Abstract
We discuss the time-reversal behavior of dynamic cross-couplings among various hydrodynamic degrees of freedom in liquid crystal systems. Using a standard hydrodynamic description including linear irreversible thermodynamics, we show that the distinct thermodynamic requirements for reversible and irreversible couplings lead to experimentally accessible differences. We critically compare our descriptions with those of existing standard continuum mechanics theories, where time-reversal symmetry is not adequately invoked. The motivation comes from recent experimental progress allowing to discriminate between the hydrodynamic description and the continuum mechanics approach. This concerns the dynamics of Lehmann-type effects in chiral liquid crystals and the dynamic magneto-electric response in ferronematics and ferromagnetic nematics, a liquid multiferroic system. In addition, we discuss the consequences of time-reversal symmetry for flow alignment of the director in nematics (or pretransitional nematic domains) and for the dynamic thermo-mechanical and electro-mechanical couplings in textured nematic liquid crystals.
Highlights
Time-reversal symmetry is one of the fundamental properties of microscopic as well as of macroscopic systems
We have shown that the behavior under time reversal plays an important role for the macroscopic description of soft matter systems
It arises due to a chiral dissipative dynamic cross-coupling as well as due a chiral static cross-coupling, which are sometimes called “dynamic” and “static” Lehmann effect, respectively
Summary
Time-reversal symmetry is one of the fundamental properties of microscopic as well as of macroscopic systems. Typical physical examples are flow alignment and backflow in nematic liquid crystals, Eqs. 82 and 83 and the dynamic reversible cross-coupling between the director and the magnetization in ferrronematics, Eqs. 54 and 55.
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