Mean-field kinetic theory analysis of vapor flow between evaporating and condensing interfaces in the presence of non-condensable gas molecules

2021 ◽  
Vol 33 (12) ◽  
pp. 122017
Author(s):  
Kotaro Ohashi ◽  
Kazumichi Kobayashi ◽  
Hiroyuki Fujii ◽  
Masao Watanabe
Keyword(s):  
Kinetic Theory ◽  
Mean Field ◽  
Vapor Flow ◽  
Theory Analysis ◽  
Gas Molecules

Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory

2011 ◽  
Vol 172-174 ◽  
pp. 321-330 ◽  
Author(s):  
Maylise Nastar
Keyword(s):  
Kinetic Theory ◽  
Structure Function ◽  
Diffusion Mechanism ◽  
Kinetic Equations ◽  
Mean Field ◽  
Early Time ◽  
Present Theory ◽  
Kinetic Coupling ◽  
Amplification Rate ◽  
Cahn Hilliard Equation

A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.

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.

Mean-field kinetic theory approach to Langmuir evaporation of polyatomic liquids

2020 ◽  
Vol 32 (9) ◽  
pp. 093314
Author(s):  
Sergiu Busuioc ◽  
Livio Gibelli
Keyword(s):  
Kinetic Theory ◽  
Mean Field ◽  
Theory Approach ◽  
Polyatomic Liquids

Kinetic theory analysis of diffusion of discontinuity plane of flow velocity

AIAA Journal ◽  
1965 ◽  
Vol 3 (9) ◽  
pp. 1763-1764 ◽  
Author(s):  
YOSHIO SONE ◽  
MAKOTO SHIBATA
Keyword(s):  
Kinetic Theory ◽  
Flow Velocity ◽  
Theory Analysis
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