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Rheologica Acta
Published in: Rheologica Acta 6/2005

01-07-2005 | Original Contribution

On the minimum of extended dissipation in viscous nematodynamics

Author: Arkady I. Leonov

Published in: Rheologica Acta | Issue 6/2005

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Abstract

This paper develops the variational principle of minimum “extended” dissipation for slow (low Reynolds number) flows of nematic liquids as described by the five parametric Leslie–Ericksen–Parodi (LEP) constitutive equations. It is shown that the Euler’s equations for minimizer of the extended dissipative functional are the Stokes equations for the LEP fluid. When the molecular (including magnetic) field is absent, the extended dissipative functional coincides with the true dissipative functional, whose Euler equations are the Stokes equations for the Ericksen fluid.
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Literature
Ericksen JL (1976) On equations of motion for liquid crystals. Q J Appl Math 29:203CrossRef
de Gennes PG, Prost G (1993) The physics of liquid crystals, 2nd edn. Clarendon Press, Oxford, p 5
Golubovich L, Lubensky TC (1989) Nonlinear elasticity of amorphous solids. Phys Rev Lett 63:1082CrossRef
Kroger M, Sellers HS (1995) Viscosity coefficients for anisotropic, nematic fluids based on structural theories of suspensions. J Chem Phys 103:807CrossRef
Leonov AI (1988) Extremum principles and exact two-side bounds of potential functional and dissipation for slow motions of nonlinear viscoplastic media. J Non-Newton Fluid Mech 28:1CrossRef
Leonov AI, Volkov VS (2005) Dissipative soft modes in viscous nematodynamics. Rheol Acta (in press)
Lisin VB, Potapov AI (1997) Variational principles in the mechanics of liquid crystals. J Non-Linear Mech 32:55CrossRef
Mikhlin SG (1952) The problem of minimum for quadratic functional (In Russian). Gostekhteoretizdat, Moscow
Virga EG (1994) Variational theories for liquid crystals. Chapman and Hall, New YorkCrossRef
Metadata
Title
On the minimum of extended dissipation in viscous nematodynamics
Author
Arkady I. Leonov
Publication date
01-07-2005
Publisher
Springer-Verlag
Published in
Rheologica Acta / Issue 6/2005
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI
https://doi.org/10.1007/s00397-005-0438-3

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