RHEOLOGICAL CHARACTERIZATION OF NON-NEWTONIAN FLUIDS WITH A NOVEL VISCOMETER

A hydrostatic head viscometer and its novel viscosity equation were developed to determine flow characteristics of Newtonian and non-Newtonian fluids. The objective of this research is to test capabilities of the hydrostatic head viscometer and its novel non-Newtonian viscosity equation by characterizing rheological behaviors of well-known polyethylene oxide aqueous solutions as non-Newtonian fluids with 60 wt.% sucrose aqueous solution as a reference/calibration fluid. Non-Newtonian characteristics of 0.3–0.7 wt.% polyethylene oxide aqueous solutions were extensively investigated with the hydrostatic head viscometer and its non-Newtonian viscosity equation over a 294–306 K temperature range, a 0.14–40 Reynolds number range, and a 55–784 s^?1 shear rate range at atmospheric pressure. Dynamic viscosity values of 60 wt.% sucrose aqueous solution were determined with the calibrated hydrostatic head viscometer and its Newtonian viscosity equation over a 3–5 Reynolds number range at 299.15 K and atmospheric pressure and compared with the literature dynamic viscosity value.     

Fluidization with viscoelastic polymer solutions in the transition flow region

Fluidization of spherical and non-spherical particle beds with shear thinning viscoelastic polymer solutions was investigated experimentally in the transition flow region. It was observed that the influence of elasticity on the anomalous expansion course weakens with the increasing value of Reynolds number. After exceeding a critical value of Reynolds number, which depends on the measure of liquid elasticity, the effect of elasticity vanishes and the expansion curves have the same linear shape as for fluidization with Newtonian (or purely viscous non-Newtonian) fluids. Semi-empirical equations based on the Carreau viscosity model were proposed for predicting the critical value of Reynolds number and the bed expansion in the region of diminishing elasticity effects.     

Falling ball method for determining zero shear and shear-dependent viscosity of polymeric systems: Solutions,melts, and composites

The falling ball method (FBM) is one of the well-established techniques for measuring the viscosity of Newtonian liquids at the room as well as at elevated temperatures and pressures. Owing to its simplicity and low cost, the possibility of extending its range of application to non-Newtonian systems including virgin and filled polymer melts, composites, polymer-solutions, and so forth, is explored here, In this work, theoretical results for the flow of power-law fluids past a sphere have been used to extract the values of the zero-shear viscosity and shear-dependent viscosity in the low-shear rate limit. The theoretical scheme outlined here has been validated by presenting comparisons with experimental results for scores of polymer solutions for which both falling sphere and rheological data are available in the literature. Indeed, the good correspondence obtained between these two independent data is encouraging and it is thus possible to use the FBM for shear-thinning systems when the resulting Reynolds numbers are such that the flow is viscosity-dominated, and the inertial effects are negligible. This implies that the Reynolds number should be ≤ ~1 for shear-thinning fluids and ≤ ~10⁻⁵ for shear-thickening fluids.     

Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems

Effects of liquid properties on the hydrodynamics of gas–liquid systems were investigated in lab-scale bubble column (BC) and internal loop airlift (ILA). Alginate solutions, a glycerol solution and a Boger fluid were adopted to separately address the effects of viscosity and of surface tension for Newtonian fluids, and the effects of relaxation time for non-Newtonian fluid characterized by approximately constant viscosity (low shear thinning). Hydrodynamic regimes were characterized in terms of overall gas holdup, gas–liquid mass transfer coefficient, drift-flux and liquid circulation velocity. The superficial gas velocities at the transition between hydrodynamic regimes (homogenous regime–vortical-spiral regime–heterogeneous regime) as a function the liquid viscosity was characterized by a maximum. The same behavior was observed for the maximum stable gas holdup and gas–liquid mass transfer coefficient in BC. Viscosity enhances homogeneous regime stability for μ<4.25 mPa s, in BC, and μ<7.68 mPa s, in ILA. For non-Newtonian fluids the transition velocity increases with liquid elasticity. The stabilization mechanism related to the relaxation time of Boger fluids has been discussed.     

Modeling rheological behavior of bentonite suspensions as Casson and Robertson-Stiff fluids using Newtonian and true shear rates in Couette viscometry

The Casson model and the Robertson-Stiff model have been used to determine whether they can describe the rheology of aqueous bentonite suspensions. The assessment utilized a total of twelve sets of experimental viscometric data from literature and from this work. Equations have been presented which allowed the determination of the true shear rates experienced by the fluids within the gap of the rotational viscometer for both rheological models. Non-linear regression has been applied to determine the two rheological parameters for the Casson model and the three rheological parameters for the Robertson-Stiff model using true shear rates and Newtonian shear rates, which are used most often in the analysis of rheometric data. The results showed that both models describe well the experimental data of these bentonite suspensions with good statistical indicators. Furthermore, analysis showed that true shear rates are always higher than Newtonian shear rates for both models. The differences depend on the particular suspension and are larger at low shear rates while they become smaller at higher shear rates indicating that the fluid behavior approaches Newtonian behavior at higher shear rates. The shapes of the rheograms remained essentially unchanged indicating that the rheological parameters determined with the use of true shear rates are very similar to the rheological parameters determined with the use of Newtonian shear rates. This was further confirmed with the computation of the rheological parameters for both models and both approaches. For the Casson model differences in the yield value computed with true shear rates were at most at 7% while for the plastic viscosity at 3%. For the Robertson-Stiff model, differences of the order of 2 to 5% were observed for the K-values, of 7% for γ˙₀-values while no differences were observed for the n-values. These small differences, however, do not justify use of Newtonian shear rates when analytical solutions exist which allow use of true shear rates without any compromise.     

The flow of non-Newtonian solutions through packed beds

The rheological behavior of aqueous solutions of Separan AP-30®, polymethylcellulose, and polyvinylpyrrolidone was studied experimentally. These solutions exhibit non-Newtonian flow behavior in simple shear, and are characterized by one of several 2, 3, or 4 parameter rheological equations. The equations used included the power law, the Ellis model, Spriggs equation, the Herschel-Bulkley equation, and Meter's model. The power law model fits the data for each of the solutions over a limited range of shear rates, whereas the other models, which include either a lower shear rate limiting Newtonian viscosity, and/or an upper shear rate limiting Newtonian viscosity, or a yield stress, fit the data well over a wide range of shear rates from 0.00675 to 1076 sec^?1. The pressure drop-flow rate data for the same aqueous solutions flowing through packed beds were correlated well by the Ergun equation using the various rheological models applied in this work to evaluate a modified fluid viscosity. In each case it was found that the rheological model which best fit the viscometric data also gave the best packed bed friction factor correlation, and that no one model, such as the powerlaw, or the Ellis model, is the best one to use in all cases for all solutions. For polyvinylpyrrolidone solutions large deviations between experimental values of friction factor and those from the Ergun equation occurred for modified Reynolds numbers greater than one. A pseudo viscoelastic parameter was used to improve the friction factor correlation empirically at high Reynolds numbers.     

An explicit equation for the terminal velocity of solid spheres falling in pseudoplastic liquids

An explicit equation is proposed which predicts directly the terminal velocity of solid spheres falling through stagnant pseudoplastic liquids from the knowledge of the physical properties of the spheres and of the surrounding liquid. The equation is a generalization of the equation proposed for Newtonian liquids. By properly defining the dimensionless diameter, d_*, a function of the Archimedes number, Ar, and the dimensionless velocity, U_*, a function of the generalized Reynolds number, Re, to account for the non-Newtonian characteristics of the liquid, the final equation relating these two variables has similar form to the Newtonian equation. The predictions are very good when they are compared to 55 pairs of Re—C_D for non-Newtonian data and 37 pairs for Newtonian data published previously. The root mean square error on the dimensionless velocity is 0.081 and much better than the only other equation previously proposed.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Experimental and CFD investigation of convective heat transfer in helically coiled tube heat exchanger

Experimental studies on isothermal steady state and non-isothermal unsteady state conditions were carried out in helical coils for Newtonian as well as for non-Newtonian fluids. Water and glycerol–water mixture (10 and 20% glycerol) were used as Newtonian, and 0.5–1% (w/w) dilute aqueous polymer solutions of Sodium Carboxy Methyl Cellulose (SCMC) and Sodium Alginate (SA) as non-Newtonian fluids are used in this study. These experiments were performed for coil curvature ratios as δ = 0.0757, 0.064 and 0.055 in laminar and turbulent flow regimes (total 258 tests). The CFD analyses for laminar and turbulent flow were carried out using FLUENT 12.0.16 solver of CFD package. The CFD calculation results (Nu_i, U, T₂ and Tw_o) for laminar and turbulent flow are compared with the experimental results and the work of earlier investigators which were found to be in good agreement. For the first time, an innovative approach of correlating Nusselt number to dimensionless number, ‘M’, Prandtl number and coil curvature ratio using least-squares power law fit is presented in this paper which is not available in the literature. Several other correlations for calculation of Nusselt number for Newtonian and non-Newtonian fluids, and two correlations for friction factor in non-Newtonian fluids (based on 78 tests and 138 tests) are proposed. These developed correlations were compared with the work of earlier investigators and are found to be in good agreement.     

二甲氧基甲烷饱和液体运动黏度

The kinematic viscosity values of the saturated liquid dtmethoxy memane are reported over the temperature range from 248. 467 to 353. 154 K along the saturation line made with a calibrated Ubbelohdetype capillary viscometer. The total experimental uncertainty is less than 0. 71%. In addition, the results were correlated as a function of temperature for the kinematic viscosity equation of saturated liquid. The absolute average deviation and the maximum deviation of the experimental results from the correlated equation are 0. 35% and 1.45%, respectively.     

Comments on the accuracy of zero shear intrinsic viscosity of high molecular weight polyacrylamide

The intrinsic viscosity of a polymer is traditionally measured with a capillary tube viscometer where the shear rate range is moderately high. Such method is valid when the polymers are non-ionic and have low to moderate molecular weight. The viscosity-shear rate curves obtained for dilute aqueous solutions of two high molecular weight polyacrylamides using two rotational viscometers indicate a strong shear-dependent viscosity in the medium to high shear rate regions. The zero shear intrinsic viscosity of the polymers determined by extrapolation from the high shear rate region to the zero shear condition may result in large errors. Its implication in predicting the molecular weight of polymers using the Mark-Houwink-Sakurada equation is discussed. A rheological equation for intrinsic viscosity as a function of shear rate is proposed.     

Analysis of gas holdup in bubble columns with non-Newtonian fluid using electrical resistance tomography and dynamic gas disengagement technique

This paper presents an experimental analysis of the influence of the liquid rheology on the gas flow pattern in a bubble column reactor. Aqueous solutions of xanthan are selected as an example of non-Newtonian shear thinning fluid. Averaged gas holdup is determined by two experimental techniques: parietal pressure probes and electrical resistance tomography (ERT). ERT is also used to provide 2D images of the gas phase distribution in a column cross-section. Bubble size distributions are evaluated by a gas disengagement technique using the parietal pressure probes. All these techniques clearly show the gas flow pattern is different in Newtonian and non-Newtonian fluids. Gas holdup values decrease when increasing the liquid viscosity and reach a minimum or a plateau. Homogeneous flow regime, observed in water at low gas velocities, tends to disappear when viscosity increases. This evolution is visualized by a much less isotropic distribution of the gas phase within cross-section of the column and by the appearance of much larger bubbles due to an increased coalescence phenomenon.     

KINEMATIC VISCOSITIES OF POLYETHYLENE GLYCOL DEXTRAN WATER SOLUTIONS

The kinematic viscosities of aqueous polyethylene glycol and dextran and polyethylene glycol + dextran + water were measured at temperatures of 30, 50, and 70°C. Polyethylene glycol with relative molecular masses of 200 and 1000 and dextran samples with nominal molecular masses of 37 500 and 2 000 000 were used. A one-parameter Grunberg-like equation proposed earlier by one of the present authors was used for estimating the values of viscosity of polyethylene glycol + dextran + water. A disposable parameter for the temperature range was calculated as 0.96 and 1.05 for PEG 200 + dextran 37 500 + water and PEG 1000 + dextran 37 500 + water, respectively, and as 2.74 and 2.80 for PEG 200 + dextran 2 000 000 + water, and PEG 1000 + dextran 2 000 000 + water, respectively. In view of our results, the proposed model works well for systems containing polyethylene glycol and dextran with different molecular masses.     

VISCOSITY OF GLYCEROL AND ITS AQUEOUS SOLUTIONS MEASURED BY A TANK-TUBE VISCOMETER

In this paper we demonstrate several series of experiments for the measurement of viscosity of neat glycerol and its aqueous solutions using a tank-tube viscometer. Measuring viscosity of highly viscous liquids with the tank-tube viscometer is easier than other types of viscometers. This inexpensive viscometer continuously generates numerous reproducible viscosity data of highly viscous neat glycerol and its aqueous solutions under given experimental conditions such as a desired temperature and a desired concentration of water in aqueous glycerol solutions.

Fabricating the tank-tube viscometer is inexpensive, since this viscometer does not need sophisticated accessories such as a high-pressure liquid pump, a sensitive pressure sensor, and an accurate flow meter. The tank-tube viscometer consists of a large-diameter reservoir and a long, small-diameter, vertical tube.

The viscosity equation was developed under the following assumptions. Both the quasi steady state approach and the negligible friction loss due to a sudden contraction between the reservoir tank and the tube are valid. The kinetic energy of the emerging stream from the bottom end of the vertical tube of the tank-tube viscometer also is assumed to be negligible. Very viscous glycerol and its aqueous solutions were used to test the viscometer by comparing viscosity values from the viscometer with those from literatures.

The main objective of this study is to demonstrate effects of water as well as temperature on viscosity of aqueous glycerol solutions, applying experimental data of accumulated amounts of aqueous glycerol solutions at various drain durations to the newly-developed viscosity equation for the fabricated tank-tube viscometer.     

RHEOLOGICAL PROPERTIES OF EMULSIONS OF OIL IN AQUEOUS NON-NEWTONIAN POLYMERIC MEDIA

The viscous flow behaviour of emulsions of oil in non-Newtonian Ellis model fluids (aqueous solutions of sodium carboxymethyl cellulose) has been studied experimentally. The addition of oil droplets to a non-Newtonian aqueous suspending media leads to an increase in the apparent viscosity of the emulsion system. The shape of the emulsion flow curves (apparent viscosity versus shear-stress plots) is found to be similar to that of the suspending media; consequently, the emulsion flow curves at various oil concentrations (0 to 70% by volume) are described adequately by the Ellis model. The relative viscosities of the emulsions of oil in non-Newtonian aqueous suspending media are significantly lower than those exhibited by emulsions of oil in Newtonian media.     

PRODUCTION OF SUB-MICROMETER SIZE O/W EMULSIONS USING A HIGH-PRESSURE WET-TYPE JET MILL

Emulsions composed of sub-micrometer size droplets were obtained by a high-pressure wet-type jet mill. Liquid paraffin as dispersed phase, aqueous sucrose solution as continuous phase, and anionic sodium dodecyl sulfate as emulsifying agent were used as the model emulsification system. Droplet size distribution, Sauter mean diameter (d₃₂), geometric standard deviation of the droplet size distribution (σ_g), and emulsion viscosity (η_e) were investigated under the various combinations of process variables: dispersed phase volume fraction (Φ), dispersed phase viscosity (η_d), continuous phase viscosity (η_c), processing pressure, and number of passages through the wet-type jet mil. d₃₂ and σ_g were correlated with the process variables. For the entire experimental range, maximum droplet diameter was varied with d₃₂ in the range of 1.7-1.9-fold, and a correlation was proposed with K (=η_d/η_c) as a variable. Above a marginal value of d₃₂, at Φ ≥ 0.1, emulsions exhibited Newtonian behavior and could be described well by the Yaron and Gal-Or model. Below the marginal values, emulsions strongly depended on d₃₂ and exhibited a shear-thinning behavior. The relation between η_e and d₃₂ for such emulsions was modeled by use of particle Reynolds number.     

Process viscometry of complex fluids and suspensions with helical ribbon agitators

The viscosity of highly inelastic shear thinning fluids and aqueous suspensions of kaolin clay particles has been investigated using a helical ribbon impeller fitted to a rheometer. Viscosity data for the single phase non-Newtonian fluids adequately processed with a generalized Reynolds number based on the impeller tip speed are shown to superimpose very well to the results obtained with a cone and plate rheometer. In the case of the two-phase system, it is shown that the data treatment for single phase system can be extended. The helical ribbon impeller yields more stable viscosity values than with the traditional geometries and no spurious flow phenomena (i.e., sedimentation, slip at the wall, etc.) was observed, making this system a superior device for suspension rheology over cone and plate and Couette flow rheometers.     

Viscoelastic Liquids in Stirred Vessels – Part I: Power Consumption in Unaerated Vessels

Different shear‐thinning and elastic fluids (STE fluids) have been stirred under unaerated conditions, in vessels equipped with Rushton disc turbines. Their power consumption has been evaluated over a wide range of stirring rates and their Metzner‐Otto constant (k_s) has been measured. A correlation has then been proposed to predict k_s values for a Rushton turbine operating in non‐Newtonian solutions. Power curves of STE fluids have been drawn and compared with reference curves (Newtonian, shear‐thinning inelastic and elastic with constant shear viscosity fluids). The STE fluids have thus been divided into two categories. The STE fluids of the first category (STE I fluids), which are concentrated viscous solutions of polymers (guar, CMC) reducing the power consumption at the beginning of the transitional region and connecting with the Newtonian reference at higher Reynolds numbers. In contrast, STE solutions of the second category (STE II fluids), which are solutions of drag reducing polymers (PAA), are less viscous and more elastic. They reduce the power consumption at the end of the transitional region and do not connect with the Newtonian reference, at least until Re = 6000. A general correlation has finally been proposed to model the power curve of STE fluids stirred by a Rushton turbine from the laminar to the turbulent regions, as a function of their elasticity.     

Influence of polyethylene oxide on absorption of carbon dioxide into aqueous <Emphasis Type="Italic">N</Emphasis>-methyldiethanolamine solution

Carbon dioxide was absorbed into aqueous polyethylene oxide (PEO) solution containing N-methyldiethanolamine (MDEA) in a flat-stirred vessel to investigate the effect of non-Newtonian rheological behavior of PEO on the chemical absorption rate of CO₂, where the reaction between CO₂ and MDEA was assumed to be a first-order reaction with respect to the concentration of CO₂ and MDEA, respectively. A unified correlation equation containing the Deborah number, which reflects the viscoelastic properties of a non-Newtonian liquid, was used to obtain the volumetric liquid-side mass transfer coefficient of carbon dioxide in aqueous PEO solution. The elastic properties of PEO accelerated the absorption rate of CO₂ compared with that of a Newtonian liquid based on the same values of viscosity.     

Trickle bed hydrodynamics and flow regime transition at elevated temperature for a Newtonian and a non-Newtonian liquid

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, trickle bed hydrodynamic behavior at elevated temperatures, on the contrary, largely remains terra incognita. This study's aim was to demonstrate experimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdup and liquid axial dispersion coefficient. These parameters were determined for Newtonian (air-water) and non-Newtonian (air-0.25% Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlations for confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden the trickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71, 319-321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything else being kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulse velocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi, 2002, Chemical Engineering Science 46, 1233-1246] predicted with very good accuracy both the pressure drops and the liquid holdups regardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and Engineering Chemistry Research 43, 4511-4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulse velocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (D_ax) extracted from the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonian and power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.