A rotational double coaxial cylinder viscometer

Summary Design principles for a rotational coaxial cylinder viscometer which directly measures viscosity and yield stress without need for any corrections have been developed. A viscometer with a rotating external cylinder is combined with one with a rotating inner cylinder. The torque is measured on a common tube which makes the inner cylindrical surface in the first viscometer and the outer one in the second one. Two rotational double cylinder viscometers are described in detail. The determinations are illustrated by measurements onNewtonian fluids, time-dependent shear thinning fluids, and a thixotropic suspension and by determination of zero shear viscosity of polymer solutions.

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Zusammenfassung Ein Viskosimeter mit einem äußeren rotierenden Zylinder ist mit einem Viskosimeter mit einem inneren rotierenden Zylinder zusammengebaut worden. Das Torsionsmoment wird an dem Hohlzylinder gemessen, der von der inneren Zylinderoberfläche des ersten Viskosimeters und von der äußeren Zylinderoberfläche des zweiten Viskosimeters abgegrenzt ist. Die Aufbauprinzipien sind entwickelt worden. Es ist möglich, die Viskosität und die Fließfestigkeit direkt als absolute Größen zu messen. Einige Messungen anNewtonschen und nicht-Newtonschen Flüssigkeiten, zeitabhängigen makromolekularen Lösungen und einer thixotropen Suspension werden mitgeteilt.

     

On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains

This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t=0⁺, is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions.     

Shear induced periodic structure changes in concentrated alumina suspensions at constant shear rate monitored by FBRM

Concentrated aqueous suspensions of alumina as disperse phase show a particular non-Newtonian time dependent flow behavior. The apparent viscosity measured by means of a rotational viscometer with coaxial cylinders at constant shear rate oscillates with time. The period of the oscillations varies on a scale of several hundred seconds. It is assumed that this behavior is caused by shear induced self-organized structure changes. In order to detect structure changes during the shear process a particle analysis system based on the focused beam reflectance measurement (FBRM) technique was applied. We have found a significant correlation between the oscillations of the viscosity and alterations of the chord length distribution.     

Rheology of coal suspensions

Proper design of operations encountered in preparation, transport and employment of suspensions like coal slurries and coal-oil mixtures require an accurate knowledge of their rheological behaviour.Such concentrated suspensions generally exhibit non-Newtonian behaviour (shearthinning) which is more pronounced at higher coal concentrations. The nature of the dispersing medium influences the aggregation state of the disperse phase and, consequently, affects the stability and the rheology of the systems. In the present paper coal suspensions prepared with different dispersing media and covering a wide range in solid phase concentration are studied, by using a rotational coaxial cylinders viscometer.Different models have been taken into consideration for correlating experimental data. In particular, in order to describe the dependence of viscosity on shear rate and solid phase concentration, the suitability of the model suggested by Smith and Bruce is evaluated. Accordingly, the aggregation state of the disperse phase as well as its dependence on shear rate and dispersing medium can be estimated.     

Heat transfer in flow of nonlinear fluids with viscous dissipation

The rotational flow of viscoplastic fluids between concentric cylinders is examined while dissipation due to viscous effects through the energy balance. The viscosity of fluid is simultaneously dependent on shear rate and temperature. Exponential dependence of viscosity on temperature is modeled through Nahme law, and the shear dependency is modeled according to the Carreau equation. Hydrodynamically, stick boundary conditions are applied, and thermally, both constant temperature and constant heat flux on the exterior of cylinders are considered. The governing motion and energy balance equations are coupled adding complexity to the already highly correlated set of differential equations. Introduction of Nahme number has resulted in a nonlinear base flow between the cylinders. As well, the condition of constant heat flux has moved the point of maximum temperature toward the inner cylinder. Taking viscous heating into account, the effects of parameters such as Nahme and Brinkman numbers, material time and pseudoplasticity constant on the stability of the flow are investigated. Moreover, the study shows that the total entropy generation number decreases as the fluid elasticity increases. It, however, increases with increasing Nahme and Brinkman numbers.     

A novel approach to high shear rate rheometry

A procedure is presented for converting torque-speed plots obtained from experiments using discs rotating rapidly in shear thinning materials into information on the viscosity function. The method is based on an exact boundary-layer solution for the power-law model and on the concept of pseudo-similarity of non-Newtonian flows. It enables the rheological behaviour to be evaluated at very high shear rates. Experimental data for concentrated shear-thinning kaolin suspensions at shear rates from 400 to 2 10⁵s^–1 are compared with values of the viscosity function obtained from customary viscometers of the Brookfield and Couette type.     

Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model

The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.     

Transient analytical solution for the motion of a vibrating cylinder in the Stokes regime using Laplace transforms

A new analytical solution for the motion of an elastic cylinder in a viscous fluid is derived using Laplace transforms. Unlike previously available solutions, full expressions for transient terms are given. The solution is compared with conventional treatments of this problem. It is expected to have particular value for applications related to viscosity measurement using vibrating-wire viscometers applied to higher viscosity fluids.     

Evaluation of high shear viscosity data from jet and concentric cylinder viscometers

Summary This work compares and evaluates viscosity data obtained on similar fluids by two widely accepted high shear techniques. Both the jet and concentric cylinder viscometers are useful high shear methods. The major limitation of the jet viscometer is an inability to distinguish quantitatively between energy losses in laminar flow and those due to capillary geometry and experimental conditions. For example, the jet viscometer gives minima in viscosity-shear rate correlations which are difficult to treat. These minima are not found in concentric cylinder viscometer data for the same and similar fluids. The apparent viscosity increase at high shear in the jet may be due to factors other thanReynold's turbulence, as previously supposed. This effect may be due to molecular relaxation phenomena in certain cases. The jet viscometer might thus be used to evaluate molecular relaxation and/or other phenomena contributing to this effect.For a variety of systems, the concentric cylinder viscometer gives significantly smaller temporary viscosity losses due to shear than do the jet viscometer data. These comparisons are made using the maximum jet shear rate at the capillary wall. The differences are, of course, larger if average shear rates are used to compare the data. It is concluded that the jet viscometer results tend to be erroneous. This is possibly due to capillary end effects or problems with kinetic energy corrections.     

Unsteady flow of an elastico-viscous fluid between two coaxial circular cylinders

Unsteady flow of an Oldroyd fluid between two coaxial circular cylinders is investigated, the fluid being set in motion as the inner cylinder moves from rest for a certain period with linearly growing speed and then stops suddenly. The Laplace transform technique is used to derive the solution. For the case when the gap between the cylinders is small, a simplified solution is obtained. The expression for the shear stress on the wall of the outer cylinder is obtained and particular cases are discussed.     

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.Originally presented at the Annual European Rheology Conference 2003, AERC 2003     

Rotational rheometry of liquid metal systems: Measurement geometry selection and flow curve analysis

In the present study, a rotational measurement technique was used to evaluate viscosities of liquid metals and metallic alloys. Three types of measurement geometries in a high temperature rotational rheometer were evaluated: cone and plate, DIN coaxial, and double concentric cylinder (DCC). The DCC geometry proved to be the most effective. An analytical solution has been presented to evaluate the viscosity as a function of shear rate for DCC geometry. The flow curves and shear viscosities of pure Al, pure Zn and Sn_95.8Ag_3.28Cu_0.92 solder alloy have been evaluated as a function of shear rate and melt superheat temperature. It is proposed that liquid metal systems are non-Newtonian and strongly shear thinning in flow behavior.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Rheological behavior of silica suspensions flocculated by bridging

The viscosity and stress relaxation behavior of silica suspensions in polyacrylamide (PAAm) solutions have been studied as a function of particle concentration, particle diameter, and molecular weight of PAAm by the use of a coaxial cylinder type rheometer. The effects of polymer adsorption on the flocculation of particles and the rheological behavior are discussed in terms of bridging. The suspensions of 10-nm silica are remarkably pseudoplastic because the particles are easily flocculated by bridging. The ability of PAAm to flocculate silica particles is very extensive at a molecular weight of 5.5 × 10⁶. For suspensions of 20-nm silica in a solution of PAAm with M_W = 5.5 × 10⁶ − 1 × 10⁷, the apparent viscosity irreversibly increases with shearing time at shear rates beyond a certain value. This may be due to the flocculation by the shear-induced bridging. The suspensions of 40-nm silica show similar flow behavior to the medium irrespective of molecular weight of PAAm. The bridging flocculation is not expected for large particles as one polymer molecule cannot bridge through many particles.     

Axial Couette flow of an Oldroyd-B fluid in an annulus

This paper establishes the velocity field and the adequate shear stress corresponding to the motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders by means of finite Hankel transforms. The flow of the fluid is produced by the inner cylinder which applies a time-dependent longitudinal shear stress to the fluid. The exact analytical solutions, presented in series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. The general solutions can be easily specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid motion are graphically illustrated.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

RETRACTED ARTICLE: Flow of fractional Maxwell fluid between coaxial cylinders

This paper deals with the study of unsteady flow of a Maxwell fluid with fractional derivative model, between two infinite coaxial circular cylinders, using Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, at time t = 0⁺, is subject to a time-dependent longitudinal shear stress. Velocity field and the adequate shear stress are presented under series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of general solutions. Finally, the influence of the pertinent parameters on the fluid motion as well as a comparison between the three models is underlined by graphical illustrations.     

Rheokinetics of urea-formaldehyde resins gelation

Rheokinetics of gelation of aqueous suspensions of urea-formaldehyde oligomers was studied. Experiments were carried out with a rotational viscometry method using two regimes of deformation: constant stress or constant shear rate. It was shown that a maximum on a viscosity vs. time curve is observed and it reflects sedimentation of rather large gelled particles. Then, gelation of a whole system (determined as the point of the unlimited growth of viscosity) takes place. Experiments carried out at different temperatures gave us an apparent activation energy which depends on the oligomer content in a composition. Characteristic points of a rheokinetic curve do not depend on the concentration of a curing agent. The problem of the temperature increase due to heat dissipation is also discussed. It was demonstrated that shear stress is a kinetic factor influencing the rate of a reaction. A master curve for a rheokinetic curve was constructed, time scale being reduced by the gel time.