Kinetic Theory of Dense Fluid Mixtures. II. Solution to the Singlet Distribution Functions for the Rice—Allnatt Model

1966 ◽  
Vol 45 (7) ◽  
pp. 2533-2544 ◽  
Author(s):  
Ching Cheng Wei ◽  
H. Ted Davis
Keyword(s):  
Kinetic Theory ◽  
Distribution Functions ◽  
Fluid Mixtures ◽  
Dense Fluid

Kinetic Theory of Dense‐Fluid Mixtures. IV. Square‐Well Model Computations

1967 ◽  
Vol 47 (6) ◽  
pp. 2082-2089 ◽  
Author(s):  
J. Palyvos ◽  
K. D. Luks ◽  
I. L. McLaughlin ◽  
H. T. Davis
Keyword(s):  
Kinetic Theory ◽  
Fluid Mixtures ◽  
Dense Fluid ◽  
Well Model ◽  
Square Well

Kinetic Theory of Dense Fluid Mixtures. I. Square‐Well Model

1966 ◽  
Vol 45 (6) ◽  
pp. 2020-2031 ◽  
Author(s):  
Ian L. McLaughlin ◽  
H. Ted Davis
Keyword(s):  
Kinetic Theory ◽  
Fluid Mixtures ◽  
Dense Fluid ◽  
Well Model ◽  
Square Well

Thermodynamic properties of dense fluid mixtures

1967 ◽  
Vol 45 (6) ◽  
pp. 595-604 ◽  
Author(s):  
M. Orentlicher ◽  
J. M. Prausnitz
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Simple Fluids ◽  
Fluid Mixtures ◽  
Functional Expansion ◽  
Residual Properties ◽  
Dense Fluid ◽  
Liquid Solutions ◽  
Point Of Departure

By using the properties of hard-sphere systems as a point of departure, equations are derived for the residual properties of mixtures of real simple fluids at liquid-like densities. The essence of the derivation lies in a functional expansion of g(r) exp [Formula: see text] about its hard-sphere value. The results obtained are useful for interpreting, correlating, and extending experimental data for both concentrated and dilute liquid solutions.

Explicit Flow-Aligned Orientational Distribution Functions for Dilute Nematic Polymers in Weak Shear

2002 ◽  
Author(s):  
M. Gregory Forest ◽  
Ruhai Zhou ◽  
Qi Wang
Keyword(s):  
Kinetic Theory ◽  
Mean Field ◽  
Distribution Functions ◽  
Small Molecular Weight ◽  
Exact Probability ◽  
Exact Probability Distribution ◽  
Orientational Distribution ◽  
Alignment Angle ◽  
Nematic Polymers ◽  
Leslie Angle

Flow-alignment of sheared nematic polymers occurs in various flow-concentration regimes. Analytical descriptions of shear-aligned nematic monodomains have a long history across continuum, mesoscopic and mean-field kinetic models, sacrificing precision at each finer scale. Continuum Leslie-Ericksen theory applies to highly concentrated, weak flows of small molecular weight polymers, giving an explicit macroscopic alignment angle formula dependent only on Miesowicz viscosities. Mesoscopic tensor models apply at all concentrations and shear rates, but explicit “Leslie angle” formulas exist only in the weak shear limit (Cocchini et. al, 90; Bhave et. al, 93; Wang, 97; Rienacker and Hess, 99; Maffettone et. al, 00; Forest and Wang, 02; Forest et. al, 02c; Grecov and Rey, 02), with distinct behavior in dilute versus concentrated regimes. Exact probability distribution functions (pdf’s) of kinetic theory do not exist for highly concentrated nematic states, even without flow, although appealing flow-aligned approximations have been derived (Kuzuu and Doi, 83; Kuzuu and Doi, 84; Semenov, 83; Semenov, 86; Archer and Larson, 95; Kroger and Seller, 95), which offer a molecular theory basis for the Leslie alignment angle. A simpler problem concerns the dilute concentration regime where the unique quiescent equilibrium is isotropic, corresponding to a constant pdf, and whose weak shear deformation is robust to mesoscopic closure approximation (Forest and Wang, 02; Forest et. al, 02c): steady, flow-aligning, weakly anisotropic, and biaxial. The purpose of this paper is to explicitly construct the weakly anisotropic branch of stationary pdf’s by a weak-shear asymptotic expansion of kinetic theory. A second-moment pdf projection confirms mesoscopic model predictions, and further yields explicit Leslie angle and degree of alignment formulas in terms of molecular parameters and normalized shear rate.

HIGH FREQUENCY GAS DISCHARGE BREAKDOWN IN NEON

1952 ◽  
Vol 30 (5) ◽  
pp. 565-576 ◽  
Author(s):  
A. D. MacDonald ◽  
D. D. Betts
Keyword(s):  
Kinetic Theory ◽  
Electric Fields ◽  
Cross Sections ◽  
Electrical Breakdown ◽  
Ionization Rate ◽  
Gas Discharge ◽  
Distribution Functions ◽  
Boltzmann Transport ◽  
Discharge Data ◽  
Confluent Hypergeometric Functions

Electrical breakdown of neon at high frequencies has been treated theoretically on the basis of the Boltzmann transport equation. Exciting and ionizing collisions are accounted for as energy loss terms in the Boltzmann equation and measured values of the ionization efficiency are used in the integral determining the ionization rate. Electrons are lost to the discharge by diffusion. The equations are treated separately for the cases in which the collision frequency is much less than or much greater than the radian frequency of the applied field. The electron energy distribution functions are expressed in terms of Bessel functions, confluent hypergeometric functions, and simple exponentials. The ionization rate and the diffusion coefficient are calculated using these distribution functions in kinetic theory formulas, and combined with the diffusion equation to predict breakdown fields. The theoretically predicted fields are compared with experiment at 3000 Mc. per sec. The breakdown equations, calculated from kinetic theory and using no gas discharge data other than collision cross sections, predict breakdown electric fields within the limits of accuracy determined by these cross sections over a large range of experimental variables.

The enthalpy of simple, dense fluid mixtures

1967 ◽  
Vol 45 (2) ◽  
pp. 78-81 ◽  
Author(s):  
M. Orentlicher ◽  
J. M. Pravsnitz
Keyword(s):  
Fluid Mixtures ◽  
Dense Fluid
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