Needle penetrometry with variable force loading for measuring viscosity of pelletized coal upon heating

A needle penetrometry was performed loading steady force in a range from 1×10⁻³ to 2 N to pelletized coal upon heating via a cylindrical needle. From the observed effects of shear rate on apparent viscosity of softening coal pellet, defined as the shear-rate to shear-stress ratio, it was found that the pellet behaved as a Newtonian fluid for shear rates lower than a critical one while as a pseudo-plastic fluid for higher shear rates. The penetrometry was also carried out varying the force with time. The variable force loading enabled to maintain the shear rate well below the critical one, and thereby to measure the apparent viscosity of coal pellets as Newtonian fluids over a temperature range from 600 to 800 K. Upon heating at 10 K min⁻¹, the apparent viscosity of Goonyella coal pellet decreased from about 10¹⁰ Pa s at 640 K down to a minimum of about 10⁴ Pa s at 755 K, and increased up to 10⁹ Pa s at 800 K. In a course of heating as above, the viscosity of Blind Canyon coal pellet decreased above 600 K, underwent a minimum of about 10⁶ Pa s at 715 K, and increased up to 10¹⁰ Pa s at 770 K. Decreasing the heating rate from 10 to 3 K min⁻¹ caused the minimum viscosities of the pellets to increase by 1-2 orders of magnitude.     

A viscosity function for thermoplastics blended with a thermotropic liquid crystalline polymer

The capillary flow behavior of thermoplastic blends containing thermotropic liquid crystalline polymers (TLCP) was studied both theoretically and experimentally. Significant viscosity reductions were observed for a polyethersulfone (PES) blended with a TLCP at 10 and 30 wt %, respectively. A viscosity function was developed and tested to evaluate the relationship between the blend viscosity reduction and weight fraction including some property-related parameters: η = η₀[1 − φ + φ/δ + K(1 − φ)(1 − λ)φ^ϵ]⁻¹, where η and η₀ stand for blend and matrix viscosity, respectively. ϕ is the weight fraction; δ, the viscosity ratio of the two parent components; λ, the critical stress ratio; and ϵ, an exponent. Interfacial slippage in the blend has been suggested as the flow mechanism by which a substantial reduction in the melt viscosity takes place upon the addition of a small amount of TLCP. The fact that experimental data could be fitted to the viscosity function with satisfactory accuracy should make the function an acceptable way of modeling, analyzing, and parameterizing the experimental rheological data of these blends. © 1996 John Wiley & Sons, Inc.     

Granular temperature in a liquid fluidized bed as revealed by diffusing wave spectroscopy

We report granular temperature and solid fraction fields for a thin rectangular bed (20×200 mm cross-section and 500 mm high) of glass particles (mean diameter of 165 μm and density of 2500 kg/m³) fluidized by water for superficial velocities ranging from 0.05U_t, which is approximately double the minimum fluidization velocity, to 0.49U_t, where U_t is the particle terminal velocity estimated by fitting the Richardson-Zaki correlation to the bed expansion data. At superficial velocities below 0.336U_t, the solid fraction and granular temperature are uniform throughout the bed. At higher superficial velocities, the solid fraction tends to decrease with height above the distributor, whilst the granular temperature first increases to a maximum before decaying towards the top of the bed. Correlation of the mean granular temperature with the mean solid fraction and the local granular temperature with the local solid fraction both suggest that the granular temperature in the liquid fluidized bed can be described solely in terms of the solid fraction. The granular temperature increases monotonically with solid fraction to a maximum at φ≈0.18 where it then decreases monotonically as φ approaches the close-packed limit.     

Cell models for suspension viscosity

Cell models for the viscosity μ of a suspension of spherical particles in Newtonian fluid of viscosity μ₀ are discussed. Various boundary conditions on the outer boundary of the spherical cell lead to different results: the viscosity predicted for a zero velocity perturbation boundary condition is higher than those predicted with zero tangential stress perturbation. However, in all cases Einstein's prediction μ/μ₀=1+2.5φ+? holds in the limit of small solid volume fraction φ?1.     

Determination of intrinsic viscosity of polyelectrolyte solutions

Intramolecular hydrodynamic contribution η_intra/C to the reduced viscosity η_SP/C of polyelectrolyte solutions is derived as a function of polymer concentration C by separating the theoretically calculated intermolecular electrostatic contribution η_inter/C from the observed reduced viscosity, assuming an additivity, η_SP/C=η_intra/C+η_inter/C. The resulting intramolecular part η_intra/C reflects nearly the net effect of the polyion conformation; it increases monotonously with decreasing polymer concentration and levels off to a constant in sufficiently dilute concentrations. The leveling-off value of η_intra/C corresponds to the intrinsic viscosity [η]. From the estimated values of [η], the ionic strength I dependence of the polyion conformation has been visualized, resulting in a similarity between two relations, η_intra/C vs. C and [η] vs. I.     

Effect of molecular weight on the electrorheological behavior of side-chain liquid crystal polymers in nematic solvents

We investigate the change in the electrorheological (ER) properties of a nematic solvent on dissolution of an end-on polyacrylate side-chain liquid crystal polymer (SCLCP) with an 11-methylene spacer. We observe a weak enhancement of the ER response, Δη[equals]δη_on−δη_off, where δη_on is the viscosity increment on dissolving polymer in the presence of a strong electric field, applied transverse to the flow, and δη_off is the corresponding increment in the absence of the field. Equating η_on and η_off, respectively, to the Miesowicz viscosities η_c and η_b, and using the theoretical prediction that δη_c/δη_b[equals]R_∥⁴/R_⊥⁴, where R_∥ and R_⊥ are the rms end-to-end distances of the chain parallel and perpendicular to the director, this indicates that the chain conformation of the SCLCP is weakly prolate. The molecular weight dependence of the conformational relaxation time, τ_r, also extracted via the hydrodynamic theory, is identical to that deduced from the GPC hydrodynamic volume in tetrahydrofuran as solvent. The hydrodynamic volume in the nematic state is larger, however, and increases with decrease in temperature. An earlier study of a polysiloxane SCLCP observed similar behavior, but with a smaller molecular weight dependence of τ_r. The difference is ascribed to dissimilar chain conformations of the two SCLCPs.     

Modelling the zero shear viscosity of bimodal high solid content latex: Calculation of the maximum packing fraction

Different rheological tests were performed on monodisperse polystyrene latices and mixtures of two different latices with different particle sizes. A critical volume fraction φ_c was defined for each of the latices. Subsequently, a method based on the estimation of the porosity of a bed of randomly placed spherical particles was adapted to allow us to define the maximum packing fraction for any bimodal system. This method can be used for any ratio of particle diameter and volume fraction for the two populations provided one has knowledge of the critical volume fractions of related monodisperse latices (see Pishvaei et al., 2005. Polymer 46, 1235-1244). The model was tested experimentally, and rheological tests allowed us to validate the values of the critical volume fraction (φ_c) of different bimodal latices. A master curve of viscosity vs. polymer concentration was obtained using the concept of reduced volume fraction. The results prove that we can predict the viscosity of multimodal systems from the knowledge of monomodal packing fraction.     

Rigid backbone polymers, XVII: Solution viscosity of polydisperse systems

When plotted against concentration V⁰₂, the viscosity η⁰ curve of isotropic solutions of lyotropic nematic mesomorphic polymers increases according to:

$\text{η}{}^0\text{=η}{}_0\text{[[η]V}{}^0{}_2\text{+(}\text{π}\text{4}\text{)[η]}{}^2\text{(V}{}^0{}_2\text{)}{}^2\text{+K}{}_2\text{(}\text{ln}\text{x}\text{)}{}^2\text{[η]}{}^3\text{(V}{}^0{}_2\text{)}{}^3\text{+…]}$

in which η₀ is the solvent viscosity, K₂ a numerical constant, x? is the average molecular axial ratio and [η] the intrinsic viscosity as defined by:

$\text{[η]=}\text{2}\text{x}{}^2\text{45}\text{1}\text{ln}\text{2}\text{x}\text{?1.84}\text{+}\text{3}\text{ln}\text{2}\text{x}\text{?0.61}\text{(+}\text{14}\text{15}\text{)}$

At the concentration $\text{v1}{}_2$ an anisotropic phase appears and the viscosity curve shows a decrease in slope followed by a change in direction at a peak viscosity η^p at v^p₂. Upon further increase in v⁰₂ the system undergoes a phase inversion and finally turns fully anisotropic at v^A₂. In the biphasic interval the viscosity is described by:

$\text{η}{}^0\text{=η}{}_{\mathrm{<mtext>mat</mtext>}}\text{1+}\text{(5λ+2)}\text{2(λ+1)}\text{V}{}_{\mathrm{<mtext>inc</mtext>}}$

where $\text{λ =}\text{η}{}_{\mathrm{<mtext>inc</mtext>}}\text{η}{}_{\mathrm{<mtext>mat</mtext>}}$, the ratio of the inclusions viscosity to the matrix viscosity, and v_inc the volume fraction of the inclusions in the system. It must be emphasized that the molecular weight of the polymer in both phases changes continuously with concentration, resulting in commensurate changes in η_ince, η_mat and their ratio λ. In the anisotropic region the viscosity first decreases moderately and then increases precipitously with v⁰₂, according to:

$\text{η}{}^0\text{=η}{}_0\text{[}\text{2}\text{x}{}^2\text{90S}\text{(}\text{5}\text{ln}\text{2}\text{x}\text{?1.8}\text{+}\text{6}\text{ln}\text{2}\text{x}\text{?0.61}\text{)+2]}\text{V}{}^0{}_2\text{1-}\text{V}{}_{\mathrm{25°}}\text{V}{}_{\mathrm{E}}$

in which S is an order parameter and V₂₅, V_E are volumes swept by the orbits of the flowing rodlike macromolecules. The equations give results in good qualitative and fair quantitative agreement with experimental data in the literature.     

Maxwell equation and classical theories of glass transition as a basis for direct calculation of viscosity at glass transition temperture

The main relaxation theories of glass transition (Leontovich-Mandelstam and Volkenstein-Ptitsyn) variously formulate the kinetic criteria of glass transition. Both of the approaches are shown to be equivalent in physical sense and provide a single expression that connects the rate of change of a melt temperature and the structure relaxtion time. The theory characterizes the width of a temperature band δT _g in which the glass transition occurs. The values of δT _g can either be obtained from the experiment or be accepted to conform to the value of a temperature step under the change of viscosity by an order of magnitude (direct method for finding by the Volkenstein-Ptitsyn theory). Using the Maxwell equation, a new equation for the calculation of the viscosity for viscoelastic relaxation was suggested, which is based on a shear modulus of glass and the cooling rate. The theory was verified basing on the published data for oxide glass. The average difference between the calculated and measured values of lgη upon glass transition comprises 0 ± 0.30. These results correspond to the cooling rate of 3 K/min and log(η, Pa s) = 12.76 ± 0.26 (for all glass considered). It is shown that the most probable cooling rate which provides the viscosity upon glass transition of ～1012 Pa s is close to 20 K/min (oxide melts). The theory predetermines the dependence of viscosity upon glass transition on the nature of a glass-forming liquid. The disadvantages of other approaches to the problem under consideration are demonstrated.     

Rheology of Concentrated AP/HTPB Suspensions Prepared at the Upper Limit of AP Content

Due to the requirements for the preparation of an ammonium perchlorate (AP)/hydroxy‐terminated polybutadiene (HTPB) based composite propellant, an upper limit content of AP applicable in the propellant, φ_max (wt%), exists. The rheology of concentrated AP/HTPB suspensions prepared at φ_max is investigated in this study. The relative viscosity, η_rφ(‐), of the suspensions prepared at φ_max is almost constant at approximately 200. For the suspensions prepared at φ_max, the HTPB layer thickness, H_φp (µm), on the AP particle, calculated from the specific surface area measured by the air‐permeability method, is closely related to the void fraction, ε_max(‐), for the loose packing of the AP powder. H_φp decreases with increasing ε_max. By reversal conclusion it was found that the relative viscosity of the suspension, of which the HTPB layer thickness is H_φp, will accordingly be η_rφ.     

Rheological properties of cellulose/ionic liquid/dimethylsulfoxide (DMSO) solutions

Rheological properties of cellulose dissolved in two ionic liquids (ILs), 1-allyl-3-methylimidazolium chloride (AmimCl) and 1-butyl-3-methylimidazolium chloride (BmimCl), with co-solvent dimethylsulfoxide (DMSO), are studied in the concentration range of cellulose from 0.070 to 6.0 wt%. The viscosities of ILs are exponentially decreased by adding DMSO in the concentration range of 0–100 wt%. The co-solvent DMSO decreases the monomer friction coefficient in cellulose solutions and has no significant change for the entanglement state of cellulose, thus results in the reduced solution viscosity, shortened relaxation time and unchanged moduli of the cross-over point. For cellulose solutions, dilute regime, semidilute unentangled regime and semidilute entangled regime were determined by steady shear experiments. In semidilute entangled regime, the specific viscosities η_sp, relaxation time τ, and plateau modulus G_N, exhibit concentration dependences as η_sp ～ C^4.4, τ ～ C^2.2, andG_N ～ C^1.9, respectively, in AmimCl-DMSO (80/20 w/w); and η_sp ～ C^4.3, τ ～ C^2.0, and G_N ～ C^2.1, respectively, in BmimCl–DMSO (80/20 w/w). Therefore, the rheological properties of cellulose/IL/DMSO solutions are approximately of IL-independence in this study. The dependence of η_sp upon cellulose concentration shows that the IL–DMSO mixture is more like a θ solvent for cellulose, and the thermodynamic properties of IL–DMSO mixtures are similar with those of ILs for cellulose at 25 °C. The conformation of cellulose in ILs would not be changed with the addition of DMSO not only in the dilute regime but also in the entanglement regime.     

Synthesis and characterisation of star branched polyesters with dendritic cores and the effect of structural variations on zero shear rate viscosity

A series of branched polyesters consisting of poly(ε-caprolactone) (PCL) (degree of polymerisation: 5-200) initiated from hydroxy-functional cores and end-capped with methylmethacrylate have been prepared. The cores were third-generation hyperbranched polyester, Boltorn, with approximately 32 hydroxyl groups, a third-generation dendrimer with 24 hydroxyl groups and a third-generation dendron with eight hydroxyl groups. Finally, a linear PCL was synthesised as a reference material. All initiators were based on 2,2-bis(methylol) propionic acid (bis-MPA). ¹³C NMR spectra of the polymers showed that those with shorter arms contained unreacted hydroxyl groups on the core. Rheological measurements of zero shear rate viscosity, η₀, showed that the branched polyesters had a considerably lower η₀ than linear polyester with similar molecular weight. The low melt viscosity and the crystallity produced a rheological behaviour suitable for the film formation process for powder coatings. Measurements of mechanical properties of cured films showed that those with low arm molecular weight, M_a, were amorphous while those of high M_a were crystalline.     

Effects of solution viscosity on heterogeneous electron transfer across a liquid/liquid interface

Scanning electrochemical microscopy (SECM) is employed to investigate the effect of solution viscosity on the rate constants of electron transfer (ET) reaction between potassium ferricyanide in water and 7,7,8,8-tetracyanoquinodimethane (TCNQ) in 1,2-dichloroethane. Either tetrabutylammonium (TBA⁺) or ClO₄⁻ is chosen as the common ion in both phases to control the interfacial potential drop. The rate constant of heterogeneous ET reaction between TCNQ and ferrocyanide produced in-situ, k₁₂, is evaluated by SECM and is inversely proportional to the viscosity of the aqueous solution and directly proportional to the diffusion coefficient of K₄Fe(CN)₆ in water when the concentration of TCNQ in the DCE phase is in excess. The k₁₂ dependence on viscosity is explained in terms of the longitudinal relaxation time of the solution. The rate constant of the heterogeneous ET reaction between TCNQ⁻ and ferricyanide, k₂₁, is also obtained by SECM and these results cannot be explained by the same manner.     

Effect of temperature on viscosity of amylose

Viscosity parameters were obtained for maize maylose (molecular weight of 107,000) in 1N KOH at 25, 30, 35, and 40°C. Intrinsic viscosity continuously decreased and Huggins' constant k' continuously increased with increasing temperature. The temperature dependence of intrinsic viscosity, d[η]/dT, was ?2.12 × 10^?2/°C.     

Predictive correlation of binary diffusion and self-diffusion coefficients under supercritical and liquid conditions

The hydrodynamic equation D/T = αη^β, where D is the infinite dilution binary diffusion or self-diffusion coefficient, T is the temperature, η is the fluid viscosity, and α and β are constants, were demonstrated to be effective for predicting both binary diffusion and self-diffusion coefficients in high density fluids, i.e. liquid and supercritical states. When a solute was specified, the correlation well represented both binary diffusion and self-diffusion coefficients, irrespective of solvent over a wide solvent viscosity range. The solute-dependent constants α and β were determined for 12 solutes with average absolute deviation of 6.2% for 1006 data points.     

Study on the operating variables of sulcis coal hydroliquefaction

The hydroliquefaction of a high sulphur and bituminous Italian coal (Sulcis, Sardinia) was studied batchwise in a 1.5 dm³ autoclave to assess the influence of coal comminution (d_p = 45?664 μm), coal/solvent (c = 0.22 to 0.37 g coal/g solvent) and catalyst/coal (Y = 0?15 mg catalyst/g coal) ratios, and reaction time (t = 60?120 min) on the overall coal conversion (η_h), yields of oil (η_o) and asphaltene (η_a) and hydrodesulphurization (η_hs) by means of a composite design technique. Significant effects were observed on η_h by d_p, on η_o and η_a by Y, and on η_hs by Y and t, by means of an F-test on the basis of Yates's method. The variables were then fitted to a quadratic expression with an overall mean standard error of about 10%.The optimal range of the operating variables under the experimental conditions (i.e., 405°C, 150 bar) was derived by statistical treatment of the hydroliquefaction yield data and found to be d_p = 0.13 mm (100–150 mesh), c = 0.3 g coal/g solvent, Y = 13–15 mg catalyst/g coal and t = 100?130 min. Operating at these conditions results in an overall coal conversion approximately equal to 92%, oil and asphaltene yields ranging from 40 to 45%, and a 90% conversion of the initial sulphur into H₂S.     

Determining the liquidus viscosity of glass-forming liquids through differential scanning calorimetry

Viscosity at the liquidus temperature (T_L), η_L, is a critical parameter for the design of new glasses, particularly for industrial glass production where crystallization must be suppressed. However, a direct viscometric determination of η_L for a glass-forming system is difficult due to crystallization. Here we propose an alternative approach for determining η_L through differential scanning calorimetry (DSC). Specifically, DSC is used to measure both the viscosity curve and liquidus temperature of a glass-forming system and then derive its η_L value. The η_L values determined using DSC are found to be in excellent agreement with those measured through viscometry. The DSC approach is applicable to various glass-forming systems covering a wide range of fragilities and η_L values spanning over five orders of magnitude. Other advantages of this approach are its accuracy and small sample requirements.     

A novel determination technique of polymer viscosity-average molecular weights with flow piezoelectric quartz crystal viscosity sensing

A new method for the determination of polymer viscosity-average molecular weights was developed with flow piezoelectric quartz crystal (PQC) viscosity sensing. The experimental setup with a 9 MHz AT-cut quartz crystal and a flow detection cell was constructed and shown to be able to give highly reproducible data under the temperature of 25 ± 0.1°C and the fluid flow rate of 1.3–1.6 mL/min. A response model for PQC in contact with dilute polymer solutions (concentration <0.01 g/mL) was proposed in which the frequency change from the pure solvent, Δf_s, follows Δf_s = −k₆η_l^1/2 + k₇, where η_l is the absolute viscosity of dilute polymer solution and k₆ and k₇ are the proportionality constants. This model was examined with poly(ethylene glycol) samples (PEG-20000 and PEG-10000) under the aforementioned experimental conditions using water as solvent. The result was Δf_s = −1587η_l^1/2 + 1443. Based on this model, the method for the determination of polymer viscosity-average molecular weights, M_η, by flow PQC viscosity sensing was described and examined with an unknown poly(vinyl alcohol) (PVAL) sample. The new method proved to be an attractive and promising alternative for the determination of polymer molecular weights based on the good agreement between the molecular weight determined by the new method (M_η = 58600) for the unknown PVAL sample with that determined by the conventional capillary viscosity method. The new method has some advantages over the conventional viscosity method; for examples, operation is simpler and more rapid; the instruments required are cheaper and portable; the needed sample quantity is smaller; and the experimental setup constructed can be used in continuous measurement. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 63–69, 2001     

Molecular dynamics study on the viscosity of glass-forming systems near and below the glass transition temperature

Temperature-dependent viscosity is critical to decipher two profound questions in condensed matter physics, namely the glass transition and the relaxation of amorphous solids. However, direct measurement of viscosity over a large temperature range is extremely difficult. Here, using classical molecular dynamics (MD) simulations, we report a novel method to calculate the equilibrium viscosity of supercooled liquid both above and below the glass transition temperature (T_g) and to estimate the nonequilibrium viscosity of glass down to room temperature. Based on the shoving model, we derived an analytical formula showing that the shear viscosity in logarithmic scale changes linearly with the shear-induced variation in shear modulus or potential energy of the glass-forming system. The shear viscosity as a function of steady-state potential energy of liquid under different shear strain rates can be directly calculated in MD simulations; together with its equilibrium potential energy, one can extrapolate the zero-strain-rate equilibrium viscosity. We verified the proposed model by reliably calculating equilibrium viscosity near T_g of four glass-forming systems (Kob–Andersen system, silica, Cu_45.5Zr_45.5Al₉, and silicon) with different fragilities. Furthermore, our model can estimate the nonequilibrium viscosity of glass below T_g; the upper-bound nonequilibrium viscosity of amorphous silica and silicon at room temperature are calculated to be ~10³² and 10²⁵ Pa·s, respectively.