Rheological study of black coal-oil suspensions

The rheological study of coal-oil suspensions is very important because of their application in many industries as alternative fuels to petroleum oil. In this work, the flow behaviour of black coal-oil suspension was studied for a range of coal volume fractions from 0.0378 to 0.427. Shear stresses were measured for shear rates up to 200 s^–1 using a Weissenberg Rheogoniometer. All the suspensions behaved like non-Newtonian liquids and exhibited significant increases in apparent viscosity on storage. The flow behaviour of both freshly prepared and aged suspensions was able to be described by power-law models. A model similar to that given by Chong was used to establish relation between the relative apparent viscosity and coal volume fraction for freshly prepared as well as all aged suspensions. A correlation was also established between ageing time and maximum coal volume fraction. a constant in eq. (9) - A, B constants - K consistency index, Pa s^–n - n power-law index - S structure - t time, hrs - µ _a apparent viscosity, Pa s - µ _r relative viscosity - volume fraction - _m maximum volume fraction - shear stress, Pa - sus suspension - sol solvent - standard deviation     

Effects of electric fields and volume fraction on the rheology of hematite/silicone oil suspensions

Electrorheological (ER) fluids composed of iron(III) oxide (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. The dielectric properties of the suspensions were first studied in order to get information about the conductivity of the solid. Rheological tests under a.c. electric fields elucidated the influence of the electric field strength and volume fraction on the field-dependent yield stress. It was found that this quantity scales as a square power law in both cases. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The ER behaviour of the suspensions was analysed by considering the fundamental forces (of hydrodynamic and electrostatic origin) acting on the particles and it is found that, at a given volume fraction, all the dependencies of relative viscosity on shear rate and field strength can be described by a single function of the Mason number, Mn. Finally, two different chain models were used to explain the shear-thinning behaviour observed: rheological measurements showed a power-law dependence of relative viscosity decrease on the Mason number, _F~Mn, with –0.95.     

PIV measurements of velocities and concentrations of wood fibres in pneumatic transport

A method for simultaneous measurement of the concentration and velocity of wood fibres suspended in air was developed. The velocity of the wood fibres was measured by the use of particle image velocimetry (PIV). The concentration of wood fibres was measured using the raw images from the PIV equipment as input data. An image processing procedure was used to determine the volume fraction of the fibre particles in the images. The method gave good qualitative and quantitative results for low volume fractions of fibres; for higher volume fractions the quantitative results were unsatisfactory.Latin letters C Concentration of fibres [g/m³] - d Diameter of fibre [m] - M_w Water mass [kg] - M_f Fibre mass [kg] - m Calibration mass flow [kg/s] - m₂₅ Calibration mass flow at C=25 g/m³ [kg/s] - n Fan rpm [-] - t Thickness of light sheet [m] - t Time between laser pulses [s] - U_i Velocity component in i-direction [m/s] - v Streamwise velocity [m/s] - v_average Average streamwise velocity [m/s] - x_i Particle displacement in i-direction [m] Greek letters _f Volume fraction of fibres [-] - _average Average volume fraction of fibres [-] - Area fraction of fibres in image [-] - Density of fibre particle [kg/m³]     

Yield stress and maximum packing fraction of concentrated suspensions

The yield stress and features of the structure of concentrated suspensions based on silica flour, with particles of average diameter around 4 m, were investigated in terms of a phenomenological model. The yield stress of a concentrated suspension of known solid volume concentration is estimated by employing a shear-dependent maximum packing fraction _m which is obtained by model fitting equilibrium viscosity data, and by incorporating a first-order kinetic equation. The model proposed was examined by using several mineral suspensions in which silica flour was mixed with metal oxide particles so that microstructural features of the suspensions could be adjusted. A cocoa fat suspension was also used as a test sample having radically different chemistry. The agreement between the model prediction and independently obtained experimental evidence is acceptable. Furthermore, a qualitative explanation is obtained by a scaling analysis in an effort to relate the model parameters with the suspension structure that stems from interactions among the suspension constituents.     

Die swell of filled polymer melts

The Barus effect in polypropylene and polystyrene blended with a variety of fillers at various concentrations was investigated using a capillary extrusion rheometer. If the die swell is defined as the square of the ratio of the extrudate diameterd to the die diameterD, it is found to depend on the apparent shear stress _W . Below a certain value of _w the relation =B _B ^A applies. The die swell, _M , of a filled polymer depends on the type, size and volume fraction of the filler. In particular,A increases as the volume fraction increases and is largest for powders, smaller for flakes and smallest for fibres, whereasB shows the opposite trend but to a lesser extent.     

An empirical equation of the relative viscosity of polymer melts filled with various inorganic fillers

Summary Based on Maron-Pierce's equation, an empirical equation was suggested, which relates the relative viscosity ( _r ) of the polymer melt filled with various inorganic filler, such as glass fiber, carbon fiber, talc, precipitated- and natural-calcium carbonate powder, and glassy small sphere, to the volume fraction () of the filler. The equation is _r = (1 –/A)^–2, whereA is a parameter relating to the packing geometry of the filler, which is similar to the parameter ₀ in Maron-Pierce's equation. In the equation _r is defined as the ratio of the viscosity of the filledsystem to that of the medium at the same shear stress not the shear rate. The applicability of the equation is above the shear stress about 10⁴ dyne/cm². The equation has a simple form and is considered to have a practical utility for filled-polymer melt systems.With 2 figures and 1 table     

Fragile networks and rheology of concentrated suspensions

Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic -Fe₂O₃ and non-magnetic -Fe₂O₃ particles in mineral oil are interpreted with the model proposed.Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G was found to follow a scaling law of the type G ( _f - _f ^c ) ^f , where _f is the volume fraction of flocs in suspension, and _f ^c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.     

A non-affine network model for polymer melts

In this paper, a network model of polymer melts is proposed in which network junction points move non-affinely. In this non-affine motion, junction points follow particle paths as seen by an observer rotating at the fluid element's net rigid-rotation rate. The speed at which junction points move is reduced as the network segments near their maximum extensions. In order to maintain a frame invariant model, it is necessary that the vorticity be decomposed into two portions, such that, = _R + _D . The deformational vorticity, _D , arises from shear deformation and is frame invariant while the rigid vorticity, _R , is frame dependent. A constitutive equation based on this finitely extensible network strand (FENS) motion is developed. The model illustrates how rotations that cause changes in the relative orientation of a fluid element with its surroundings can be incorporated into a constitutive equation using the deformational vorticity. The FENS model predicts a shear-thinning viscosity, and the Trouton viscosity predicted by the model is finite for all elongation rates. Finally, stochastic simulation results are presented to justify a mathematical approximation used in deriving the constitutive equation.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.     

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u _i , electric displacement D _i and volume fraction ρ _I of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction ρ _I of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch. The project supported by the National Natural Science Foundation of China (10572138).