TY - JOUR
T1 - Analytical solution for thermal convection in a layer of liquid crystal with free surface
AU - Zhukov, M. Yu
AU - Vladimirov, V. A.
N1 - Funding Information:
The authors are grateful to Professor J. W. Goodby for useful discussions and for providing the data for MBBA. The research was supported by the Hull Institute for Mathematical Sciences and Applications (HIMSA). ·Correspondence author. E-mail: m.y.zhukov@maths.hull.ac.uk.; zhuk@ns.math.rsu.ru
PY - 2004
Y1 - 2004
N2 - An Oberbeck-Bussinesq type model for convection in isothermically incompressible liquid crystals (nematics and cholesterics) is proposed. For its derivation, the nonequilibrium thermodynamics and asymptotic methods are employed. The model is based on the Leslie-Ericksen-Parodi (LEP) continuum theory [1-4] taken with some minor modifications. The problem of the thermal gravity convection in a plane horizontal layer with 'free undeformable' boundary and under the action of external magnetic or electric field is considered. Solution of this problem is obtained and presented in an explicit analytical form. Existence of the explicit analytical solution is very useful, since it allows us to investigate the influence of various parameters (Leslie coefficients, Frank moduli, anisotropic thermo-diffasivity, etc.) at the onset of convection.
AB - An Oberbeck-Bussinesq type model for convection in isothermically incompressible liquid crystals (nematics and cholesterics) is proposed. For its derivation, the nonequilibrium thermodynamics and asymptotic methods are employed. The model is based on the Leslie-Ericksen-Parodi (LEP) continuum theory [1-4] taken with some minor modifications. The problem of the thermal gravity convection in a plane horizontal layer with 'free undeformable' boundary and under the action of external magnetic or electric field is considered. Solution of this problem is obtained and presented in an explicit analytical form. Existence of the explicit analytical solution is very useful, since it allows us to investigate the influence of various parameters (Leslie coefficients, Frank moduli, anisotropic thermo-diffasivity, etc.) at the onset of convection.
KW - Analytical solution
KW - Cholesterics
KW - Nematics
KW - Thermal convection
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U2 - 10.1080/15421400490437079
DO - 10.1080/15421400490437079
M3 - Conference article
AN - SCOPUS:12844277432
SN - 1542-1406
VL - 413
SP - 279/[2415]-290/[2426]
JO - Molecular Crystals and Liquid Crystals
JF - Molecular Crystals and Liquid Crystals
T2 - Proceedings of the 19th International Liquid Crystal Conference, ILCC2002
Y2 - 30 June 2002 through 5 July 2002
ER -