Effect of Temperature on Viscosity

Effect of Temperature on Viscosity Increase of temperature decreases the shear viscosity in such a way that the viscosity follows the reverse Arrhenius equation (17.29), to a good approximation. The Arrhenius equation in rheology is reverse because the common Arrhenins eqnation is typically applied to velocities 

TABLE 17.2 Zero-shear viscosity and weight-average molecular weight for HDPE at 190°C [12] 

Of course, the activation energy in Eq. (17.29) has a principally different meaning from that in equations for temperature dependencies of rates of chemical reactions, such as in chemical kinetics. 

Compared to the velocities of chemical reactions, the viscosity of polyolefins changes with temperature much less, hence, lower energy of activation values for hot melts. The so-called temperature coefficient for chemical reactions, that is, a change of the velocity by each 10°C, is typically between 2 and 3 that corresponds to energy of activation between 28 and 44 kcal/mol (116-183 kJ/mol), if measured between 170 and 180°C. This can be compared to some typical (generic) values of the energy of activation for the shear viscosity of HDPE (6.3-7.0 kcal/mol, or 26-29 kJ/mol), LDPE (11.7 kcal/mol, or 49 kJ/mol), polypropylene (9-10 kcal/mol or 38 2 kJ/mol) ([13], p. 46). In other words, the temperature coefficient for the viscosity of said plastics is equal to 1.18 for HDPE, 1.34 for LDPE, and 1.26 for PP. 

The equation that expresses the temperature coefficient through the activation energy (E) and the temperature range is as follows  

A wide range of temperatures are encountered during processing and storage of fluid foods, so that the effect of temperature on rheological properties needs to be documented. The effect of temperature on either apparent viscosity at a specified shear rate (Equation 2.42) or the consistency index, K, of the power law model (Equation 2.43) of a fluid can be described often by the Arrhenius relationship. The effect of temperature on apparent viscosity can be described by the Arrhenius relationship  

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986)  

The magnitudes of the parameters of the Arrhenius and the Fulcher equations for the studied concentrated apple and grape juices are given in Tables 2-6 and 2-7, respectively. The physical interpretation of the three constants in the Fulcher equation is ambiguous, but by translating them in terms of the WLF parameters their significance can be clarified and it is functionally equivalent to the WLF equation (Ferry, 1980 Soesanto and Williams, 1981)  

Effect of Temperature on Concentrated Apple and Grape Juices (Rao et al., 1986)  

Specifically, Too and B are related to Cj, c , and a reference temperature 7b, often called the glass transition temperature, by the following two equations  

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The second generalisation relates to the effect of temperature on flow. An increase in temperature increases the rate of flow. It also increases the rate of cross-linking. It is commonly observed that at low temperatures the effect of temperature on viscosity predominates and the total flow occurring before cross-linking increases with temperature. 

Equation (9.7) implies that if we know the viscosity at some temperature T we can estimate the viscosity at the Tg and hence in turn estimate the viscosity at another temperature Tj, i.e. the WLF equation gives the effect of temperature on viscosity. 

In order to allow for the effect of temperature on viscosity a shift factor, ar is often used. The Carreau equation then becomes... 

Figure 7.8 The effect of temperature on viscosity. Adapted from as Figure 7.5.

Viscosity decreases as the temperature increases, and the rate of change appears to depend primarily on the nature or composition of the petroleum, but other factors, such as volatility, may also have an effect. The effect of temperature on viscosity is generally represented by the equation... 

Table 3.7 Example Viscosity Data at Two Temperatures and Two Shear Rates. Data Shows the Effect of Temperature on Viscosity...

The figure also shows the effect of temperature on viscosity. At low pressures, gas viscosity increases as temperature increases. However, at high pressures gas viscosity decreases as temperature increases. The reciprocal of viscosity is called fluidity. 

Eq. (15.35) gives a fair description of the effect of temperature on viscosity for a number of polymers. For some other polymers, however, considerable deviations are found. According to Eq. (15.35), ri(T)/ri(Tg) should be a universal function of (T — Tg), which is not confirmed by experimental data. 

For a number of polymer solutions experimental data on the effect of temperature on viscosity are available. By way of example, Fig. 16.4 shows log t] against 1/T for polystyrene in xylene, together with the curve for the melt and the straight line for the pure solvent. 

The exponential behavior of viscosity as a function of time for varying compositions is shown in Figures 8 and 9. The pronounced effect of temperature on viscosity is shown in Figure 10. Pryor (23) pointed out... 

This heat must be dissipated by cooling, which can be done but only to a limited extent The ability to dissipate heat efficiently is usually the factor that limits the speed of electrophoresis, since excess heat leads to non-uniform electrophoresis and a decrease in resolution. The main reason for this is convection in matrix-free electrophoresis in solution, and the effect of temperature on viscosity and diffusion. High temperatures can also lead to denaturation of proteins and nucleic acids. The thinner the layer used for electrophoresis, the more readily is the heat dissipated, and the higher the voltages that can be used. The thickness of the layer will be a compromise between a desire to have a thin layer to minimise heat problems whilst maintaining sufficient capacity to ran samples that can be detected easily. Consis-... 

Rao, M. A., Shallenberger, R. S., and Cooley, H. J. 1986. Effect of temperature on viscosity of fluid foods with high sugar content, in Engineering and Food, eds. M. LeMaguer and P. Jelen, Vol. I, pp. 23-31, Elsevier Applied Science Publishers, New York. 

Saravacos, G. D. 1970. Effect of temperature on viscosity of fruit juices and purees. J. Food Sci. 35 122-125. 

Effect of Temperature on Viscosity. The viscosity of mobility control polymers decreases with increasing temperature and an Arrhenius type relationship is obeyed ... 

Effect of Temperature on Viscosity of Fluid Foods with high Sugar Content" LeMaguer, M Jelen, P., Eds. Engineering and Food Elsevier Applied Science Publishers New York, 1986 Vol.l, p. 33. 

The effect of temperature on viscosity of various vegetable oils and fatty acids was investigated by Noureddini and co-workers (1992). The relationship was expressed as... 

F ow P/LOpcAtlei Under this heading come the viscosity of the fluid and the effect of temperature on viscosity. The latter might be a theoretically derived function, or an arbitrary function such as the viscosity index, or even a grossly empirical evaluation of the viscosity at two or more selected temperatures. Low temperature flow properties are frequently evaluated by the ASTM pour point determination [5], but the inadequacies of this method of evaluation have led to the use of pumpability tests which have a better empirical relation to service conditions. 

In adiabatic frictional flow, the temperature of the gas changes. The viscosity also varies, and the Reynolds number and friction factor are not actually constant. In gas flow, however, the effect of temperature on viscosity is small, and the effect of Reynolds number on the friction factor / is still less. Also, unless the Mach number is nearly unity, the temperature change is small. It is satisfactory to use an average value for /as a constant in calculations. If necessary,/ can be evaluated at the two ends of the conduit and an arithmetic average used as a constant. 

Because of distortions in the flow field from the effects of temperature on viscosity and density, Eq. (12.16) does not give accurate results. The heat-transfer rates are usually larger than those predicted by Eq. (12.16), and empirical correlations have been developed for design purposes. These correlations are based on the Graetz number, but they give the film coefficient or the Nusselt number rather than the change in temperature, since this permits the fluid resistance to be combined with other resistances in determining an overall heat-transfer coefficient. 

For liquids the effect of temperature is much greater than for gases because of the rapid decrease in viscosity with rising temperature. The effects of k> Cp, and li in Eq, (12.37) all act in the same direction, but the increase in A with temperature is due mainly to the effect of temperature on viscosity. For water, for example. A,-increases about 50 percent over a temperature range from 50 to lOO C. For viscous oils the change in A,- may be two- or threefold for a 50°C increase in temperature. 

Molecular Meaning of aT. The effect of temperature on viscosity is related to its effect on the friction coefficient, which, in turn, depends on the fractional free volume according to the equation ... 

Figure 7 Effect of temperature on viscosity at a constant rate of shear of 100 s, includes 55.0 vol% AI2O3 and 45 vol% ethylene-vinyl acetate. (After Ref. 3).

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