Non-Newtonian behavior in steady flow over the range from the lower to the upper Newtonian region for polystyrene solution

Graessley's entanglement theory of viscosity modified by a frictional viscosity parameter η_fric is applied to data on solutions of polystyrene in diethyl phthalate at various concentrations and different temperatures. All the data modified give a single master curve over the entire rates of shear, as obtained previously with polydimethyl-siloxanes of various molecular weights and their solutions of various concentrations. The zero-shear viscosity η₀, the upper Newtonian viscosity η_∞, and η_fric are compared. Three activation energies for flow are estimated from η₀, η_∞ and η_fric, and are compared. The result suggests that the flow behavior in the upper Newtonian region is much more dependent on η_fric than on the entanglement viscosity term η_ent. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric can be used as a measure of the non-Newtonian behavior of the present solutions. Non-Newtonian behavior of the investigated polymer solution becomes appreciable at about η_ent,0/η_fric = 2.5. These results are in agreement with previous conclusions based on comparison between η₀, η_∞ and η_fric for polydimethyl-siloxanes and their solutions.     

Modified graessley theory for non-newtonian viscosities of polydimethylsiloxanes and their solutions

A deviation from Graessley's theory of entanglement viscosity appears at very high shear rates when the flow of polydimethylsiloxanes of various molecular weights and their solutions with various concentrations is measured by the capillary method. In order to explain this deviation, a modified Graessley theory is proposed according to the previously reported suggestion that frictional viscosity appears not to be negligible at high shear rates. A reducing procedure taking a frictional viscosity parameter into account was performed. All of the reduced data are combined to give a master curve in spite of a wide range of molecular weight, concentration, and shear rate (from the lower Newtonian to very highest non-Newtonian flow region). The findings from the reducing procedure completely explain the mechanism of non-Newtonian flow for the bulk polymers with various molecular weights, including those below the critical molecular weight for entanglement, and for polymer solutions at any concentration. The viscosity of the linear polymer system consists of the shear-dependent entanglement term η_ent proposed by Graessley and the shear-independent frictional term η_fric. The non-Newtonian behavior depends on the ratio of η_ent/η_fric at the shear rate of measurement. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric and the critical shear rate for onset of the non-Newtonian flow may be used as a measure of the non-Newtonian behavior of the system and a measure of capability for its rising, respectively. The Graessley theory is to be included in the present modified theory and is applicable to the case of η_entη_fric ? 1.     

Viscosity of aqueous Ni(NO3)2 solutions at temperatures from (297 to 475) K and at pressures up to 30 MPa and concentration between (0.050 and 2.246) mol · kg−1

Viscosity of nine aqueous Ni(NO₃)₂ solutions (0.050, 0.153, 0.218, 0.288, 0.608, 0.951, 1.368, 1.824, and 2.246) mol · kg⁻¹ was measured in the temperature range from (297 to 475) K and at pressures (0.1, 10, 20, and 30) MPa. The measurements were carried out with a capillary flow technique. The total experimental uncertainty of viscosity, pressure, temperature, and composition measurements were estimated to be less than 1.6%, 0.05%, 15 mK, and 0.02%, respectively. All experimental and derived results are compared with experimental and calculated values reported in the literature. Extrapolation of the solution viscosity measurements to zero concentration (pure water values) for the given temperature and pressure are in excellent agreement (average absolute deviation, AAD = 0.13%) with the values of pure water viscosity from IAPWS formulation [J. Kestin, J.V. Sengers, B. Kamgar-Parsi, J.M.H. Levelt Sengers, J. Phys. Chem. Ref. Data 13 (1984) 175–189]. The viscosity data for the solutions as a function of concentration have been interpreted in terms of the extended Jones–Dole equation for strong electrolytes. The values of viscosity A-, B-, and D-coefficients of the extended Jones–Dole equation for the relative viscosity (η/η₀) of aqueous Ni(NO₃)₂ solutions as a function of temperature are studied. The derived values of the viscosity A- and B-coefficients were compared with the results predicted by Falkenhagen–Dole theory (limiting law) of electrolyte solutions and the values calculated with the ionic B-coefficient data. The measured values of viscosity for the solutions were also used to calculate the effective rigid molar volumes in the extended Einstein relation for the relative viscosity (η/η₀).     

High‐pressure rheology of polystyrene melts plasticized with CO2: Experimental measurement and predictive scaling relationships

A high‐pressure extrusion slit die rheometer was constructed to measure the viscosity of polymer melts plasticized by liquid and supercritical CO₂. A novel gas injection system was devised to accurately meter the follow of CO₂ into the extruder barrel. Measurements of pressure drop, within the die, confirm the presence of a one‐phase mixture and a fully developed flow during viscosity measurements. Experimental measurements of viscosity as a function of shear rate, pressure, temperature, and CO₂ concentration were conducted for three commercial polystyrene melts. The CO₂ was shown to be an effective plasticizer for polystyrene, lowering the viscosity of the polymer melt by as much as 80%, depending of the process conditions and CO₂ concentration. Existing theories for viscoelastic scaling of polymer melts and the prediction of T_g depression by a diluent were used to develop a free volume model for predicting the effects of CO₂ concentration and pressure on polymer melt rheology. The free volume model, dependent only on material parameters of the polymer melt and pure CO₂, was shown to accurately collapse the experimental data onto a single master curve independent of pressure and CO₂ concentration for each of the three polystyrene samples. This model constitutes a simple predictive set of equations to quantify the effects of gas‐induced plasticization on molten polymer systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3168–3180, 2000     

Thermal analysis for heat transfer enhancement in electroosmosis-modulated peristaltic transport of Sutterby nanofluids in a microfluidic vessel

Viscosity plays a crucial role in the flow and heat transfer process of nanofluids. To effectively calculate and predict the changing characteristics of nanofluids viscosity, this study presents a theoretical model combining the static interface layer and dynamic Brownian motion mechanisms of spherical nanoparticles for water-based Newtonian nanofluids. The model describes the reasonable dependences of nanofluids viscosity on physical properties of nanoparticles (density, volume fraction, size) and base fluid (temperature, viscosity, density). Taking four kinds of typical water-based Newtonian nanofluids containing spherical oxide nanoparticles (Al₂O₃, CuO, SiO₂ and TiO₂) as examples, the prediction performance of different viscosity models is analyzed in detail. From the comparison studies, it is demonstrated that the new viscosity model developed in this paper can exhibit better prediction performance than many well-known theoretical models and empirical correlations. Not only do the predicted results of model agree well with the experimental data from various studies, but also the effects of different factors are reflected effectively.

     

Experimental investigation toward obtaining a new correlation for viscosity of WO3 and Al2O3 nanoparticles-loaded nanofluid within aqueous and non-aqueous basefluids

In this study, the effect of temperature and mass fraction of Al₂O₃ and WO₃ nanoparticles dispersed in deionized water and liquid paraffin was investigated on dynamic viscosity of nanofluid. The results of the TEM tests showed that the size of Al₂O₃ and WO₃ nanoparticles was ranged from 10 to 60 nm, and the results showed that nanoparticles were semi-spherical. Also the results of DLS and zeta potential tests, respectively, exhibited the uniform size and high stability of the nanoparticles in the basefluid environment. The findings showed that adding a certain amount of nanoparticles to water and liquid paraffin increases dynamic viscosity, and in the case of various shear rates, the viscosity is constant for the water-based nanofluids, which indicates the Newtonian behavior of the nanofluid. In addition, for those prepared by liquid paraffin as a basefluid, the viscosity does not remain constant at different shear rates and at low amount of shear rate the viscosity achieves higher value, indicating non-Newtonian behavior of liquid paraffin-based nanofluids. The results showed that by increasing the temperature in liquid paraffin-based nanofluid the uniformity and linearity of the viscosity curve at various shear rates could be observed, which represents an approach for Newtonian behavior of nanofluid at higher temperatures. These results also showed that with increasing the mass fraction of nanoparticles in water and liquid paraffin, the viscosity increases at different shear rates. Finally, the correlation presented in this study shows that for nanofluid viscosity as a function of nanoparticles load and temperature, the deviation of correlated data from experimental values is less than 10%.

     

Viscosity of n-alkyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ionic liquids saturated with compressed CO2

The viscosity of imidazolium-based ionic liquids (ILs) saturated with gaseous, liquid and supercritical carbon dioxide (CO₂) was measured by a high-pressure viscometer at three different temperatures (25, 50, and 70 °C). The high-pressure viscosity of 1-ethyl-3-methylimidazolium ([EMIm]), 1-n-hexyl-3-methylimidazolium ([HMIm]), and 1-n-decyl-3-methylimidazolium ([DMIm]) cations with a common anion, bis(trifluoromethylsulfonyl)amide ([Tf₂N]), saturated with CO₂ was measured up to a maximum of 287 bar. As CO₂ pressure is increased the viscosity of the IL mixture dramatically decreases. While, the ambient pressure viscosity of 1-alkyl-3-methyl-imidazolium [Tf₂N] ILs increases significantly with increasing chain length, the viscosity of all the CO₂-saturated ILs becomes very similar at high CO₂ pressures. From previous vapor–liquid equilibrium data, the viscosity with concentration was determined and found to be the primary factor to describe the fractional viscosity reduction. Several predictive and correlative methods were investigated for the mixture viscosity given pure component properties and include arithmetic mixing rules, the Irving (Predictive Arrhenius) model, Grunberg equation, etc. The modified Grunberg model with one adjustable parameter provided an adequate fit to the data.     

Solution characterization of poly(isobornyl methacrylate) in tetrahydrofuran

Thermodynamic and hydrodynamic properties of dilute solutions of poly (isobornyl methacrylate) (PIMA) in tetrahydrofuran (THF) were characterized by using viscosity, static, and dynamic light scattering measurements. PIMA samples with different molecular weight were obtained by fractional precipitation of PIMA solution. Chain dimension parameters (R_g and R_H), together with second virial coefficient A₂ and intrinsic viscosity [η], were used to calculate various solution parameters characterizing polymer chains in polymer solutions. The experimental results are compared with calculation, indicating that PIMA behaves as a flexible coil in THF. © 1994 John Wiley & Sons, Inc.     

Measuring the solubility of CO2 and H2S in sulfolane and the density and viscosity of saturated liquid binary mixtures of (sulfolane + CO2) and (sulfolane + H2S)

The density and viscosity of liquid sulfolane saturated (loaded) with single CO₂ and H₂S gases were measured simultaneously with the solubility of the single CO₂ and H₂S gases in sulfolane at temperatures ranging from (303.15 to 363.15) K and pressures of up to about 2.4 MPa using a new experimental set-up developed in our laboratory. The experimental density and viscosity values were correlated using a modified Setchenow-type equation. It was observed that the density and viscosity of mixtures decrease by increasing temperature and acid gas solubility (loading) in sulfolane. Acid gas loading has a much profounder effect on the viscosity of solutions than on their density, i.e. at a concentration of 1 mol CO₂/H₂S per kg of sulfolane the density decreases by less than 3%, but viscosity decreases by more than 30%. Results show that at fixed temperature and pressure H₂S is more than four times as soluble as CO₂ in sulfolane. The measured solubility and density values were respectively used to obtain Henry’s law constants and partial molar volumes at infinite dilution for dissolution of CO₂ and H₂S gases in the liquid sulfolane at the temperatures studied. The Henry’s law constants obtained at different temperatures were used to determine infinite dilution partial molar thermodynamic functions (Gibbs free energy, enthalpy and entropy) of solution. The measured solubility data were correlated by using a model comprised of the extended Henry’s law and the Pitzer’s virial expansion for the excess Gibbs free energy.     

Viscosity and shrinkage of porous and quartzoid glasses of the Na<Subscript>2</Subscript>O-B<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript> system

Shrinkage of porous glasses on heating from 20 to 800°C was studied and temperature dependences of the viscosity in the range of 10¹¹–10¹³ P were determined for quartzoid (sintered) glasses based on five glasses with different compositions in the Na₂O-B₂O₃-SiO₂ system. The shrinkage of porous glasses and the viscosity of quartzoid glasses were analyzed in relation to their composition and temperature of preliminary thermal treatment.     

Physicochemical Properties of Solutions of Amides in H2O and in D2O

Excess volume, partial molar volumes, viscosity, and ultrasound velocity in H₂O and D₂O solutions of formamide (FM), acetamide (AM), dimethylformamide (DMF), and dimethylacetamide (DMA) were studied at 20°C. The change in the excess volume of the various amide solutions on substitution of D₂O for H₂O varies both in magnitude and direction. On the other hand, the isotope effect on the ultrasound velocity behaves similarly in all cases. Its magnitude is greatest for pure water and then decreases monotonically with increasing amide concentration. Although the behavior of the concentration dependence of viscosity is similar to that for ultrasound velocity, the isotope effect on the viscosity behaves in a different way. For methyl-substitued amides, a maximum isotope effect is observed at amide mole fraction 0.2, but the isotope effect for FM and AM increases monotonically with increasing amide concentration. The differences in the behavior of amides in aqueous solution are discussed in terms of their interactions with water.     

Aqueous polysaccharide blends based on hydroxypropyl guar gum and carboxymethyl cellulose: synergistic viscosity and thixotropic properties

Aqueous polysaccharide blends, formed from 2.5% (w/v) solution of hydroxypropyl guar gum (HPG) and 2.5% (w/v) solution of carboxymethyl cellulose (CMC) according to different blending ratios, were investigated at 20 °C in terms of their shear-dependent viscosity and thixotropic properties. The Cross viscosity equation was found to fit the shear-dependent viscosity data with reasonable accuracy. When the HPG solution with the mass fraction (f _HPG) of 0.87 was mixed, the zero shear viscosity (η _o) of the corresponding blend was found to be 168.5753 Pa s, while the η _o values of component HPG and CMC solutions were found to be 3.3859 and 98.6525 Pa s, respectively. For the aqueous HPG/CMC blends investigated, the resulting zero shear viscosity was observed to be much greater than the combined zero shear viscosity of the component polysaccharide solutions, showing a synergistic viscosity property. The quantitative determination of the hysteresis loop area, developed during viscometer tests on shear rate–shear stress reverse paths, was used to describe the thixotropic behavior. When compared with aqueous solutions of the component polysaccharides, these polysaccharide blends could afford enhanced thixotropic property. Maximum thixotropy synergism was observed for the HPG/CMC blend with the f _HPG of 0.67.     

Rheological properties of ionic and nonionic polyacrylamide solutions

Non-Newtonian shear viscosities were measured over six decades of strain rate k for 13 solutions of both the ionic and nonionic forms of polyacrylamide. By using the Weissenberg rheogoniometer with both the cone-and-plate and the parallel-plate attachments, the normal stress functions σ₁ (k²) and σ₂(k²) were obtained for four of the solutions. From the measurements of the shear viscosity and the normal stresses at low rates of strain, characteristic times τ and τ_N, respectively, were determined for each solution. The quantity τ was then used to nondimensionalize the strain rate τk, and when plotted versus the reduced shear viscosity, found successfully to correlate the experimental data for all the polyelectrolyte solutions over the entire range of τk and the data for the concentrated solutions of the nonionic polymer over a smaller range of τk. However, in order to correlate the normal stress data for the polyelectrolyte solutions, a second reduced strain rate (τ_Nk) was used. Thus, two different times were required to correlate all the observed data. The shear viscosity data for the dilute solutions of the nonionic polymer were well represented by the two-parameter, non-Newtonian intrinsic viscosity function that has been computed by Fixman.     

Steady-shear viscosity of polydimethylsiloxanes over the range from the lower to the upper Newtonian region

The mechanism of non-Newtonian behavior for flow from the lower to the upper Newtonian region is explained by a modification of Graessley's theory. In the theory proposed here, a viscosity η_fric, which is based on friction between polymer segments and is almost shear-independent, is introduced in addition to Graessley's entanglement viscosity η_ent, which decreases with increasing shear rate. The theory is applied to previously obtained data on steady flow of polydimethylsiloxanes of different molecular weights. The agreement between calculated and experimental results is good. In polymers with the molecular weight above the critical molecular weight for entanglement M_c, the major contribution to viscosity near zero shear rate is η_ent. As the shear rate increases, the flow curve has an inflection where η_fric cannot be disregarded in comparison with η_ent. In the upper Newtonian region, η_fric has more influence on the viscosity than η_ent. The theory can also explain the experimental results on flow of polymers with molecular weight below M_c, which were shown to be slightly non-Newtonian in the previous paper.     

Transport Coefficients in Water Plasma: Part I: Equilibrium Plasma

Knowledge of the transport coefficients of steam water plasma is important for modeling plasma flow processes and heat transfer. In this study, calculations of these properties were performed in a temperature range from 400 to 30,000 K and at pressures of 0.5, 1.0, 5.0 and 10 bar. Herein the composition of water plasma was determined at equilibrium. First, the most recent data on potential interactions and elastic differential cross sections for interacting particles were carefully examined in order to choose those most appropriate for determining the collision integrals. Second, we restricted the number of species to ten (e, H, O, H⁺, O⁺, O⁺⁺, H₂, O₂, OH and H₂O) and tested our collision integrals by comparing the thermal conductivity and viscosity to experimental data for water (at low temperatures). Finally, the total thermal conductivity, viscosity and electrical conductivity were calculated for different pressures.     

The variation of viscosity with composition for polystyrene/polycarbonate blends and its dependence on method of sample preparation

The dependence of viscosity on composition for blends of up to 10% polycarbonate in polystyrene is reported for samples prepared by three different methods. For solvent east materials dried below the T_g of PS, a minimum in viscosity is observed at 1% PC. For solvent cast materials dried above the T_g of PS and for melt blended samples, viscosities are higher and log viscosity vs composition is approximately additive. The minimum in viscosity is attributed to the presence of residual solvent whose level in the samples, after incomplete drying, is composition dependent as a result of the composition dependence of the polymer-polymer interaction parameter, χ.     

Detailed study of a two component smectic 4TPB–8OCB system with a nematic gap. Phase diagram and viscosity study

Abstract

The phase diagram of a two component system composed of two smectic compounds: 4-octyloxy-4′-cyanobiphenyl (8OCB) and 4-isothiocyanatophenyl 4-butylbenzoate (4TPB) was investigated. Three Miesowicz viscosity coefficients η₁, η₂, η₃ and the refractive indices at different temperatures as well as the enthalpies of the phase transitions were measured. It was stated, that the properties of the induced nematic phase, for example, the nematic phase existing between two smectic regions, are the same as the ones observed in the case of low viscosity nematic mesogens.     

Pressure dependence of the viscosity of dilute polystyrene solutions in toluene

The effect of pressure on the viscosity of dilute solutions of anionically polymerized polystyrene (M?_w = 209,000; M_w/M_n = 1.12) in toluene has been studied at different temperatures and concentrations using a falling-body viscometer. Measurements were performed in the concentration range from 0.0025 to 0.02 g/mL and at temperatures from 25 to 45°C under pressure up to 1057 bars. The viscosity coefficient η increases exponentially with pressure at a given temperature and concentration, while the apparent volume of activation V^? decreases with increasing temperature. The hypothesis that the pressure dependence of η is given by the pressure dependence of the activation energy holds true under the prevailing thermodynamic conditions. Log η increases linearly with increasing concentration at a given pressure. Intrinsic viscosity increases with increasing pressure, whereas the Huggins constant decreases.     

Effect of molecular structure on polyethylene melt rheology. II. Shear-dependent viscosity

The investigation of the effect of molecular structural variables on the melt viscosity of polyethylene was extended to the shear dependent region by application of a reduced variables treatment following, in a formal sense, that of Bueche. Viscosity–shear rate data were obtained for a series of experimentally polymerized linear polyethylene samples having a range of molecular weights and molecular weight distributions as characterized primarily by gel permeation chromatography. These data could be superimposed on a single reduced variables flow curve using parameters which were a function only of temperature, limiting Newtonian viscosity, M?_w, and M?_w/M?_n. The same treatment was successfully applied also to branched (low-density) fraction data discussed in a previous paper, with additional correction for long-chain branching. However, different reduced variables curves were obtained for the branched and linear cases.     

Energy transfer from 3,5-xylenol to 2,6-diphenylpyridine in solvents of different viscosity

Energy transfer from 3,5-xylenol to 2,6-diphenylpyridine (DPP) in a very dilute solution of the molecules in solvents of different viscosity, from 0.29 to 4.30 Cp, at 300 K is discussed. Excited xylenol does not form an exciplex with DPP. Non-radiative deactivation of the excited state of the xylenol proceeds through dissipation of excitational energy from the S₁ state of xylenol to the S₁ state of DPP. A suitable relation that takes into account the low concentrations of 3,5-xylenol and DPP in different solvents has been used to calculate the energy transfer quantum efficiency, f_XY. In non-polar or polar solvents, the non-radiative part of energy transfer efficiency increases and the radiative part decreases as the concentration of DPP is increased. The non-radiative energy transfer rate constant, K_XY, for the system of xylenol and DPP in solvents of different viscosity gradually decreases with increasing viscosity of the medium. In all solvents, the value of K_XY, is larger than the collisional diffusion controlled rate and the Förster critical transfer distance, R_O, is much greater than the collisional separation distance r_X + r_Y, the sum of the radii of xylenol (X) and DPP (Y) molecules. It is suggested that a diffusion-assisted long range dipole-dipole interaction is mainly responsible for energy transfer from xylenol to DPP. The efficiency of energy migration is negligibly small.