Viscosity of water at 20°C

The viscosity of water in the 19.5–25.5°C temperature range was redetermined by a group of workers at the Norwegian Institute of Technology in 1988, under the stimulus from the IUPAC Subcommittee on Transport Properties headed by Professor J. Kestin. This Note explains an apparent discrepancy, reported in the original work, between the damping-sensitive and the period-sensitive solutions of the working equations employed. The disagreement between the two viscosities reduces to 0.0001 mPa · s, or 0.01 %, when the appropriate corrections to the period are introduced.Paper dedicated to Professor Joseph Kestin.     

Oscillating Cup Viscosity Measurements of Aluminum Alloys: A201, A319 and A356

An oscillating cup viscometer was developed to measure the absolute viscosities of molten metals. Previous experiments established the capability of the apparatus to characterize the viscosities of molten nickel-based superalloys. However, modifications to the instrument and its theoretical analysis were required for reliable measurements on molten aluminum alloys, presumably due to their lower densities and lower viscosities. The theoretical literature for the fluid flow inside an oscillating cup is reviewed, and a working equation without any correction factor is developed for the improved viscometer. Some design parameters of the viscometer that directly affect the accuracy of viscosity estimation by using the working equation are discussed. A special vertical furnace was adopted to uniformly heat a longer cylindrical sample (10 mm inner diameter and 120 mm length) with a temperature difference of less than 2°C over the sample length. The measuring procedure was also improved to get more accurate motion parameters. It is estimated that the working equation and improved instrument provide an uncertainty of less than 4%. In addition, applications and experimental data are presented for pure aluminum and three aluminum alloys: A201, A319, and A356.     

Mixed convection flow in a porous medium bounded by two vertical walls

The aim of the investigation is to study the fully developed mixed convection flow in a porous medium bounded by two vertical walls having a linear axial temperature variation. Solution of the governing second order simultaneous differential equations, derived by non-dimensionalising the momentum and energy equations, has been obtained by converting them into a fourth order differential equation. It has been found that the fourth order differential equation has five different solutions depending upon the values of the Darcy number, Rayleigh number and ratio of the effective viscosity of the porous domain to the viscosity of the fluid. Graphical representation of the analytical solution shows that the flow is of parabolic type only for higher Darcy number whereas there is a reverse type of motion for lower Darcy numbers. The effect of the ratio of the effective viscosity of the porous matrix to the viscosity of the fluid is to decrease the velocity field.     

An Absolute Viscometer-Densimeter and Measurements of the Viscosity of Nitrogen, Methane, Helium, Neon, Argon, and Krypton over a Wide Range of Density and Temperature

An apparatus for the simultaneous measurement of viscosity and density of fluids is presented. The viscometer-densimeter covers a viscosity range up to 150 µPas and a density range up to 2000 kgm^–3 at temperatures from 233 to 523 K and pressures up to 30 MPa. Very accurate density measurements with uncertainties of ±0.02 to ±0.05% have always been carried out with this apparatus, although in its first version it was necessary to calibrate the viscosity measuring system on a reference fluid in order to achieve uncertainties of ±0.6 to ±1.0% in viscosity. After significant improvements, the apparatus now achieves uncertainties in viscosity of less than ±0.15% in the dilute gas region and less than ±0.4% for higher densities. Moreover, the viscosity measuring system can be described in an absolute way; calibration is no longer necessary. In order to test the advanced apparatus and to determine viscosity-density values of very high quality, comprehensive measurements on nitrogen, argon, and methane were carried out in the entire working range of the viscometer-densimeter. In addition, viscosity-density measurements on helium, neon, and krypton were made on two selected isotherms each. All measurements show that the estimated total uncertainty of ±0.15 to ±0.4% in viscosity and of ±0.02 to ±0.05% in density is clearly met. In order to verify the results of the combined viscometer-densimeter, a new apparatus for very accurate viscosity measurements was designed. While the working range of this apparatus is restricted to the dilute gas region, it yields uncertainties of less than ±0.07% in viscosity. Measurements carried out with this apparatus confirmed the previously measured values of the combined viscometer-densimeter within ±0.03%.     

Measurement of the viscosity of HCFC 123 in the temperature range 233–418 K and at pressures up to 20 MPa

The viscosity of HCFC 123 was measured over the range of temperature from 223 to 418 K and pressure up to 20 MPa. The experimental method was that of the capillary flow and a closed-circuit high-pressure viscometer was used. The sample fluid was circulated through a Pyrex glass capillary from a high-pressure plunger system. The constant of the Pyrex glass capillary was calibrated against the reference standard, pure water. The viscosity of the sample was calculated from the flow rate, the pressure drop at the capillary, and the capillary constant using the Hagen-Poiseuille equation. Measurements were made on seven isotherms. In the case of the transpiration method, the density is needed for calculation of the viscosity from the kinematic viscosity. The available density data of HCFC 123 are less reliable than those for CFC 11. Therefore, uncertainty in the viscosity of HCFC 123 is larger, although the measured kinematic viscosity itself has a reproducibility of 0.1 %. HCFC 123 is proposed as an alternative to CFC 11. Comparisons of the data for these two substances show that the viscosity of HCFC 123 is similar in magnitude to that of CFC 11 at temperatures around 350 K, higher at lower temperatures, and lower at higher temperatures. The pressure gradients for these two corresponding substances are similar over the entire temperature range.     

The theory of oscillating thick wings in subsonic flow. Lifting line theory

Summary On the basis of the fundamental solutions method developped by the author in some previous papers, in this paper a theory of oscillating thick wings in subsonic flow is given. In this way the representation of the general solution for arbitrary wings and the integral equation of the problem are obtained. The known solutions for the stationary motion and the plane problem are regained as particular cases. General solutions and integral equations for the incompressible fluid and for the two and three dimensional motion at Mach number one are also put into evidence. In the last part of the paper the theory of oscillating lifting line is given.     

Measurements of the viscosities of saturated and compressed fluid 1-chloro-1,2,2,2-tetrafluoroethane (R124) and pentafluoroethane (R125) at temperatures between 120 and 420 K

The shear viscosities of saturated and compressed fluid 1-chloro-l,2,2,2-tetrafluoroethane (R124) and pentafluoroethane (R125) have been measured with two torsional crystal viscometers at temperatures between 120 and 420 K and at pressures up to 50 MPa. At small molar volumes, the fluidity (reciprocal viscosity) increases linearly with molar volume at fixed temperature and weakly with temperature at fixed volume. We have described this behavior with simple empirical equations and have compared the data of Shankland and of Ripple with them. The data of Ripple are in good agreement with our data for both fluids.     

Electroviscoelastic stability of a Kelvin fluid layer

The electroviscoelastic stability of a Kelvin fluid layer under the effect of a constant tangential electric field is discussed. The linear perturbation is considered. The analysis includes all possible modes of perturbations. A fourth-order partial differential equation is introduced to control the fluid motion. Applications of the boundary conditions lead to two simultaneous ordinary differential equations. A transcendental dispersion equation is obtained. A case of large viscosity is considered in order to simplify the complexity of the dispersion relation. The growth rate with respect to the retardation time parameter is carried out. The necessary and sufficient conditions for stability are introduced. It is found that the retardation time parameter has a stabilizing effects as well as the viscosity parameter, in the presence of the field. It is also, shown that viscosity and elastic parameters play against the density destabilization effects. It is shown that the tangential electric field plays a dual role in the stability criteria.     

A High-Temperature Viscometer for Molten Materials

An oscillating-cup viscometer for the measurement of the viscosity of molten materials from room temperature to 1400 K was developed. The instrument is described in detail and the working equations are presented. The operational behavior was tested with water at room temperature. Preliminary measurements show that the new viscometer is capable of measuring the viscosity of water at room temperature to within 0.2%. As the primary objective of this work is the establishment of standard reference data for high-temperature viscosity measurements in molten salts, molten metals, and molten semiconductors, references of earlier viscosity measurements of molten KNO₃ are given.     

Physical property measurements for the mathematical modeling of fluid flow in solidification processes

Measurement methods are being developed to provide values for the density, viscosity, heat capacity, enthalpy, fraction solid, surface tension, and thermal diffusivity and conductivity of commercial alloys in the liquid and mushy states. These data are needed for the mathematical modeling of heat and fluid flow in solidification processes. This paper briefly describes the present state of development of apparatus for the measurement of density by the levitated drop and hydrostatic probe methods and viscosity by the oscillating viscometer in our laboratory. Paper presented at the Fourth Asian Thermophysical Properties Conference, September 5–8, 1995, Tokyo, Japan.     

Magnetic Damping Effects in Forced-Oscillation Vibrating-Wire Viscometers

Vibrating wire viscometers rely on the principle that the viscosity of the fluid surrounding the wire provides the dominant damping action on the motion of the wire. However, some residual damping is always present due to other effects such as internal friction of the wire (anelastic relaxation), losses through the wire supports, and magnetic damping. Magnetic damping is a physical mechanism that has received relatively less attention than internal friction in the context of viscometers. The phenomenon arises because the current induced by the motion of the wire contributes to the magnetic field in such a way as to oppose its own motion. For a test circuit using a 40 μm diameter tungsten wire in a 0.3 T magnetic field, surprisingly, the effect of magnetic damping was found to be of a similar order of magnitude to other non-viscous damping effects. The effect can be accounted for by including the internal impedance of the oscillating voltage source in the model and it disappears completely for a perfect oscillating current source.     

Transversely Oscillating MEMS Viscometer: The “Spider”

The analysis of a new viscometer that takes the form of an oscillating plate, fabricated from silicon using the methods of micro-electro-mechanical-systems (MEMS) is considered. The instrument is designed principally for experimental use in the oil industry. The plate is 1.6 mm wide, 2.4 mm long, and 20μm thick. It is suspended from a 0.4 mm thick support by 48 square cross-section legs, each of length 0.5 mm width and depth of 20μm. The process of lithography is used to deposit layers atop the silicon. These layers can then be formed into resistors and metallic tracks. The tracks traverse the supporting legs to provide connections between the plate and external electronics. The oscillating plate is a mechanical element that can be set in motion by the force produced by the interaction between an electric current flowing in the plate and an externally applied magnetic field. The viscometer can be operated either in forced or transient mode and is intended for use in both Newtonian and non-Newtonian fluids. The motion of the viscometer is analyzed for incompressible fluids, using the Navier–Stokes equations to model the flow for both a Newtonian viscous fluid and a viscoelastic fluid where the stress is modeled by a reduced form of Maxwell’s equations.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system

The motion of electrically conducting, Oldroyd-B and incompressible fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower plate is at rest and the upper plate is oscillating in its own plane. The governing partial differential equation of this problem, subject to boundary conditions are solved analytically. The expressions for the steady and unsteady velocity fields for the conducting Oldroyd-B fluid are obtained. The graphs are plotted for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field, the rotation and the material parameters of the fluid.     

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

In the petroleum industry, measurements of the density and viscosity of petroleum reservoir fluids are required to determine the value of the produced fluid and the production strategy. Measurements of the density and viscosity of petroleum fluids require a transducer that can operate at reservoir conditions, and results with an uncertainty of about ±1% in density and ±10% in viscosity are needed to guide value and exploitation calculations with sufficient rigor. Necessarily, these specifications place robustness as a superior priority to accuracy for the design. A vibrating plate, with dimensions of the order of 1 mm and a mass of about 0.12 mg, clamped along one edge, has been fabricated, with the methods of Microelectromechanical (MEMS) technology, to provide measurements of both density and viscosity of fluids in which it is immersed. The resonance frequency (at pressure p = 0 is about 12 kHz) and quality factor (at p = 0 is about 2800) of the first order bending (flexural) mode of the plate are combined with semi-empirical working equations, coefficients obtained by calibration, and the mechanical properties of the plate to provide the density and viscosity of the fluid into which it is immersed. When the device was surrounded by argon at temperatures between 348 and 423 K and at pressures between 20 and 68 MPa, the density and viscosity were determined with an expanded (k = 2) uncertainty, including the calibration, of about ±0.35% and ±3%, respectively. These results, when compared with accepted correlations for argon reported in the literature, were found to lie within ±0.8% for density and less than ±5% for viscosity of literature values, which are within a reasonable multiple of the relative combined expanded (k = 2) uncertainty.     

Surface Oscillations of an Electromagnetically Levitated Droplet

The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k−ɛ turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.     

Viscosity Correlation for Isobutane over Wide Ranges of the Fluid Region1

A new representation of the viscosity of isobutane has been developed. The representative equations include zero-density and initial-density dependence correlations. The higher density contributions to the residual viscosity are formed by a combination of double polynomials in density and reciprocal temperature and of a free-volume term with a temperature-dependent close-packed density. The new full surface correlation is based on primary experimental data sets selected as a result of a critical assessment of the available information. The validity of the representation extends from the triple point to 600 K and 35 MPa in accordance with the modified Benedict–Webb–Rubin equation of state by Younglove and Ely (1987). The uncertainty of the representation varies from ±0.4% in the dilute gas phase between room temperature and 600 K to ±3% in the thermodynamic ranges in which the equation of state is valid as well as where primary experimental data are available.     

On the effectiveness of variation in the physical variables on the steady MHD flow between parallel plates with heat transfer

The influence of variation in physical variables on the steady Hartmann flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal and electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing non‐linear coupled equations of motion and the energy equation is obtained. The effect of magnetic field, the temperature dependent viscosity, thermal conductivity, and electric conductivity on both the velocity and temperature distributions is examined. Copyright © 2005 John Wiley & Sons, Ltd.     

Viscosity of Gaseous HFC-125 (Pentafluoroethane) Under High Pressures

This paper reports experimental results lor the viscosity of gaseous HFC-125 (pentafluoroethane) under high pressures. The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K and at pressures up to the saturated vapor pressures at each temperature at subcritical conditions or up to 9 MPa at supercritical temperatures. Intermolecular scaling parameters of HFC-125 for the extended corresponding states were determined from the viscosity data at 0.1 MPa. An empirical viscosity equation is proposed to interpolate the present experimental results as a function of temperature and density.     

Viscous Equations of Fluid Film Dynamics

We model viscosity in the framework of the exact nonlinear equations of fluid film dynamics. The proposed approach yields monotonic dissipation of energy and guarantees that viscous forces are not engaged when the film undergoes rigid motion. With the addition of viscosity, the governing system has all the essential elements - inertia, surface tension, interaction with the ambient medium, influence of external fields and, now, viscosity - for accurate prediction and interpretation of experimental observations. The fluid film is modelled as a two-dimensional manifold. The film's thickness is represented by a surface density function. The resulting system is the fluid film equivalent of the classical Navier-Stokes equations. The domain of definition of the fluid film equations is a deforming manifold which makes computer simulation the mostly likely course for obtaining solutions.     

Viscosity of saturated R152a measured with a vibrating wire viscometer

Earlier reported values of the viscosity coefficient of the refrigerant R152a (1,1-difluoroethane) have been recalculated with an improved value for the mechanical damping of the vibrating wire viscometer. The measurements were taken along the saturation line both in the saturated liquid and in the saturated vapor every 10 K from 243 up to 393 K by means of a vibrating wire viscometer The damping of the vibration of the wire is a measure for the viscosity provided that the mechanical damping is subtracted. The latter is usually measured in vacuum. It turns out that the damping value measured in this way depends on the vacuum pressure and on the way the wire has been handled before. It appeared that the damping applied previously, measured after 6 days of pumping, is too small, resulting in values of the viscosity coefficient which are too large. The effect on the data for the saturated-liquid viscosity is small, but the new saturated-vapor viscosity data agree much better with the unsaturated-vapor data reported by Takahashi et al.