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Entropy 2016, 18(6), 202; doi:10.3390/e18060202

Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle

1,†
,
2,†
,
3
and
1,2,4,*
1
Beijing Computational Science Research Center, Beijing 100193, China
2
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
3
Departments of Mathematics and Biomedical Engineering, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
4
Department of Mathematics, Interdisciplinary Mathematics Institute and NanoCenter at USC, University of South Carolina, Columbia, SC 29028, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Giorgio Sonnino
Received: 5 December 2015 / Revised: 30 April 2016 / Accepted: 17 May 2016 / Published: 24 May 2016
View Full-Text   |   Download PDF [340 KB, uploaded 24 May 2016]

Abstract

We articulate and apply the generalized Onsager principle to derive transport equations for active liquid crystals in a fixed domain as well as in a free surface domain adjacent to a passive fluid matrix. The Onsager principle ensures fundamental variational structure of the models as well as dissipative properties of the passive component in the models, irrespective of the choice of scale (kinetic to continuum) and of the physical potentials. Many popular models for passive and active liquid crystals in a fixed domain subject to consistent boundary conditions at solid walls, as well as active liquid crystals in a free surface domain with consistent transport equations along the free boundaries, can be systematically derived from the generalized Onsager principle. The dynamical boundary conditions are shown to reduce to the static boundary conditions for passive liquid crystals used previously. View Full-Text
Keywords: active liquid crystals; nonequilibrium thermodynamics; hydrodynamics; free surface boundary conditions active liquid crystals; nonequilibrium thermodynamics; hydrodynamics; free surface boundary conditions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Yang, X.; Li, J.; Forest, M.G.; Wang, Q. Hydrodynamic Theories for Flows of Active Liquid Crystals and the Generalized Onsager Principle. Entropy 2016, 18, 202.

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