Sketch of the mesoscopic description of nematic liquid crystals

Beyond the usual 5-field theory (the basic fields are the mass density, velocity, internal energy), additional variables are needed for the unique description of complex media. Beside the conventional method of introducing additional fields by their balances, another procedure, the mesoscopic theory, is here discussed and applied to Cosserat continua. IntroductionContinuum mechanics is based on the balance equations of mass, momentum, angular momentum or spin, total or kinetic energy, and internal energy. Additionally, one has to consider the balance of entropy for taking into account the second law. In nonrelativistic physics, all these balances are defined with respect to time and position (x, t). Beyond the quantities whose balance equations are mentioned above, complex materials need more variables for their unique description. Examples for these additional quantities are internal variables, order and damage parameters, Cosserat triads, directors and alignment and conformation tensors.In principle, there are two possibilities to include these additional quantities into the continuum theoretical description: One can introduce additional fields and their balance equations defined with respect to (x, t) as in the case of Cosserat continua, or the additional quantities, the so-called mesoscopic variables, are introduced as variables extending space-time to the so-called mesoscopic space. This description introducing the mesoscopic space is called the mesoscopic theory. According to its W. Muschik ( )

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“…Up to now, liquid crystals [22], micro-cracks [27,24] and ferrofluids [23] are mesoscopically described.…”

Section: Discussionmentioning

confidence: 99%

Cosserat Continua Described by Mesoscopic Theory

Muschik

Papenfuß

2010

Advances in Mechanics and Mathematics

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“…Because mixture theory is well developed [24,25] mesoscopic balance equations can be written down very easily [26]. The special case of liquid crystals is considered in [27].…”

Section: The Mesoscopic Theorymentioning

confidence: 99%

“…A particle of the liquid crystal continuum theory contains a lot of molecules of different orientations, resulting in a mean orientation belonging to the considered particle described by a unit vector d. This unit vector-called the macroscopic director-is a basic field d(x, t) of the macroscopic director theory of nematic liquid crystals [28,29] (the Ericksen-Leslie theory [27]) whose microscopic background is out of scope (If the microscopic background is taken into account, the Ericksen-Leslie one-director theory allows only parallel or planar orientation of the microscopic directors [30].). As an internal variable, the macroscopic director needs an evolution equation (see Section 4.2.4).The macroscopic director as a basic field does not contain any information about the degree of orientation of the microscopic directors.…”

Section: General Remarksmentioning

confidence: 99%

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

Papenfuß

Muschik

2018

Entropy

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Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.

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“…where the index j denotes that there is a dot product between the covariant differential operator ∇ and the contravariant current density j A , the continuity equation (29) for the electric dipoles can be recast as,…”

Section: Time Evolution Of the Electric Dipolesmentioning

confidence: 99%

“…Here, we show how our formalism accounts for the Lehmann effect. It is worth mentioning that the irreversible thermodynamics of a continuum of nematic liquid crystals has been examined by Müller [5] and Muschik [28,29], even though these authors did not explicitly deduce the Lehmann effect from their formalism. The "director" vector field they introduced corresponds to the preferred axisn of the continuum of liquid crystals.…”

Section: Lehmann Effectmentioning

confidence: 99%

Thermodynamics of a continuous medium with electric and magnetic dipoles

Brechet

Ansermet

2013

Eur. Phys. J. B

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The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.PACS. 05.70. Ln, 75.76.+j,

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Sketch of the mesoscopic description of nematic liquid crystals

Cited by 15 publications

References 46 publications

Cosserat Continua Described by Mesoscopic Theory

Cosserat Continua Described by Mesoscopic Theory

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

Thermodynamics of a continuous medium with electric and magnetic dipoles

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