Trouton’s ratio

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

Screttas, C.G., and M. Micha-Screttas. 1991. Some properties and trends of enthalpies of vaporization and of Trouton s ratios of organic compounds. Correlation of enthalpies of vaporization and enthalpies of formation with normal boiling points. /. Org. Chem. 56 1615-22. 

In Chapter 8, along with tables of measured thermophysical data, we saw some fairly simple techniques for estimating these values when experimental results are not available. Among these techniques were Kopp s Rule for the heat capacity of both liquids and solids, and Trouton s ratio for latent heats of fusion and vaporization, along with Kistiakowski s temperature correction for the latter. 

Here dv/dr is the extensional strain rate, and 77 is the extensional viscosity. The correlation between the ideal extensional viscosity and the shear viscosity for a Newtonian fluid can be described by the Trouton s ratio (Trouton 1906), as given by... 

The molecular theory of extensional viscosity of polymer melts is again based oti the standard tube model. It considers the linear viscoelastic factors such as reptation, tube length fluctuations, and thermal constraint release, as well as the nonlinear viscoelastic factors such as segment orientations, elastic contractimi along the tube, and convective constraint release (Marrucci and lannirubertok 2004). Thus, it predicts the extensional stress-strain curve of monodispersed linear polymers, as illustrated in Fig. 7.12. At the first stage, the extensional viscosity of polymer melts exhibits the Newtonian-fluid behavior, following Trouton s ratio... 

Hence, for Newtonian liquids, the tensile stress growth coefficient is a constant quantity and the extensional viscosity is three times the shear viscosity. This result was verified experimentally in 1906 by TroutonOD and is known as Trouton s rule. In addition, the ratio of the extensional viscosity to the shear viscosity is known as Trouton s ratio. 

In situations of low elongational rate one can simply apply Trouton s ratio [Eq. (3), where is the elongational viscosity and is shear viscosity the subscript S is often omitted]. 

For liquid chlorine, M. Pellaton 22 found the value of f in J. D. van der Waals equation log (pefp) =f TcjT—1) is nearly 2 5 the ratio of the critical density to that calculated by the formula of a normal gas Z>=Mpc/22412(l-fa (.), namely 0 15765 3 635=DC/D and an application of Trouton s rule, 67 5 X70 92-y238 5 gives 20 67. Each of these three values is characteristic of what is obtained with non-associated liquids. 

There are several expressions that have developed, but our primary interest is with water, Trouton s rule states that the ratio of the molal heat of vaporization of a material at its normal boiling point (i.e., at 1 atm) to the absolute temperature is a constant ... 

Besides Trouton s rule we must also mention the modification introduced by Hildebrand, who suggested that the entropies of vaporization should be taken not at the boiling point, but at a temperature such that the concentration c=pjRT) in the vapour phase is a constant. In general, Hildebrand s rule holds more accurately than Trouton s rule. It should be noted, however, that neither of these rules follows from the law of corresponding states, according to which the entropies should be the same at corresponding temperatures, that is to say for a definite value of the ratio T/Tc- ... 

According to Trouton s rule the ratio of molecular latent heat to boiling-point is constant, and this statement is by no means very far from the truth. In so far as it holds it means that the expression... 

Consider the following facts Water freezes spontaneously at — 5°C and 1 atm, and ice has a more ordered structure than liquid water. Explain how a spontaneous process can lead to a decrease in entropy. Ammonium nitrate (NH4NO3) dissolves spontaneously and endothermically in water. What can you deduce about the sign of A5 for the solution process Calculate the equilibrium pressure of CO2 due to the decomposition of barium carbonate (BaC03) at 25°C. (a) Trouton s rule states that the ratio of the molar heat of vaporization of a liquid (AT/yap) to its boiling point in kelvins is approximately 90 J/K mol. Use the following data to show that this is the case and explain why Trouton s rule holds tme ... 

Trouton s third rule states that the latent molar entropies are obtained from the ratio of the latent molar enthalpies by the absolute thermodynamic temperature of the transformation ... 

This ratio of the standard vaporization enthalpy Ay pH° to the normal boiling temperature (at 1 bar), that is, the standard vaporization entropy AvapS , is called Trouton s constant Frederick Trouton, see box). Table 3.1.4 indicates that the values of AvapS are in the range 70-110 Jmol K , and we can use 90 J mol as a... 

Trouton s rule states that the ratio of latent heat of evaporation to the... 

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