A phenomenological master curve for viscosity—structure data for two phase polymer systems in simple shear flow

A master curve hypothesis is established based on a mass balance and an assumption of continuous stress through interfaces for well dispersed two phase systems with “defined” zero shear viscosity. The master curve, which is in reasonable accordance with experimental data is represented in a double logarithmic plot of log (η_T/_T,0) against log \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{\eta _{T,0} M_C H\rho}}{{c^2 RT}}\dot \gamma _T} \right) $\end{document}. M_c is the molecular weight between entanglements, H = M?_w/M?_n, ρ is the density, c is the polymer concentration, all defined for the continuous phase. η_T and η_T,0 are the viscosity and zero shear viscosity of the blend, η_T is the apparent shear rate, R the gas constant, and T is absolute temperature.     

The relation between melt flow properties and molecular weight of polyethylene

The non-Newtonian behavior of commercial linear polyethylene samples and their fractions were studied at 190°C. The viscosity η versus shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} curves of whole polymers could be superimposed onto a single master curve despite the variations of their molecular weights and molecular weight distributions. For fractions, however, the same master curve was inapplicable, and the sensitivity of the viscosity to shear rate was found to be greater than those of the whole polymers. The zero-shear viscosities η₀ of fractions were related to the 3.42 power of the weight-average molecular weight M_u as follows: For whole polymers, the zero-shear viscosities were found to be considerably higher at the same M_w and markedly lower at the same z-average molecular weight M_z than those of the fractions. Thus, it was concluded that η₀ corresponds to an average of molecular weight between M_w and M_z. It was found that the molecular relaxation time τ is proportional to M_z^5.3 for whole polymers and to η₀M_w for fractions. Using these relations it was possible to relate the flow ratio, the ratio of flow rates at two different shear stresses, with the molecular weight distribution.     

Elastic behavior of concentrated solutions of acrylonitrile copolymers

The elastic behavior of concentrated solution of acrylonitrile copolymer was investigated by the capillary end correction method. The results were as follows. (1) The shear stress is proportional to recoverable shear strain in accordance with Hooke's law below critical concentration; above a critical concentration, however, the shear modulus depends on shear stress. (2) The log–log plots of zero shear modulus against polymer concentration and molecular weight fall on two straight lines with different slopes. The intersection of lines is considered to be the onset of elastically deformable entanglement network. We denote this inflection point as (C_c)_e or (M_c)_e. (3) The log–log plot of viscosity against polymer concentration does not show a change of slope at the critical concentration (C_c)_e. (4) By the application of the kinetic theory of rubberlike elasticity to the pseudo-network structure of concentrated polymer solution, in the range of C_c < C < (C_c)_e or M_c < M < (M_c)_e, the number of chain entanglement per molecule is kept one; moreover, in the range of C > (C_c)_e, or M > (M_c)_e, the number of chain entanglement increases to three.     

Residence time distributions and reaction kinetics in a fuel cell anode

A method which treats the fuel cell anode as a chemical reactor is developed to predict fuel cell performance. The method is based on experimentally measured residence time distribution parameters and differential cell kinetic data. The apparatus and experimental technique used to obtain the gas-phase residence time distributions are described. Kinetic data obtained from differential cell tests of the electrodes are used to evaluate an empirical rate expression.Axial dispersion model solutions for flow with volume change are obtained, based on the measured Peclet numbers and empirical rate expressions, and compared with experimental data from operating large high-temperature molten carbonate fuel cells. Agreement between the model and the experimentally determined data is very good, but only for low conversions of the fuel.Notation A cross-sectional area, cm² - C concentration of hydrogen. (g mole/cm³) - c=C/C _o dimensionless concentration of hydrogen - D dispersion coefficient cm²/s - d _e equivalent diameter, cm - F Faraday's constant - I total current, A - J current density, mA/cm² - k reaction rate constant, appropriate units - L length, cm - M number of moles - N =D/UL dispersion number - n order of reaction - n _e number of electrons transferred - –r rate of reaction based on volume of fluid, moles of reactant reacted/ cm³ s - S _e surface of electrode, cm² - T absolute temperature, °K - mean residence time, s - U velocity component in Z direction, cm/s - u = U/U ₀ dimensionless velocity - V _a volume of system, cm³ - V operating voltage, V - v volumetric flow rate, cm²/s - fractional conversion, degree of conversion of hydrogen - y mole fraction of hydrogen - Z space coordinate, cm - z =Z/L fractional length Greek letters coefficient of expansion - _m molar density of fuel, g mole/cm³ - overvoltage, V - dimensional variance, s² - ² dimensionless variance - =V_a/v ₀ space time, s     

Rheology of polyphosphazene melts and solutions—some surprises

Rheological tests are reported for two types of polyorganophosphazenes, one being a fluorinated alkoxy terpolymer (PNFT) and the other an aryloxy copolymer (PAP). Non-Newtonian viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) and complex viscosity components η′(ω) and η″(ω) were measured as functions of shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document} and oscillatory frequency ω, using a Weissenberg rheogoniometer, and a limited amount of normal stress data was also obtained. Solutions of both polymers in tetrahydrofuran were tested, over a concentration range 0-22 percent for PNFT and 0-35 percent for PAP. Melts of PNFT were examined for temperatures 50-178°C, and melts of PAP at 210°C even though they were not truly fluid at this temperature. Solution and melt data are shown to obey conventional superposition principles to give master curves. For solutions, superposition is achieved by using the Bueche relaxation time as a concentration reducing factor with no adjustable parameters, and the Spriggs model also proves useful in predicting normal stress and shear stress results. For PNFT melts, master curves are fitted by the new WS²H² model which incorporates detailed molecular weight distribution (MWD) information and extracts the entanglement length M_e from the data. Temperature shift factors a_T show Arrhenius behavior and the corresponding activation energies E_re are reported. Results for PNFT melts were complicated by lack of agreement between two samples of nominally the same composition; η′(ω) shapes and levels and E_re values differed widely. This is interpreted in terms of detailed MWD information and the possibility of mesomorphic phase transitions occurring in these nominally amorphous materials.     

Effect of crosslink density on molecular relaxations in diepoxide-diamine network polymers. Part 2. The rubbery plateau region

A comparison of the prediction of the theory of rubber elasticity with the experimentally observed variation of the shear storage modulus, G, as a function of crosslink concentration shows that deviations occur when the network strand concentration in diepoxide-diamine polymers exceeds approximately 1.5 mole kg^?1. The rapid rise in G above this level is accounted for in terms of the increasing importance of non-Gaussian chain statistics and steric interactions. It is also established that the contribution from entanglements is significant and the behavior over the entire crosslink density range can be described by the following equation where v and ?T_e are the concentrations of elastically active strands which orginate from fixed points and entanglements respectively, ψ is an empirical constant related to the importance of the non-ideal behavior, and ? is the so-called “front factor”. This latter constant is found to depend on the functionality of the network junctions, varying from 0.9, for a system with tetrafunctional junctions, to an average of 0.53 for those networks with trifunctional junctions.     

Melt viscosity of poly(vinyl chloride) formulations

Commercial, suspension-type PVC resin, poly (vinyl chloride), molecular weight M_w × 10^?4 = 8.6 ± 0.9, polydispersity M_w/M_n = 2.26, was mixed with plasticizer di(2-ethyl hexyl)phthalate (DOP) and organo-tin stabilizer in four different proportions. The mixtures were milled and pressed into sheets for testing. The polymer content in these samples was 97, 80, 60, and 40 wt percent. The viscoelastic properties of the materials were investigated using a Weissenberg rheogoniometer in a cone-and-plate, steady-state shearing mode. The viscosities and primary normal stress difference coefficients were measured at shear rates of 10^?2 ≤ \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^. $\end{document} (sec^?1) ≤ 10² and at temperatures from 151 to 246°C. The zero shear viscosities, plotted as log η₀ vs 1/T (T is the absolute temperature) did not follow either a straight line dependence, reported for PVC melts at low shear rates at 170–190°C, nor was any discontinuity found near 195°C as by others; the data follows a continuous concave curve. The apparent activation energy of flow increases steeply with decreasing temperature. The data can be represented by a WLF type of equation, but the magnitudes of the parameters of this relation differ from expected values. A crossplot of log η₀ (T = const.) vs log w (where w is the polymer content) also demonstrates a faster increase of η₀ with w than expected from the straight line dependence. The primary normal stress difference coefficient was found to increase with w and decrease with T, paralleling the observed dependencies of η₀.     

Linear low density polyethylenes and their blends: Part 2. Shear flow of LLDPE's

The steady state and dynamic shear behavior of eleven commercial linear low density polyethylenes (LLDPE) and one low density polyethylene (LDPE) resin were measured in capillary and parallel plate geometries at T = 150 to 230°C. The extrudate swell and the Bagley correction were determined. A large pressure effect on capillary flow of narrow molecular weight distribution LLDPE was observed and a new corrective procedure was proposed. After the correction the steady state viscosity was found to be equal to the dynamic (not complex) viscosity: η(\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}) = η'(ω = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}). A newly proposed four parameter relation between η and the deformation rate was found to provide a simple means for computation of the zero shear viscosity, ηo, and the primary relaxation time. Both these parameters showed a high degree of correlation. The expected relation: ηo ∝? M_w^3.4 was observed for low molecular weight samples with low polydispersity. The LLDPE activation energy of flow, E_σ=29.9 ± 1.8 kJ/mole, was determined.     

The effect of shear rate on the molecular weight determination of acrylamide polymers from intrinsic viscosity measurements

The rheological response of dilute solutions of high molecular weight polyacrylamides at low shear rates has been measured using a capillary viscometer that provided for a fivefold variation in shear rate at each concentration. The non-Newtonian effects were found to be significant for polyacrylamides with number-average molecular weights exceeding 10⁶. The molecular weight average–intrinsic viscosity relationship most widely used in the literature, [η] = 6.80 × 10^?4M , was found to be valid when [η] was measured at high shear rates where the polymer solutions approached Newtonian behavior. A new relationship was developed relating M _n to the intrinsic viscosity extrapolated to zero shear rate.     

A model relating the elastic properties of high-density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady-shear melt viscosity of high-density polyethylene to the molecular weight distribution is applied toward predicting the steady-shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ_m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ_c, the maximum relaxation time allowed at ${\rm \dot \gamma }$. Equations relating molecular weight and relaxation time to the steady-shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady-shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone-and-plate viscometer. The assumed proportionality constant between τ_c and 1/${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ_m = 1.4 × 10^?19 (M)^3.33. Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.     

Chain orientation in sheared molten poly(ethylene oxide) fractions by measurement of infrared dichroism

Rheo-infrared spectroscopy was used to study the development of orientation of molten narrow molar mass fractions of poly(ethylene oxide) [molar masses between 18,000 and 120,000 g/mol] during non-Newtonian shear flow at shear rates between 2 and 270 s^?1 and temperatures between 75 and 100°C. The steady state degree of orientation [expressed as the Hermans orientation function (f_ss)] reached a saturation level with increasing shear rate; f_ss increased with increasing molar mass (M) according to f_ss = C₁ ? C₂/M (C₁ and C₂ are coefficients; the latter depended on shear rate and temperature). The coefficient C₁ (f_ss) for a polymer with infinite molar mass took a universal value close to 0.05 for the temperatures and shear rates used. Under large shear stresses, the relationship between stress and orientation deviated markedly from linearity. The time to establish a steady state level of orientation was proportional to M^1/2. The recovery of the isotropic state after the cessation of shear could initially be described by a simple exponential relaxation law: f ∝ e, where τ_ρ is the relaxation time. The latter showed a weak molar mass dependence according to τ_r ∝ M^0.6 and an Arrhenius temperature dependence with an activation energy of ～60 kJ/mol. The relaxation of the shear stress after the cessation of shear was more rapid than the recovery of the isotropic state.     

Melt rheology and extrudability of polyethylenes

Commercial high density polyethylene (HDPE), low density polythylene (LDPE), and linear low density polyethylene (LLDPE) resins were tested at 150, 170, and 190°C in steady state, dynamic, and extensional modes. Within the low rates of deformation \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω ≤ 0.3, the steady state and dynamic functions agreed: η = η′ and N₁ = 2G′; at the higher rates, the steady state parameters were larger. The elongational viscosity, η_e, was measured under a constant rate, \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}, or stress, σ, condition. In the first case for LLDPE, the transient η reached an equilibrium plateau value, η_e. For HDPE, η increased up to the break point. For LDPE, stress hardening was recorded. Under constant stress the η_e, could always be determined; its value, within experimental error, agreed with the maximum value of η determined in a constant \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document} experiment. The maximum strain at break was only ε = 1.5 for HDPE and 3, to 4 for LDPE and LLDPE. The rate of deformation dependence of the η (or η′) and η_n may be discussed in terms of the Trouton ratio, R_T = η_e/3η at \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} = ω = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon$ \end{document}: R_T ≤ 1.2 for LLDPE, R_T ≤ 2.5 for HDPE, and R_T ≤ 15 for LDPE. The PE resins were extruded at 190°C through a laboratory extruder equipped with a slit or rod die. The rotational speed of the screw varied from 0 to 90 rpm. Extrusion pressure, output, and energy were measured and correlated with the rheological parameters of the resins.     

Copper recovery from dilute solutions in the Falling-Film cell

The removal of copper from dilute solutions is examined in electrochemical reactors where the electrolyte flows as a thin film in an inclined channel between a plane plate and a sheet of expanded metal (Falling-Film cell). Copper is recovered as a thin sheet from the plane plate. The results are compared with a known simplified model and the variations of the faradaic yield with the operating conditions are discussed.Nomenclature A _e electrode surface area - b width of inclined channel - C(t) copper concentration at timet - C ₀ initial copper concentration - d interelectrode distance - overall current density - overall limiting current density - overall mass transfer coefficient - L length of the channel - Q _v volumetric flow rate - Q _vl volumetric flow rate per unit of channel width (=Q _v/b) - t time - t _s residence time in the reactor, defined by Equation 1 - mean flow velocity of the liquid film, defined by Equation 2 - V volume of electrolyte in the circuit - V _R reactor volume - v _sn normalized space velocity, defined by Equation 9 - inclination angle with respect to the horizontal - instantaneous faradaic yield - time-averaged faradaic yield - v _e number of electrons exchanged in the electrochemical reaction     

Strukturrheologische Untersuchung des Verhängungs-netzwerkes bei Polyvinylacetat in Dioxan

Rheological measurements with polyvinylacetate in dioxane are described and evaluated according to the principles of structure rheology. For the network solution, a concentration independent mass of network strand M_e of 2,5 · 10⁵ is found, and an equivalent chain element for c = 0 of Å = 37 Å. The penetration of the network is significantly hindered, the hindrance being smaller for higher concentrations.     

Electrodiffusional determination of momentum transfer in annular flows: Axial developing and swirling decaying flows

Two types of developing flows were studied: the axial developing flow occuring downstream of fixed beds of spheres, and the swirling decaying flow induced by a tangential inlet. In both flows, the momentum transfer was investigated for different axial distances and for a Reynolds number range of 90 to 3780 using an electrochemical method. Measurement of the wall shear stress was achieved by means of the limiting electrodiffusional current on circular microelectrodes. Comparisons of swirling flow and axial developing and developed flows are made in terms of velocity gradients and friction factors.Notation A microcathode surface area - C _s potassium ferricyanide concentration - d microelectrode diameter - e=R ₂–R ₁ thickness of the annular gap - F Faraday constant - f _ax,f _df,f _e friction factors - I _L limiting diffusional current - k _F local mass transfer coefficient - L _e entrance length - R ₁ external radius of the inner cylinder - R ₂ internal radius of the outer cylinder - Reynolds number - S _ax,S _df,S _e velocity gradients - U _m mean axial velocity - x axial coordinate - kinematic viscosity This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

Enhanced mass transfer in electrochemical cells using turbulence promoters

Many electrochemical processes suffer in varying degrees from mass transfer limitations. These limitations may require operation at considerably less than economic optimum current densities. Mass transfer to a surface may be considerably enhanced by insertion of turbulence promoters in the fluid flow path near the affected surface.An instrument was developed to measure local current densities in the hydrodynamically very difficult region near the turbulence promoter. A general method for the relative evaluation of hydrodynamic conditions has been developed. Generalization of the data permits optimization of hydrodynamic cell design using the promoter shapes investigated.

Notation

Symbols A Coefficient for cell power costs, $ m² (As)^–1 - A _c Cell area, m² - a Constant in Equation 4 - B Coefficient for area-proportional costs, $ A (m² s)^–1 - C Coefficient for pumping power costs, $ A (m² s)^–1 - C _b Bulk concentration, kg mol m^–3 - C _bi Inlet bulk concentration, kg mol m^–3 - C _e Energy cost, $ (Ws)^–1 - C _i Interfacial concentration, kg mol m^–3 - ¯C _s Amortized area cost, $ (m² s)^–1 - D Current—density-insensitive costs, $ s^–1 - D _e Equivalent diameter, m - D Diffusion constant, m² s^–1 - e Current efficiency - F _d Cell feed rate, m³ s^–1 - F 96.5×10⁶ A s kg eq^–1 - g Channel width, m - h Channel height, m - i Current density, A m^–2 - i _opt Economic optimum current density, A m^–2 - K Total costs of running cell, $ s^–1 - (K–D)_ideal Total sensitive costs under hydrodynamically ideal conditions, $ s^–1 - k _c Convective mass transfer coefficient, m s^–1 - L Total length of flow path, m - l Promoter spacing, m - N Mass flow rate to surface due to convection, kg mol m² s^–1 - n _e Number of electrons transferred in electrode reaction - P _c Power required by cell, W - P/L Average pressure gradient in channel, N m^–3 - R _av Effective cell resistance, m² - S Open channel cross-section, m² - S ₀ Minimum channel cross-section at promoter, m² - s _i Stoichiometric coefficient of species i - t _i Transport number of species i in solution - ¯t _i Effective tranport number of species at polarized surface - V Average fluid velocity, m s^–1 - x Distance from inception of concentration disturbance, m - ₁ Electrical power conversion efficiency - ₂ Pumping power conversion efficiency - Solution viscosity, kg (m s)^–1 - Solution density, kg m^–3 Dimemionless groups Fanning friction factor - Reynolds number - R h/g Channel aspect ratio - D _e/l Promoter frequency - S/S ₀ Contraction coefficient - Sherwood number - Degree of reaction - Dimensionless total sensitive - Dimensionless current density - Energy cost ratio     

Characterization of polyisobutylene-based model urethane networks

Polyisobutylene-based model urethane networks have been prepared by crosslinking liquid α, ω-di(hydroxyl)polyisobutylenes, i.e., PIB-diols carrying exactly two ? CH₂OH functions, F _n = 2.0 ± 0.1, and rather narrow molecular weight distributions, M _w/M _n = 1.5?1.6, with tritriphenylmethyl isocyanate \documentclass{article}\pagestyle{empty}\begin{document}$$\rm{HC}\ (\hskip-6pt\hbox{---}p\rm{C}_6\rm{H}_4\hbox{---}\rm{NCO})_3$$\end{document}. Networks prepared with M _n = 1400 and 7500 PIB-diols, and with 90/10 and 80/20 mixtures of these PIB-diols (bimodal networks), have been characterized by extraction, by the Flory–Rehner swelling method, and by the Mooney–Rivlin equilibrium modulus method, and tested by stress–strain measurements. M _c values of the M _n = 1400 PIB-diol network obtained by swelling (1550) and by equilibrium modulus studies (1500) were in excellent agreement with the M _n of the prepolymer. Also the C₂ parameter was negligible in comparison to C₁, suggesting the absence of interchain entanglements. This is the first hydrocarbon-based polyurethane network that exhibits a negligible C₂ value by stress–strain measurements of unswollen samples. The M _c values of the M _n = 7500 PIB-diol were also in good agreement with the M _n of the prepolymer; however, C₂ was larger than C₁, indicating interchain entanglements. Evidence for strain-induced toughening was observed with both networks prepared with the M _n = 1400 and 7500 PIB-diols. The ultimate properties of the two bimodal networks did not show improvement over those of the individual constituents; however, the M _n's of the constituents were not very different.     

An l-amino acid electrode for monitoring beer fermentation

A membrane covered amperometric l-amino acid electrode is described, employing l-amino acid oxidase immobilized on a Pt disc electrode with rabbit albumin and glutaraldehyde. The electrode response to a range of l-amino acids and a theoretical treatment for the rate determining step are presented. Results are also given for the application of the electrode in monitoring beer fermentations. Appropriate amino acid utilisation is vital for both yeast cell growth and beer flavour development.List of symbols A electrode area - D diffusion coefficient - e reduced enzyme concentration - e total enzyme concentration - F Faraday constant - i electrode current - i_D l/A - I l/k_ME - j flux - L thickness of the electrolyte layer - L _M thickness of the membrane - k_cat rate constant for enzyme/substrate reaction - k rate constant for electrode reaction - k_ME electrochemical rate constant for the enzyme reaction - k_S mass transfer rate constant for substrate in membrane - K membrane constant - K _s partition coefficient of substrate in membrane - K_M Michaelis constant - n number of electrons S substrate - Ii_D/[S] - y (^–1 – 1)/[S]     

Rheology and viscosity scaling of the polyelectrolyte xanthan gum

The viscosity as a function of concentration for xanthan gum in both salt‐free solution and in 50 mM NaCl is measured and compared with a scaling theory for polyelectrolytes. In general, the zero shear rate viscosity and the degree of shear thinning increase with polymer concentration. In addition, shear thinning was observed in the dilute regime in both solvents. In salt‐free solution, four concentration regimes of viscosity scaling and three associated critical concentrations were observed (c* ≈ 70 ppm, c_e ≈ 400 ppm, and c_D ≈ 2000 ppm). In salt solution, only three concentration regimes and two critical concentrations were observed (c* ≈ 200 ppm and c_e ≈ 800 ppm). In the presence of salt, the polymer chain structure collapses and occupies much less space resulting in higher values of the critical concentrations. The observed viscosity‐concentration scaling is in very good agreement with theory in the semidilute unentangled and semidilute entangled regimes in both salt‐free and 50 mM NaCl solution. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Viscosity of bead suspensions in polymeric solutions

Viscosity measurements made by a cone-plate viscometer on polyisobutylene in decalin solutions at different concentrations and their corresponding glass bead suspensions with filler loadings up to 40% by volume are reported. The range of shear rate $ \dot \gamma $ investigated is between 0.1 and 1000 sec^?1. The solutions show shear-thinning behavior, and the relative viscosity η_r of the slurries generally decreases with increasing shear rate. The results indicate two different types of mechanism, respectively at high and low shear rates. At low $ \dot \gamma $, the relative viscosity can be correlated extending relations already well known for suspensions in Newtonian liquids which are based on the mechanism of aggregate disruption. The behavior at high $ \dot \gamma $ values is believed to be due to the influence of the filler on the flow properties of macromolecules, in particular on relaxation time. Through a shifting procedure, an increase in relaxation time which depends on filler content and not on polymer concentration is shown.