosity of the blends as a function of time at various shear rates. The time to attain the steady state and the normalized steady-state apparent viscosity of the blends depend on shear rate and the fluoroelastomer concentration. The reduction in the apparent viscosity is caused by adhesive failure at the interface between the HDPE melt and the fluoroelastomer layer which was formed on the die wall surface during the extrusion of the blends. The presence of the fluoroelastomer layer on the die wall surface was confirmed by x-ray photoelectron spectroscopy and rheological measurements. Based on our previous work and this work, we have discovered that there are at least two different mechanisms— adhesive failure at the interface between the extrudate and the lubricating layer or cohesive failure in the lubricant layer—for viscosity reduction in polymer blends.

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Negative ER Effect and Electrical Properties
of a Teflon/Silicone Oil Suspension

C. W. Wu* and H. Conrad
Advanced Materials Technology Laboratory
Department of Materials Science and Engineering
North Carolina State University
Raleigh, NC 27695, USA

*Visiting Professor from Research Institute of Eng. Mech.
Dalian University of Technology, Dalain 116024
People's Republic of China

Abstract

A suspension (phi = 0.2) of Teflon particles in silicone oil exhibited a negative ER response with a dc electric field. This was in keeping with the fact that the conductivity of the host liquid was considerably greater than that of the particles sigma_p, giving for the complex dielectric mismatch parameter parameter beta* = -1/2. Microscopy observations revealed that with application of a dc electric field the Teflon particles migrated to the positive electrode resulting in a structure which consisted of two layers or zones; (a) a relatively pure liquid and (b) a more concentrated suspension The thickness of the liquid zone increased with field strength, which led to the decrease in the shear stress with field. A numerical analysis was developed for the electrical properties of the segregated suspension, which gave good agreement with measured values.

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The Effect of Die Materials and Pressure-Dependent Slip
on the Extrusion of Linear Low-Density Polyethylene

Timothy J. Person* and Morton M. Denn**
Materials Sciences Division, Lawrence Berkeley National Laboratory and
Department of Chemical Engineering, University of California at Berkeley
Berkeley, CA 94720-1462 USA

*Present address: Union Carbide Corporation, Weston Canal Center,
P.O. Box 450, Somerset, NJ 08875

**Corresponding author. e-mail: denn@cchem.berkeley.edu

Abstract

The flow of linear low-density polyethylene through stainless-steel slit dies occurred at shear rates approximately 12% higher than in identical alpha-brass dies at the same wall shear stresses, indicating near-wall slip. The flow curves were independent of gap spacing. We show through the slip theory of Hill and coworkers (1990) that a measurable gap dependence of the flow curve is not a necessary consequence of wall slip; the flow curves for both stainless steel and alpha-brass dies can be fit with the same rheological parameters, with a difference in the work of adhesion accounting for the differences in the flow curves.

X-ray photoelectron spectroscopy revealed differences in the chemistry of brass surfaces with different pretreating, corresponding to small differences in flow curves. Fluorocarbon-coated die surfaces showed no more slip than stainless steel, while the flow curve with gold-coated surfaces followed stainless steel at intermediate stress and brass at high stress.

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Characterization of the Rheological Properties
of a Fast-Curing Epoxy-Molding Compound

Sejin Han, K. K. Wang, C. A. Hieber
Sibley School of Mechanical & Aerospace Engineering
Cornell University, Ithaca, NY

C. Cohen
School of Chemical Engineering
Cornell University, Ithaca, NY

Abstract

The viscosity of an epoxy-molding compound (EMC) has been characterized using a parallel-plate viscometer and a specially-developed slit rheometer. In particular, steady-state and dynamic viscosities at low temperatures and shear rates have been determined with a parallel-plate viscometer. Measurements with this instrument indicate that an extended Cox-Merz relation can be used to relate the dynamic viscosity to the steady shear viscosity for the given EMC. For measurements at high shear rates and high temperatures, a special slit rheometer has been built. In this viscometer, the slit is preceded by a disk-shaped reservoir where curing of the specimen takes place. The sample fills the thin reservoir fast and has its temperature raised by heat conduction from the hot wall. Because the reservoir is thin, specimen quickly reaches the wall temperature with negligible cure and then cures under approximately isothermal conditions. The degree of cure of the sample is measured by quenching the specimen as it is extruded out of the slit and then performing differential-scanning-calorimeter (DSC) measurements.

By combining results from these two viscometers, the viscosity of the EMC has been obtained over the typical processing range of shear rates, temperature and degree of cure encountered during chip encapsulation. The measurement results indicate that the EMC viscosity exhibits a yield-stress behavior at low shear rates and a power-law behavior at high shear rates. The temperature dependence can be described by the WLF equation and the degree-of-cure dependence at low cure by an equation proposed by Macosko.

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Thermodynamic Approach to Rheological
Modeling and Simulations at the Configuration
Space Level of Description

R.J.J. Jongschaap, A.I.M. Denneman, and W. Conrads
Rheology Group, Faculty of Applied Physics, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands

Abstract

The so called Matrix Model is a general thermodynamic framework for micro-rheological modeling. This model has already been proved to be applicable for a wide class of systems, in particular to models formulated at the configuration tensor level of description. For models formulated at the configuration space level of description a matrix formulation is readily obtained, but for the subsequent analysis one still needs an explicit solution of the configuration space distribution functions. In the present paper we describe a new approach in which this problem is solved by combining the matrix model with a Lagrangian simulation method in configuration space developed recently by Szeri and Leal. The result is a consistent and unified formulation of stress tensor expressions, including the stress averaging, and the evolution equations. This formulation is also suited for numerical simulations. In this way the range of applicability of the matrix model is extended substantially. In order to clarify the principles of the method and some aspects of its implementation a simple example is discussed in some detail.

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Solution Rheology of a Hydrophobically-Modified
Alkali-Soluble Associative Polymer

Robert J. English¹, Harpreet S. Gulati¹, Richard D. Jenkins², and Saad A. Khan¹*

¹Department of Chemical Engineering, North Carolina State University
Raleigh, NC 27965-7905

²UCAR Emulsion Systems, Union Carbide Corporation
410 Gregson Drive, Gary, NC 27511

*Corresponding author. Ph:919-515-4519; Fax: 919-515-3465
email: khan@che.ncsu.edu

Abstract

Rheological and photophysical data are presented for a hydrophobically-modified alkali soluble copolymer, of a constitution similar to materials currently employed as rheology modifiers in water-borne coatings. The copolymer comprises a polyelectrolyte backbone bearing ethoxylate side chains capped with complex alkylaryl groups of a high molar volume. In aqueous alkaline media, the hydrophobes associate dynamically, the topology of the network so formed being dependent on the polymer concentration. Photophysical studies, employing pyrene as a hydrophobic fluorescent probe, indicate presence of hydrophobic associations. At concentrations below the coil overlap concentration, c*, these associations are predominantly intramolecular. At higher polymer concentrations, intermolecular interactions become more probable. This change in network topology is in qualitative agreement with previous theoretical considerations of associative polymer systems and is reflected in an unusually high concentration dependence of the zero shear viscosity, with eta₀ ~ c⁸ . Evidence for shear induced structuring in steady shear, large amplitude oscillatory shear and parallel superposed steady and dynamic shear is presented. Such structuring is more pronounced at lower polymer concentrations, consistent with the formation of intermolecular associations at the expense of intramolecular. In contrast to the simple linear telechelic associative polymers considered in a number of previous studies, the network dynamics of the polymer are no longer represented by a single characteristic time. This deviation from a classical Maxwellian response in oscillatory shear is interpreted as a broadening of the relaxation spectrum, arising from the coexistence of both hydrophobic associations and topological entanglements. Mechanistically, stress relaxation is better envisaged in terms of "hindered reptation" [Liebler et al. (1991 )] of the chains, rather than Rouse-like behavior moderated purely by the hydrophobe disengagement rate [Annable et al. (1993)].

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Exploiting Accurate Spinline Measurements
for Elongational Material Characterization

V.V. Ramanan¹, V. Gauri², K.W. Koelling², S.E. Bechtel¹, and M.G. Forest<sup>3

1</sup>Department of Aerospace Engineering, Applied Mechanics and Aviation
The Ohio State University, Columbus, Ohio

²Department of Chemical Engineering
The Ohio State University, Columbus, Ohio

³Department of Mathematics
University of North Carolina, Chapel Hill, North Carolina

Abstract

We have constructed an apparatus which provides enhanced resolution in the measurement of the free surface profile and the axial force exiting the die during spinning of a liquid filament. In this paper we demonstrate how this information can be exploited to give quantitative information about rheological material properties in isothermal elongational flows. The fiber spinning experiments are coupled with mathematical models that serve as inverse problems to deduce material properties when the fiber profile and upstream axial force are experimentally known. We first develop integral and differential forms of the fiber spinning momentum balance which describe how stress varies down the length of the filament for an incompressible material, independent of rheology. These forms are then combined with experiments to deduce the evolution of the elongational viscosity along the spinline and verify the accuracy of free surface measurements. A fiber spinning model specialized to the Giesekus constitutive equation is then combined with spinline measurements to determine material constants within the Giesekus constitutive assumption. In particular, our technique is used to characterize the elongational rheology of a Boger test fluid. We obtain significantly different values for the relaxation time (as did Denn et al. (1975)) and mobility parameter than we obtain via shear rheometry; the solvent and polymer viscosities deduced from our spinline and shear experiments are essentially the same.

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The Elastic Stress in 'Film Fluids'

R. G. Larson
Department of Chemical Engineering
University of Michigan
Ann Arbor, MI 48109-2136

Abstract

Micro-mechanical models for the instantaneous elastic stress tensor tau of 'film fluids', i.e., fluids with internal interfaces such as foams, emulsions, and immiscible blends, yield formulas that are similar to each other and are well approximated simply by tau [proportional to] C^1/2, where C is the Cauchy strain tensor. This expression can be derived as an approximation by assuming that the interfaces deform affinely and that the tension in the interface is independent of the deformation. The expression tau [proportional to] C^1/2 is therefore the analog of the classical expression tau [proportional to] C^-1 for the instantaneous elastic stress in polymeric 'line fluids'. The second normal stress difference of a 'film fluid' is predicted to be negative and of comparable magnitude to the first normal stress difference.

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On the Non-Linear Rheology of a Worm-Like Micellar System
in the Presence of Sodium Salicylate Salt

A. Aït-Ali and R. Makhloufi
Université de Metz, Laboratoire de Physique des Liquides et des Interfaces
Groupe Rhéophysique des Colloïdes, 1, Bd Arago 57078 Metz Cedex 03 France

Abstract

The non-linear rheology of an aqueous worm-like micellar system made of Cetyltrimethylammonium Chloride (CTAC) with Sodium Salicylate (NaSal) is studied in this work. At high NaCl salt concentration the rheological measurements show a Maxwell behavior for all the solutions. The data of these samples are analyzed with respect to Spenley, Cates and McLeish model. The dimensionless quantities sigma_plateau/G₀ and gamma_c tau_R which characterize the non-linear rheology are compared to the predictions of this model. At a fixed surfactant concentration these quantities are found to be insensitive to changes in salt concentration and in temperature, respectively. The experimental value of the ratio sigma_plateau/G₀ we find is close at hand to the theoretical one. A discrepancy between the theory and the experiments occurs however in comparing the Weissenberg number defined by the product gamma_c tau_R.

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Measurements of Velocity Profile Development in the Spinning
Flows of Liquid Crystalline Polymer Solutions

N. Mori*, Y. Hamaguchi, and K. Nakamura
Department of Mechanical Engineering
Faculty of Engineering
Osaka University
2-1 Yamadaoka Suita
Osaka 565, Japan

*Corresponding author

Abstract

The development of velocity profile inside a filament was studied for spinning flows of LCPs using a hydrogen bubble method. Both isotropic (33 wt%) and liquid crystalline (50 wt%) aqueous solutions of hydroxypropylcellulose were used as the test fluids. The velocity profile for the 33 wt% solution varies from a convex profile to a uniform one similar to that for Newtonian fluids. For the 50 wt% solution, however, an anomalous profile of the velocity, that is a concave profile, is found beyond a distance of one radius of the nozzle downstream from the exit. Since this concave profile persists far downstream from the nozzle exit, it may affect the molecular orientation distribution inside a fiber.

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A Smoluchowski Theory with Simple Approximations for
Hydrodynamic Interactions in Concentrated Dispersions

R. A. Lionberger
Department of Mathematics
University of Melbourne
Parkville, Victoria 3052 AUSTRALIA

W. B Russel
Department of Chemical Engineering
Princeton University
Princeton NJ 08544

Abstract

In the literature there exist many theories that provide predictions for the rheological properties of concentrated colloidal suspensions, some in excellent agreement with existing experimental data. However, the manner in which hydrodynamic interactions are included differs greatly among the various approaches. Here we incorporate hydrodynamic interactions into the formalism developed previously to account for many body thermodynamic interactions in concentrated suspensions. A conservation equation involving two particle conditional averages of the hydrodynamic functions is derived and solved with different approximations for the functions, including the dilute limit, the rescaling due to Brady, and a lubrication approximation from our previous work.

Through our previous calculations without hydrodynamic interactions we have a well characterized approximation for the thermodynamic couplings in concentrated suspensions. The addition of approximations for the hydrodynamic interactions allows prediction for hard sphere suspensions of the low shear viscosity, linear viscoelasticity, long-time self-diffusion coefficient, dichroism, and the nonequilibrium structure for comparison with extensive experimental data.

We demonstrate that the form of the nonequilibrium structure is relatively insensitive to the model for the hydrodynamic interactions, while its magnitude is increased by the overall slowing down of relaxations. The calculation of the stress is dominated by the structure near contact at volume fractions approaching random close packing while at intermediate volume fractions it is more sensitive to the model for the interaction functions over the entire range of separations. Comparison of the predictions with a wide range of experimental measurements and simulation results suggests that existing hydrodynamic approximations are of the correct magnitude, while existing thermodynamic approximations are correct in form but underestimate the magnitude of the nonequilibrium structure.

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Oscillatory Shear of a Confined Fiber Suspension

Richard L. Schiek and Eric S. G. Shaqfeh
Department of Chemical Engineering
Stanford University
Stanford, California 94305-5025 USA

Abstract

Starting from a nonlocal description of the stress in a slender, rigid fiber suspension (Schiek and Shaqfeh 1995), we calculate the dynamic properties of a free fiber suspension under oscillatory shear in a very narrow gap. For a fiber suspension, three field quantities including the fluid velocity, the fiber concentration and the fiber configuration strongly effect the suspension's behavior. When the width of the gap confining the suspension is of the same scale as a suspended fiber's length, then all three of the important field quantities change rapidly on that scale. The nonlocal stress equation is coupled to the momentum conservation equation for the fluid velocity and a Fokker-Plank equation for the fiber's probability density function resulting in a closed set of nonlinear, integro-differential equations. These equations were solved in the limit of small Péclet number, where Brownian motion dominates, for arbitrary gap widths and oscillation frequencies. From the calculated stress fields, we obtained the real and imaginary viscosities which one would measure in flow experiments. The dependence of all four dynamic properties on gap width was investigated and we find that below a critical gap width (equivalent to one full fiber length) all dynamic properties undergo dramatic changes. Additionally, as the gap width shrinks, the relaxation time of the suspension was found to decrease, approaching the relaxation time of the pure Newtonian solvent in the limit of zero gap width. Scalings for the relaxation time as a function of small gap width are also presented.

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Electrorheological Effect in Immiscible Polymer Blends

Kozo Tajiri, Keiichi Ohta, Hiroshi Orihara, Yoshihiro Ishibashi, Masao Doi
Department of Applied Physics, School of Engineering
Nagoya University, Furo-cho Chikusa-ku, Nagoya 464-01, Japan

Akio Inoue
Central Laboratory, Asahi Chemical Industry Co., Ltd.
2-1 Samejima, Fuji-shi, Shizuoka-ken 416, Japan

Abstract

A new model of the electrorheological (ER) effect for immiscible polymer blends is proposed on the basis of microscopic observations. In the absence of an electric field the polymer with high viscosity is dispersed as droplets in the other polymer with low viscosity, while in the presence of an electric field, the droplets stretch and coalesce to form bridges between electrodes, resulting in the increase of the macroscopic viscosity. A few experimental results are given to confirm the validity of this model.

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Full Tensor Optical Rheometry of Polymer Fluids

Sokratis G. Kalogrianitis and Jan W. van Egmond
Department of Chemical Engineering
University of Massachusetts
Amherst, MA 01003

Abstract

A novel three dimensional flow birefringence technique has been developed to measure the real time, three-dimensional, optical anisotropy in flowing polymer solutions. Full Tensor Optical Rheometry (FTOR) utilizes three polarization-modulated beams to probe all independent elements of the refractive index tensor and is thus used as a quantitative probe of time-dependent, three-dimensional average molecular orientation. We present results for shear flow of polystyrene (PS) in a 6% semi-dilute solution of tricresyl phosphate (TCP) over a range of shear rates. Although the time-dependent behavior of N₂ has not been widely reported, probably because of experimental difficulties, it can be a powerful means of testing rheological models. Experimental measurements of the transient behavior of N₂ and -N₂/N₁ on inception and cessation of simple shear flow are compared with the predictions of the Doi-Edwards and Giesekus models. The Giesekus model is in qualitative agreement with most of the time-dependent features observed for N₂ and -N₂/N₁. On flow inception overshoots in N₂ and -N₂/N₁ are observed. Further, on flow cessation, N₂ relaxes more slowly than N₁ and -N₂/N₁ shows a strong nonexponential increase to a constant value of ~ 0.9 at long times. The Doi-Edwards model is less successful in predicting transient results but agrees quite well with observed steady-state dependence of N₂ with shear rate.

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The Rheology of Charge Stabilized Silica Suspensions

M. E. Fagan and C. F. Zukoski
Department of Chemical Engineering and Beckman Institute
University of Illinois, Urbana, IL 61801

Abstract

The flow properties of aqueous suspensions of silica particles with diameters ranging from 117 to 780 nm were measured as a function of volume fraction, ionic strength and continuous phase composition. Dense, aqueous suspensions of all sizes displayed similar behavior with a yield stress in the limit of low shear rate, shear thinning as the stress was raised and, above a critical volume fraction, shear thickening. Master flow curves which are weakly dependent on particle size, volume fraction, surface potential, magnitude of the decay length for the electrostatic forces or particle size distribution are produced when stress is scaled on the suspension's elastic modulus, G, and shear rate on G/eta_c. Here eta_c is the continuous phase viscosity. For suspensions which ordered at rest and of sufficiently high volume faction, shear thickening occurred as a discontinuous decrease in shear rate as the stress increased. This behavior was not observed in suspensions altered so that no order occurred at rest. When the continuous phase viscosity was increased by suspending the particles in a glycerin solution, no evidence for a yield stress or ordering were observed. These suspensions thinned with increasing stress to a minimum viscosity where thickening occurred as a smooth transition. The elastic scaling that successfully produced master curves for the aqueous suspension failed for the glycerin suspensions.

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Viscoelastic Properties of Colloidal Gels

C. J. Rueb and C. F. Zukoski
Department of Chemical Engineering and Beckman Institute
University of Illinois, Urbana, IL 61801

Abstract

The microstructure and scaling of mechanical properties of dense colloidal gels were investigated as a function of volume fraction and strength of interparticle attraction. Gels were reversibly formed by cooling suspensions of octadecyl silica particles in decalin or tetradecane. Shear history independence of mechanical properties was ensured by preshearing the suspensions in the gelled state. Gelation resulted in suspensions with apparent fractal dimensions of 1.4. Shear densification resulted in an apparent fractal dimension of 2.5 for structures containing many particles. When the gelled suspension was presheared, just after the shear rate was set to zero, elastic moduli were small. Over time, the moduli recovered to a time independent value, G'_infinity, at a rate alpha. When measured over a wide range of volume fraction, phi, and strength of interparticle attraction, G'_infinity, alpha, and the strain limiting the extent of linear response to oscillatory deformations, gamma_M, fell onto master curves when plotted as a function of phi/phi_G for l .1 < phi/phi_G < 5. Here phi_G is the gel volume fraction which varied from 0.11 to 0.59 for temperatures studied.

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