Kinetic theory moment method

Identical results were obtained using the kinetic theory moment method by Kikuchi, Pooley, Ryder, and Yeomans [28, 29]. 

The kinetic theory can also be used for polyfunctional systems with unequal reactivities of groups and substitution effects, but an explicit solution of the partial differential equation corresponding to Eq. (23) derived for the equireactive system is not possible. One can use, however, the method of moments for derivation of certain averages as was explained in... 

At low and moderate pressures, the viscosity of a gas is nearly independent of pressure and can be correlated for engineering purposes as a function of temperatnre only. Eqnations have been proposed based on kinetic theory and on corresponding-states principles these are reviewed in The Properties of Gases and Liquids [15], which also inclndes methods for extending the calculations to higher pressures. Most methods contain molecular parameters that may be fitted to data where available. If data are not available, the parameters can be estimated from better-known quantities such as the critical parameters, acentric factor, and dipole moment. The predictive accuracy for gas viscosities is typically within 5%, at least for the sorts of small- and medinm-sized, mostly organic, molecules used to develop the correlations. 

Theodosopoulou, M. Dahler, J.S. (1974a). The kinetic theory of polyatomic liquids I. The generalized moment method. J. Chem. Phys., 60, 3567-3582. 

The kinetic equation (11.1) is a nonlinear integro-differential equation, general theory of which does not exist. Its known exact solutions are based on the use of operational methods with reference to a case of linear dependence K(V,w) on each of drop volumes [2]. To solve the equation (11.1) with more general kernel, the approximate methods are used - parametric methods and method of moments, and also numerical methods. Parametric methods and method of moments are based on transforming the kinetic equation into a system of equations for the moments of drop distribution over volumes. However, the resulting system of equations is, as a rule, incomplete, since, apart from the integer moments,... 

Effective diffusivity can be evaluated in a single pellet (113,168,169) or in a stirred vessel (115,170,171) or in a packed bed (113). The method of moments is usually used in parameter estimation. The method of moments and the theory of chromatography were also used extensively by Smith and coworkers in packed bed systems (113) for estimation of adsorption rate constants, particle diffusivity (172) and kinetic constants (173). Use of... 

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