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.
Similar content being viewed by others
References
Ericksen JL (1976) On equations of motion for liquid crystals. Q J Appl Math 29:203
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 63:1082
Kroger M, Sellers HS (1995) Viscosity coefficients for anisotropic, nematic fluids based on structural theories of suspensions. J Chem Phys 103:807
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 28:1
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 32:55
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 York
Acknowledgements
The author thanks Professor Valery Volkov for valuable discussion.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Leonov, A.I. On the minimum of extended dissipation in viscous nematodynamics. Rheol Acta 44, 573–576 (2005). https://doi.org/10.1007/s00397-005-0438-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-005-0438-3