A dynamic approach to study variable diffusion coefficients in nematic liquid crystals

1982 ◽  
Vol 53 (7) ◽  
pp. 5333-5335 ◽  
Author(s):  
H. Hakemi
Keyword(s):  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Nematic Liquid Crystals ◽  
Dynamic Approach ◽  
Study Variable ◽  
Variable Diffusion ◽  
Variable Diffusion Coefficients

Soret Effect for a Ternary Mixture in Porous Cavity: Modeling With Variable Diffusion Coefficients and Viscosity

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
T. J. Jaber ◽  
Y. Yan ◽  
M. Z. Saghir
Keyword(s):  
Thermal Diffusion ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Soret Effect ◽  
Left Wall ◽  
Porous Cavity ◽  
Buoyancy Convection ◽  
Variable Diffusion ◽  
Variable Diffusion Coefficients ◽  
The Right

A porous cavity filled with methane (C1), n-butane (nC4), and dodecane (C12) at a pressure of 35.0MPa is used to investigate numerically the flow interaction due to the presence of thermodiffusion and buoyancy forces. A lateral heating condition is applied with the left wall maintained at 10°C and the right wall at 50°C. The molecular diffusion and thermal diffusion coefficients are functions of temperature, concentration, and viscosity of mixture components. It has been found that for permeability below 200md the thermodiffusion is dominant; and above this level, buoyancy convection becomes the dominant mechanism. The variation of viscosity plays an important role on the molecular and thermal diffusion.

scholarly journals ERROR ESTIMATES FOR A CLASS OF FINITE DIFFERENCE-QUADRATURE SCHEMES FOR FULLY NONLINEAR DEGENERATE PARABOLIC INTEGRO-PDES

2008 ◽  
Vol 05 (01) ◽  
pp. 187-219 ◽  
Author(s):  
IMRAN H. BISWAS ◽  
ESPEN R. JAKOBSEN ◽  
KENNETH H. KARLSEN
Keyword(s):  
Finite Difference ◽  
Error Estimates ◽  
Viscosity Solutions ◽  
Diffusion Coefficients ◽  
Jump Diffusion ◽  
Bellman Equations ◽  
Variable Diffusion ◽  
Degenerate Parabolic ◽  
Variable Diffusion Coefficients ◽  
Nonlinear Degenerate

Error estimates are derived for a class of finite difference-quadrature schemes approximating viscosity solutions of nonlinear degenerate parabolic integro-PDEs with variable diffusion coefficients. The relevant equations can be viewed as Bellman equations associated to a class of controlled jump-diffusion (Lévy) processes. The results cover both finite and infinite activity cases.

Ansiotropy of the Diffusion Coefficient in Nematic Liquid Solutions Measured by NMR Techniques

1973 ◽  
Vol 28 (6) ◽  
pp. 964-967
Author(s):  
G. J. Krüger ◽  
H. Spiesecke
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Small Molecules ◽  
Diffusion Coefficients ◽  
Nematic Phase ◽  
Nematic Liquid Crystals ◽  
Gradient Coil ◽  
Liquid Solutions ◽  
Nmr Techniques ◽  
Relative Measurements

A gradient coil has been constructed for exact relative measurements of the longitudinal (Dʟ) and transverse (Dᴛ) diffusion coefficients of nematic liquid crystals and of small molecules dissolved therein. Some small molecules dissolved in the nematic phase of Licristal IV showed a Dʟ/Dᴛ ratio varying from about 1.1 to 1.25, depending on the concentration. In contrast, tetramethylsilane dis­solved in p-methoxy-benzylidene-p'-n-butyl-aniline showed no anisotropy in the nematic phase.

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