Analytical solution for thermal convection in a layer of liquid crystal with free surface

M. Yu Zhukov, V. A. Vladimirov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
JournalMolecular Crystals and Liquid Crystals
Volume413
DOIs
Publication statusPublished - 2004

Fingerprint

Liquid Crystals
free convection
Liquid crystals
convection
liquid crystals
Cholesteric liquid crystals
asymptotic methods
nonequilibrium thermodynamics
Nematic liquid crystals
free boundaries
Gravitation
derivation
Electric fields
Thermodynamics
Magnetic fields
gravitation
continuums
electric fields
coefficients
magnetic fields

Keywords

  • Analytical solution
  • Cholesterics
  • Nematics
  • Thermal convection

ASJC Scopus subject areas

  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics

Cite this

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abstract = "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.",
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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.

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