Order Tensor Theories

  • André M. Sonnet
  • Epifanio G. Virga


The history of order tensor theories is a long and winding one. Since DE GENNES introduced what he called the tensor order parameter in [57, 58] to phrase a LANDAU- GINZBURG-type theory for the nematic order, many steps have been taken toward a general continuum theory of nematics with tensorial order. Using standard methods of nonequilibrium thermodynamics, HESS [142, 143] and later OLMSTED and GOLDBART [254, 255] obtained constitutive theories for homogeneous alignments, later generalized by HESS and PARDOWITZ to include also spatial variations [145]. All these attempts were impaired by not yielding the full anisotropy of viscosities predicted by the ERICKSEN-LESLIE director theory. An extension using a codeformational model was proposed in [144], and while it recovered the complete anisotropy of viscosities, it failed to be otherwise fully consistent with the phenomenological ERICKSEN-LESLIE theory [267].


Isotropic Phase Dissipation Function Order Tensor Tricritical Point Elastic Energy Density 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • André M. Sonnet
    • 1
  • Epifanio G. Virga
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of StrathclydeGlasgowUK
  2. 2.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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