Temperature dependence of viscosity

All fluid properties are dependent upon temperature. For most fluids the viscosity is the property that is most sensitive to temperature changes. 

For liquids, as the temperature increases, the degree of molecular motion increases, reducing the short-range attractive forces between molecules and lowering the viscosity. The viscosity of various liquids is shown as a function of temperature in Appendix A. For many liquids, this temperature dependence can be represented reasonably well by the Arrhenius equation  

For non-Newtonian fluids, any model parameter with the dimensions or physical significance of viscosity (e.g., the power law consistency, m, or the Carreau parameters r,]co and j/0) will depend on temperature in a manner similar to the viscosity of a Newtonian fluid [e.g., Eq. (3-34)]. 

As indicated by the above discussion, it is important to know the temperature dependence of viscosity. It has become standard industrial practice to use an empirical equation, known as the Vt el-Fuklier-Taiiimann (VFT) equation to describe this temperature dependence. For silicate glasses, the VFT equation often fits the temperature dependence over ten orders of magnitude in viscosity. The VFT equation involves three empirical constants (t/, C and Tj,) and can be written 

Originally, the various constants had no particular physical meaning, though one does note that the viscosity becomes infinite when T = Tj,. The VFT equation runs into some difficulties in fitting data near the glass transition temperature but the success of the empirical approach has often led subsequent theoreticians to interpret their models in terms of the VFT equation. 

A simple theoretical approach to the temperature dependence of viscosity would be to consider it a thermally activated process and utilize the Arrhenius equation, i.e.. 

There is a strong relationship between diffusion and viscosity, in that both involve the movement of atoms in a body. Indeed, viscous flow is often consid- 

This expression is known as the Williams-Landel-Ferry (WLF) relation. 

There is a wide-spread literature on methods for temperature-dependent viscosity estimation. Their discussion and further references can be found elsewhere [1,2,17,18,19,20,21], Usually, these methods are based on various input data, such as density, boiling point, and critical point. Dynamic viscosities of most gases increase with increasing temperature. Dynamic viscosities of most liquids, including water, decrease rapidly with increasing temperature [18]. 

Two mathematical expressions, the Arrhenian equation and the Vogel-Fulcher-Tamman equation, are commonly used to express the temperature dependence of the viscosity of glass forming melts. At one extreme, we find that the viscosity can often be fitted, at least over limited temperature ranges, by an Arrhenian expression of the form  

This expression is most often written in the form actually used by Fulcher  

While the VFT equation provides a good fit to viscosity data over a wide temperature range, it should be used with caution for temperatures at the lower end of the transformation region, where AH becomes constant. The VFT equation always overestimates the viscosity in this temperature regime. 

The degree of curvature of viscosity/temperature plots can vary over a wide range due to variations in the value of Tq relative to Tg. If To is equal to zero, the viscosity/temperature curve will exhibit Arrhenian behavior over the entire viscosity region, from very fluid liquid to the transformation range, with a single value for AH. On the other hand, as To approaches Tg, the curvature will increase and the difference between AH, for the fluid melt and in the transformation region will become very large. 

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In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

For the same polymer this parameter has values of 4.47 X 10" and 5.01 X 10 " kg sec" at 298 and 398 K, respectively. Since density is far less sensitive to temperature, these results show that the primary temperature dependence of viscosity is described by the temperature dependence of f. 

Temperature dependence of viscosity of the gas over a wide range of temperatures is given by equation 1 where Tis in Kelvin and T q is the value of Ti at 273 K. 

The temperature dependence of viscosity of resin solutions can be expressed by the WLE equation (eq. 3) where the reference temperature T is taken as the lowest temperature for which data ate avaUable (92,93). 

Example 8.9 Find the temperature distribution in a laminar flow, tubular heat exchanger having a uniform inlet temperature and constant wall temperature Twall- Ignore the temperature dependence of viscosity so that the velocity profile is parabolic everywhere in the reactor. Use art/P = 0.4 and report your results in terms of the dimensionless temperature... 

Monkos, Karol 1997. Concentration and temperature dependence of viscosity in lysozyme aqueous solutions. Biochimica et Biophysica Acta 1339, 304-310. 

Figure 8.7 Temperature dependences of viscosity for several solvents measured with conventional Ostwald viscometers. Markers exhibit experimental results. Data points were interpolated by polynomial function the calculated curves are drawn with lines.

The temperature dependence of viscosity of 23 room-temperature ionic liquids was investigated. The size and symmetry of the cations and anions were shown to have a marked effect on viscosity (79). 

Okoturo, 0.0. and Van der Noot, T.J., Temperature dependence of viscosity for room temperature ionic liquids, ]. Electroanal. Chem., 568,167, 2004. 

Figure 3.4 is a logarithmic plot that illustrates the temperature-dependence of viscosity for some selected liquids. These data were prepared from fits in the form... 

The Sutherland law is also a widely used expression to express the temperature dependence of viscosity... 

The experiments show that the time-temperature dependence of viscosity in the non-Newtonian region of flow may be represented as ... 

The temperature dependence of viscosity r is given by the conventional Arrhenius equation ... 

As already mentioned, the viscosity of a base oil decreases with increasing temperature. Therefore, it is important to know, not only the viscosity at a certain temperature, but also how much it changes within a temperature range given by operating conditions. To characterize the temperature dependence of viscosity in 1929 the American Society for Testing and... 

Clearly, then, the temperature dependence of viscosity, on the one hand, and the viscous dissipation term that depends on the magnitude of the local rate of deformation, on the other hand, couple the energy equation with the equation of motion, and they must be solved simultaneously. 

Both shear thinning and temperature dependence of viscosity strongly affect the melting rate. Their effect on the rate of melting can be estimated by considering a case in which convection is neglected and viscous dissipation is low enough to permit the assumption that the viscosity variation across the film is determined by a linear temperature profile ... 

Incorporating both the effect of convection in the Him and the temperature dependence of the viscosity into the model improves the agreement between predictions and experimental measurements. It should be noted, however, that experimental conditions were such that viscous dissipation was insignificant and the temperature drop across the film was relatively small. Consequently, non-Newtonian effects, and effects due to the temperature dependence of viscosity, were less significant than were convection effects. This may not be the case in many practical situations, in particular with polymers, whose viscosity is more temperature sensitive than that of HDPE. 

From the temperature dependence of viscosity, which yields an Arrhenius form, the activation energy for flow and the hydrodynamic volume p0 were determined as... 

Fig. 7. Temperature dependence of viscosity obtained from the MD simulations.

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