Ericksen-Leslie Liquid Crystal Theory Revisited from a Mesoscopic Point of View

Muschik, W.; Ehrentraut, H.; Blenk, Stefan

doi:10.1515/jnet.1995.20.1.92

Cited by 18 publications

(18 citation statements)

References 7 publications

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“…This means mesoscopically investigated, locally total or planar alignment of all molecules [30]. If the ODF is uniaxial, the alignment tensor has the Maier-Saupe form (22).…”

Section: Discussionmentioning

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%

“…Apart from this, the following statement is true: If the macroscopic director is a basic field, as in the well-known Ericksen-Leslie theory, all microscopic directors are perfectly aligned along the symmetry axis of the ODF or perpendicular to it [30].…”

Section: The Mesoscopic Root Of the Alignment Tensor Familymentioning

confidence: 99%

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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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“…This means mesoscopically investigated, locally total or planar alignment of all molecules [30]. If the ODF is uniaxial, the alignment tensor has the Maier-Saupe form (22).…”

Section: Discussionmentioning

confidence: 99%

Section: General Remarksmentioning

confidence: 99%

See 1 more Smart Citation

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

Papenfuß

Muschik

2018

Entropy

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“…In this respect, each observer takes himself as a standard frame of reference, what he can do without restrictions. The transformation between these standard frames of reference are given by (25) and (26). For objective quantities, all frames are standard frames of reference because of their tensor properties under changing the observer.…”

Section: Ordermentioning

confidence: 99%

“…The result is different from Müller [6]: The heat flux density is objective under changing the observer, but it depends on the material's motion with respect to the standard frame of reference. Finally two different descriptions of liquid crystals are juxtaposed with respect to changing the observer: The macroscopic Ericksen-Leslie theory [22,23] and the mesoscopic theory of liquid crystals [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example

Muschik

Restuccia

2008

Arch Appl Mech

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In this paper objectivity and material frame-indifference are systematically discussed, because changing the observer and changing the motion of a material with respect to an observer independent standard frame of reference have to be distinguished carefully. Objectivity and observer invariance of the physical laws and of the constitutive mappings are introduced. Semi-objectivity and objectivity of different time derivative operators are investigated. As examples, changing the observer in liquid crystal theory and changing the motion in linear heat conducting materials is considered.

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A note on couette flow of nematic crystals according to the Ericksen–Leslie theory

2019

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In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians. Analytical and numerical solutions for the fields are derived for different boundary conditions and will subsequently be discussed.

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Ericksen-Leslie Liquid Crystal Theory Revisited from a Mesoscopic Point of View

Cited by 18 publications

References 7 publications

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

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

Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example

A note on couette flow of nematic crystals according to the Ericksen–Leslie theory

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