Temperature and Pressure on Viscosity

It is evident from the discussions in Chapters 2 and 3 that the various aspects of hydrodynamic lubrication problems can range from the classical isoviscous, isothermal solutions of the simple Reynolds equation to short-time squeeze film behavior on impact. In dealing with elastohydrodynamic and impact problems, viscosity can no longer be taken as constant but instead must be introduced in a manner which correctly accounts for its response to temperature and pressure. As background for the appreciation of the intricacies of such problems we shall examine the effects of temperature and pressure on the viscosity of liquids, particularly those which can be used as lubricants. 

The Walther Equation and ASTM Viscosity-Temperature Charts 

This equation is empirical. In an early version v was in centistokes and a was 0.8. Using essentially this type of log-log relationship, the American Society for Testing and Materials developed charts on which viscosity data for lubricating oils give straight lines when plotted against temperature [24]. The older version of the charts 

For viscosities in the range 2 to 20,000,000 centistokes the following empirical evaluation of Z is used  

To carry the chart into the region of viscosities lower than 2.00 centistokes the evaluation of Z must be modified  

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Theories of liquid viscosity such as are presented in this chapter afford an insight into the mechanism of viscosity even when it becomes necessary to resort to adjustable constants in dealing with real liquids, other than those of the simplest molecular structure. The potential significance of such theories for practical lubrication lies in the development of general relations between viscosity behavior and molecular structure in lubricating liquids, relations which can talte the prediction of the effect of temperature and pressure on viscosity out of the realm of the grossly empirical and permit confident extrapolation of easily obtained data for use in difficult circumstances. 

MOTOSH, N. "Cylindrical journal bearings under constant load, the influence of temperature and pressure on viscosity", Proc. IME, in, Pt 3N, 1963, 148-160. 

Temperature and pressure affect the operation of fluid-particle systems because they affect gas density and gas viscosity. It is the variation in these two parameters that determine the effects of temperature and pressure on fluid-particle systems. Increasing system temperature causes gas density to decrease and gas viscosity to increase. Therefore, it is not possible to determine only the effect of gas viscosity on a system by changing system temperature because gas density is also changed and the resulting information is confused. Very few research facilities have the capability to change system pressure to maintain gas density constant while the temperature is being changed to vary gas viscosity. 

The effects of temperature and pressure on fluidized-bed systems cannot be considered independently of particle size. Whether temperature and pressure have an effect (and indeed, even the direction of that effect) on a system, depends strongly on particle size. In addition, the type of interaction between gas and solids, i.e., whether the interaction is due to momentum or drag, determines if gas viscosity has an effect upon the system. As will be shown, gas viscosity is not important in systems in which momentum is important, but is important in systems dominated by drag. 

Viscosity is an important property of residual fuel oils, as it provides information on the ease (or otherwise) with which a fuel can be transferred from storage tank to burner system under prevailing temperature and pressure conditions. Viscosity data also indicate the degree to which a fuel oil needs to be preheated to obtain the correct atomizing temperature for efficient combustion. Most residual fuel oils function best when the burner input viscosity lies within a certain specified range. 

Non-Newtonian fluids are generally those for which the viscosity is not constant even at constant temperature and pressure. The viscosity depends on the shear rate or, more accurately, on the previous kinematic history of the fluid. The linear relationship between the shear stress and the shear rate, noted in Equation (1), is no longer sufficient. Strictly speaking, the coefficient of viscosity is meaningful only for Newtonian fluids, in which case it is the slope of a plot of stress versus rate of shear, as shown in Figure 4.2. For non-Newtonian fluids, such a plot is generally nonlinear, so the slope varies from point to point. In actual practice, the data... 

The dielectric constant of supercritical water is in the range of 2 to 3. This range is similar to the range of nonpolar solvents such as hexane or heptane, which have dielectric constants of 1.8 and 1.9, respectively. When hazardous wastes are heated to high temperature and pressure, physical properties such as density, dielectric constant, viscosity, diffusivity, electric conductance, and solubility are optimum for destroying organic pollutants. Table 10.2 lists the characteristics of supercritical water, and Figure 10.3 illustrates the influence of temperature and pressure on the dielectric constants and density of water. As both temperature and pressure increase, the dielectric constants and density of water decrease dramatically. 

Theory of matter but this subject is beyond the scope of this book. It is interesting to note that these effects of temperature and pressure on the viscosity of gases were first predicted by theory and then experimentally verified. As the pressure on a perfect gas is increased it becomes imperfect and its behavior approaches that of a liquid. Con-... 

Very few of the elements listed on the Periodic Table of Elements exist as liquids at standard temperature and pressure. On the other hand, approximately three-fourths of our planet is covered with the liquid known as water, so you should be very familiar with the properties of liquids. Unlike solids, liquids do not have definite shape. If you pour a liquid from a cylindrical bottle into a square container, it changes shape to match the container. This is possible because the motion of the individual particles within the liquid is much less restricted than in a solid. The particles are not locked into fixed positions, and they push past each other, allowing the liquid sample to flow. Some liquids, such as water, flow readily, whereas other liquids, such as molasses, are said to be viscous and flow slowly. The viscosity of a liquid is its relative resistance to flow. Regardless of how fluid a liquid is, the space that a liquid occupies is more fixed, and it will not expand to occupy an entire vessel the way a gas will. 

The HCToolkit is a set of Perl modules that implement four equations of state, two flash algorithms and a multi-component, multiphase, temperature- and pressure-dependent viscosity prediction. The modules have been successfully run on MS Windows, Mac OSX and Redhat Linux. These modules can be called from another Perl code, or (via an ActiveX interface) from a front-end written in either Visual Basic or a VBA application such as Excel. 

For a polymer of constant composition, it is a common practice to determine its viscosity curve, as the one shown in Figure 22.6. The obtained curve is valid for a given set of experimental conditions, that is, for a given pressure and temperature. In general terms, the viscosity increases as temperature decreases or pressure increases. According to Reference 23 at lower values of shear rate, a decrease of temperature has a similar effect to an increase of pressure. There is a method that makes use of a semiempirical relationship to take into account the effects of temperature and pressure on the viscosity curve. This method is based on the concept of a master curve and essentially it allows for the construction of a viscosity curve from a reference curve and a single viscosity value [15]. 

A master curve can be constructed as indicated in Figure 22.8, where the zero-shear-rate viscosity t]q has to be evaluated for each one of the indicated viscosity curves. Both, the effect of temperature and pressure on the viscosity versus shear rate curve can be addressed by considering a shift factor that may be related, for instance, to the free volume of the system by means of the Williams, Landel, and Ferry (WLF) equation [9, 15, 23, 24]. With the aid of this shift factor, the new viscosity curve can be constructed from known viscosity values and the reference curve at the prescribed values of temperature and a pressure. The use of shift factors to take into account the temperature dependence on the viscosity curve was also used by Shenoy et al. [19-21] in their methodology for producing viscosity curves from MFI measurements. 

Generally, diffusivity is faster and viscosity lower for supercritical fluids than for liquids. A standard value of the diffusivity of solutes in liquids is roughly 10 cm s [4] the diffusion coefficient of naphthalene in CO2 at 10 MPa and 40 °C is 1.4 10 cm s and the self-diffusion coefficient of CO2 itself is two orders of magnitude higher than that of liquids [9]. The effect of temperature and pressure on the self-diffusivity of CO2 is illustrated in Figure 6. Diffusivity is obviously a major consideration in reactions whether they be homogeneously, heterogeneously, or not catalyzed, and it will determine whether a reaction is controlled kinetically or by diffusion. 

From a kinetic viewpoint, salinity action on the water solution structure is similar to the action of temperature and pressure. This was a reason to compare the effect of temperature and pressure, on the one hand, and salinity, on the other, on the mobility of solution components, and therefore, on its structure. In this connection John Desmond Bernal (1901-1971) and Ralph Howard Fowler (1889-1944) introduced the concept of structural temperature of the solution. Under their definition, structural temperature of a given solution is equal to the temperatme of pine water with the solution s structural properties (viscosity, density, refraction, etc.). Ions with positive hydration work as lowering of temperature and have structural temperature below the solution temperature ions with negative hydration - as increase of temperature, and their structural temperature is higher than the solution s temperature. Non-polar compounds occupy plentiful space, thereby lowering the intensity of translation motion of the water molecules, lowering the structural temperature of the solution, as in a case of positive hydration. 

A generalized analysis that combines the effects of shear, temperature and pressure on the rheological parameters, may lead to an expression of a so-called effective viscosity, p, for a power-law liquid in a limited operational range. 

In Chapter 1 of this book, the necessary parameters for both RDE/RRDE analysis in ORR study, such as O2 solubility, O2 diffusion coefficient, and the viscosity of the aqueous electrolyte solutions, are discussed in depth in terms of their definitions, theoretical backgroimd, and experimental measurements. The effects of type/concentration of electrolyte, temperature, and pressure on values of these parameters are also discussed. To provide the readers with useful information, the values of these parameters are collected from the literature, and summarized in several tables. In addition, the values of both the O2 solubility and diffusion coefficient in Nafion membranes or ionomers are also listed in the tables. Hopefully, this chapter would be able to serve as a data source for the later chapters of this book, and also the readers could find it useful in their experimental data analysis. 

A critical step in the data analysis procedure is the correction of the calculated apparent viscosity for the influences of pressure and viscous heating. The key element in this procedure is the approximation that the fractional change in the viscosity of the polymer solution due to pressure and viscous heating effects is equal to the corresponding fractional change in the viscosity of a hypothetical Newtonian fluid which exhibits the same rheological properties as the polymer solution at low-shear rates where it approaches Newtonian behavior. The hypothetical Newtonian fluid would have a constant viscosity at all shear rates equal to the viscosity of the polymer solution at low-shear rates, and the influence of temperature and pressure on the viscosity of this Newtonian fluid would be identical to the influence of these variables on the low-shear rate viscosity of the polymer solution. 

To a first approximation, the vapor phase of an alkali metal may be considered as a binary mixture of monomer and dimer species, whose molar fractions are dependent on both temperature and pressure. The viscosity of such a binary mixture with mole fractions yw and yu (subscripts M and D refer to monomer and dimer respectively) is well described by the first-order Chapman-Enskog theory (Hirschfelder et al. 1954 ... 

Wax usually refers to a substance that is a plastic solid at ambient temperature and that, on being subjected to moderately elevated temperatures, becomes a low viscosity hquid. Because it is plastic, wax usually deforms under pressure without the appHcation of heat. The chemical composition of waxes is complex all of the products have relatively wide molecular weight profiles, with the functionaUty ranging from products that contain mainly normal alkanes to those that are mixtures of hydrocarbons and reactive functional species. 

A mixing rule developed by Kendall and Monroe" is useful for determining the liquid viscosity of defined Iiydi ocai bon mixtiai es. Equation (2-119) depends only on the pure component viscosities at the given temperature and pressure and the mixture composition. 

The penetration behavior of resins into the wood surface also is influenced by various parameters, like wood species, amount of glue spread, press temperature and pressure and hardening time. The temperature of the wood surface and of the glue line and hence the viscosity of the resin (which itself also depends on the already reached degree of hardening) influence the penetration behavior of the resin [79]. 

Now, we should ask ourselves about the properties of water in this continuum of behavior mapped with temperature and pressure coordinates. First, let us look at temperature influence. The viscosity of the liquid water and its dielectric constant both drop when the temperature is raised (19). The balance between hydrogen bonding and other interactions changes. The diffusion rates increase with temperature. These dependencies on temperature provide uS with an opportunity to tune the solvation properties of the liquid and change the relative solubilities of dissolved solutes without invoking a chemical composition change on the water. 

Viscosity is one of the most important properties of hydraulic fluids. It is a measure of a fluid s resistance to flow. A liquid such as gasoline which flows easily has a low viscosity, and a liquid such as tar which flows slowly has a high viscosity. The viscosity of a liquid is affected by changes in temperature and pressure. As the temperature of liquid increases, its viscosity decreases. That is, a liquid flows more easily when it is hot than when it is cold. The viscosity of a liquid will increase as the pressure on the liquid increases. 

Molecular weight, temperature, and pressure have little effect on elasticity the main controlling factor is MWD. Practical elasticity phenomena often exhibit little concern for the actual values of the modulus and viscosity. Although MW and temperature influence the modulus only slightly, these parameters have a great effect on viscosity and thus can alter the balance of a process. 

In the previous sections of this chapter, the calculation of frictional losses associated with the flow of simple Newtonian fluids has been discussed. A Newtonian fluid at a given temperature and pressure has a constant viscosity /r which does not depend on the shear rate and, for streamline (laminar) flow, is equal to the ratio of the shear stress (R-,) to the shear rate (d t/dy) as shown in equation 3.4, or ... 

Specific heat of each species is assumed to be the function of temperature by using JANAF [7]. Transport coefficients for the mixture gas such as viscosity, thermal conductivity, and diffusion coefficient are calculated by using the approximation formula based on the kinetic theory of gas [8]. As for the initial condition, a mixture is quiescent and its temperature and pressure are 300 K and 0.1 MPa, respectively. 

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