Chung equation

Generally, for spherical and other irregular-shaped particles (intalox saddles, rasching rings, berl saddles), the particle Peclet number is found to be between 0.3 and 0.8 for Reynolds number between 0.01 and 150 (Ebach and White, 1958). For a wide range of values of the Reynolds number, the Chung equation can be used (Chung and Wen, 1968) ... 

For nonpolar components, the vapor thermal conductivity can be estimated by the Chung equation [85]... 

Estimate the thermal conductivity of gaseous 2-methyl pentane at T = 373.15 K and P = 0.1 MPa using the Chung equation. The given data are... 

A. Maury, D. Ouma, D. Boning, J. Chung, A Modification to Preston s Equation and Impact on Pattern Density Effect Modeling, Conf. for Advanced Metallization and Interconnect Systems for VLSI Applications, San Diego, CA, Oct. 1997. 

Chung successfully used cinnamaldehyde not only as a CO but also as a reactant styrene source. The PKR was achieved using Rh/Co colloidal nanoparticles (Equation (11))." ... 

More recently, Chung introduced a combination of a well-designed GO surrogate 30 and ruthenium colloidal particles (RuCNC) (Equation (12)). =... 

Chung, Kai Lai, and Z. Zhao From Brownian Motion to Schrodinger s Equation, Springer-Verlag. Inc., New York, NY. 1995. 

Broyles, A. A., S. U. Chung, and H. L. Sahlin Comparison of Radial Distribution Functions from Integral Equations and Monte Carlo. J. Chem. Phys. 37, 2462 (1962). 

In cases where readily oxidized functional groiqis are also present in either the substrate or the product of the reaction, overoxidation can occur. However, this can sometimes be advantageous. For example, in the total synthesis of ( )-steiepolide Trost and Chung effected the deprotection of the MPM ether (40) with DDQ in moist dichloromethane. Under the conditions of the reaction, furtiier oxidation of the allylic alcohol took place to afford the final product (equation 30). However, separate treatment of the allylic alcohol with PDC in dichloromethane was found to be more effective. Similarly, treatment of the ether (41) with pyridinium tosylate followed by excess DDQ afforded the Ireland alcohol (42), a key intermediate for the synthesis of tirandamycin A (equation 31). Propargylic alcohols, however, would appear to be less susceptible to oxidation. ... 

The equations to quantify this effect were developed by Mason and Weaver in 1924 [2]. For monosize distributions Brownian motion leads to broadened measured distributions [3] but the effect is reduced as the width of the distribution increases [4,5]. Chung and Hogg [6] carried out theoretical and experimental studies of clay particles using centrifugal and gravitational sedimentation. Agreement between theory and practice was not too good. 

Chung, H. S. On the Macedo-Litovitz hybrid equation for liquid viscosity. J. Chem. Phys. 44, 1362 (1966). 

Chung and Wen (1968) and Wen and Fan (1975) have proposed a dimensionless equation using the dependency of the dispersion coefficient on the (particle) Reynolds number Re (Eq. 6.169) for fixed and expanded beds. It is an empirical correlation based on published experimental data and correlations from other authors that covers a wide range of Re. Owing to two different definitions of the Reynolds number, the actual appearance varies in the literature. Since the particle diameter dp, is the characteristic value of the packing, Eq. 6.168 based on the (particle) Peclet number Pe (Eq. 6.170) is used here ... 

Calculations by this method have shown remarkable Insensitivity to the nonlinear parameters of the complex part of the trial function. For the 2s autolonlzlng state, for which Equation 14 Is the trial function, Chung and Davis (33) obtained Ej. 57.8483 eV and r 0.12468 eV which compare well with the experimental (34) values of Ej. 57.8210.04 eV and T 0.13810.15 eV. The saddle point complex-rotation method Is strictly speaking another variant of CCI, but It demonstrates the premium In accuracy and efficiency to be gained from a well chosen trial function. In this case one In which the Feshbach Q-space (resonance) part of the trial wave-function Is optimized. 

The method expressed In Equations 18-23 has seen only a few numerical applications, but It represents the ultimate application of the generalized complex variational principle in that only real valued eigenvalue calculations are required. Doubtless the use of this idea coupled with more cleverly chosen trial functions, such as those of Junker (19,20) and Chung and Davis (33) described above will also be possible. 

Robinson, D. B., D. Y. Peng, and S. Y.-K. Chung. 1985. The development of the Peng-Robinson equation and its application to phase-equilibrium in a system containing methanol. J. Fluid Phase Equil. 24 25-41. 

References Naraghi and Chung [300] Naraghi [299] Definitions H = hir, X= -H2 cot2 0)1 2 Governing equations ... 

Chung, D.S. and Pfost, H.B., Adsorption and desorption of water vapor by cereal grains and their products. Part II Development of the general isotherm equation, Trans. ASAE, 10(4) 552-555 (1967). 

The discretization of the conservation equations via FDM, FVM or FEM leads to a large system of algebraic equations in each time step which, in order to be solved, is usually linearized. Thus, the problem of solving a complex multiphase flow, with possibly chemical reactions, is reduced to the solutions of large linear systems. Further details for the various solution approaches, together with additional references, can be found in Chung [11]. 

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