Viscosity coefficients pressure dependence

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

The pressure dependence of effective viscosity obviously depends upon the value of the momentum accommodation coefficient. Momentum accommodation data are relatively rare, but some representative data are given in Table 1. Note that all values are relatively close to unity. Because of this observation, momentum accommodation coefficients are normally assumed to be unity in applications... 

Here the pre-exponential factor At is the product of a temperature-dependent constant (ksT/h) = 2 X 10 °Ts where ke and h are the Boltzmann and Planck constants, and a solvent-specific coefficient that relates to both the solvent viscosity and to its orientational relaxation rate. This coefficient may be near unity for very mobile solvent molecules but may be considerably less than unity for viscous or orientationally hindered highly stractured solvents. The exponential factor involves the activation Gibbs energy that describes the height of the barrier to the formation of the activated complex from the reactants. It also describes temperature and pressure dependencies of the reaction rate. It is assumed that the activated complex is in equilibrium with the reactants, but that its change to form the products is rapid and independent of its environment in the solution (de Sainte Claire et al., 1997). 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

It should be noted again that the numerical coefficient above has units of mole. According to this equation, the gas viscosity coefficient should be independent of pressure and should increase with the square root of the absolute temperature. The viscosities of gases are in fact found to be substantially independent of pressure over a wide range. The temperature dependence generally differs to some extent from because the effective molecular diameter is dependent on how hard the molecules collide and therefore depends somewhat on temperature. Deviation from hard-sphere behavior in the case of air (diatomic molecules, N2 and O2) is demonstrated by Eq. (4-19). 

For binary and multicomponent mixtures of gases the viscosity coefficient depends on the concentrations, and the results of the accurate kinetic theory are quite complicated. In terms of the viscosities of the pure of the pure components at the same pressure and temperature, //,, a useful empirical formula is [5], [9]. 

Figure 9.9 Exceptional physical properties of liquid water (solid lines) temperature dependences (upper diagrams) of the density d (45) and isothermal compressibility Xt (adapted from Refs. (45 7)) pressure dependences (lower drawings) of the shear viscosity 7] at various temperatures (adapted from Ref. (48)) and of the isothermal diffusion coefficient Z) at 0 (adapted from Ref. (49)). Dashed lines sketch typical dependences displayed by almost all other liquids. Note that at —15 °C no value is given for 17 at/ > 300MPa, because of a phase transition towards ice V (Figure 8.5).

The pressure dependence of the melt viscosity (r ) can be estimated by using Equation 13.19 (derived from classical thermodynamics to relate the pressure and temperature coefficients of r [V]), where p is the hydrostatic pressure, K is the isothermal compressibility, a is the coefficient of volumetric thermal expansion, and d is a partial derivative. The sign of the pressure coefficient of the viscosity is opposite to the sign of the temperature coefficient. Consequently, since r decreases with increasing T, it increases with increasing p. Equation 13.20 is obtained by integrating Equation 13.19. 

If the film parameter A is equal to 1, boundary lubrication and asperity contact occurs mixed lubrication occurs when A = 1 - 3, and EHD lubrication occurs when A = 3 - 10. The minimum film thickness (h) is dependent on a (the pressure-viscosity coefficient), rj0 (kinematic viscosity), v (entraining velocity), R (effective radius), E (effective elastic modulus), and L = load of a unit line contact. These are interrelated by the following dimensionless parameters ... 

We derived estimates of relative mixing times by considering the volume of fluid that is needed to move in each scenario in order to reach equilibration and the relative mixing drive (an instantaneous initial volumetric rate) as estimated from the permeability, viscosity and pressure difference or diffusion coefficient depending upon the mixing mechanism. 

The consideration of the dependence of viscosity upon pressure has allowed for the prediction of the correct order of magnitude for the friction coefficient, contrarily to the classical theory... 

The dimensions of a are the same as those of the diffusion coefficient and of the kinematic viscosity, therefore the process of heat transport due to conduction can be treated as the diffusion of heat with the diffusion coefficient a, bearing in mind that the transport mechanisms of diffusion and heat conductivities are identical. The coefficient of heat conductivity of gases increases with temperature. For the majority of liquids the value of k decreases with increasing T. Polar liquids, such as water, are an exception. For these, the dependence k(T) shows a maximum value. As well as the coefficient of viscosity, the coefficient of heat conductivity also shows a weak pressure-dependence. 

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