Mesoscopic theory of liquid crystals

Muschik, W.; Papenfuß, Christina; Ehrentraut, H.

doi:10.1515/jnetdy.2004.006

Cited by 17 publications

(16 citation statements)

References 38 publications

(52 reference statements)

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“…The general mesoscopic concept was introduced by Muschik and his coworkers [1][2][3] in order to model microstructural effects within a continuum mechanical framework. Part of this concept is the introduction of a statistical function describing the microstructural distribution; in our case, this is the arrangement of bubbles or pores.…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Weinberg¹,

Böhme²

2008

Journal of Non-Equilibrium Thermodynamics

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In this work, the damage in biological soft tissue induced by bubble cavitation is investigated. A typical medical procedure with such damaging side effects is the kidney stone fragmentation by shock-wave lithotripsy. We start with a mesoscopic continuum model that allows the consideration of microstructural information within the macroscopic balance equations. An evolution equation for the temporal development of the bubble distribution function is derived. Furthermore, the constitutive relations of bubble expansion are deduced by means of a spherical shell model. Numerical simulations are presented for a typical soft tissue material and different definitions for a damage parameter are discussed.

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Section: Introductionmentioning

confidence: 99%

Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Weinberg¹,

Böhme²

2008

Journal of Non-Equilibrium Thermodynamics

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“…The usual way to describe complex materials is to include additional fields and their governing equations (9). The di‰culty which arises is the knowledge of these additional equations (9) and of the material equations F 0 ðx; tÞ and S 0 ðx; tÞ.…”

mentioning

confidence: 99%

“…The mesoscopic balance equations (13) have to be solved by methods which are also applied to the balances (1). Examples for mesoscopic variables are the dryness fraction in a two-phase flow, the microscopic director in liquid crystal theory [9], the damage parameter in crack theory [10] and the orientation of microcrystallites in microstructured media.…”

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confidence: 99%

Remarks on thermodynamical terminology

Muschik¹

2004

Journal of Non-Equilibrium Thermodynamics

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Registration Number 025 Often di‰culties in understanding thermodynamics arise from using di¤erent terminology or semantics. Therefore here some few remarks are made for tending towards a unified thermodynamical terminology. First of all one has to distinguish between two di¤erent description of thermodynamical systems: Such a system can be described as a discrete (or lumped) system or by field formulation. Discrete systems are separated from its environment by partitions. The interaction between the discrete system and its environment can be described by exchanges, namely by heat exchange, by power exchange and by material exchange (Schottky system) [1]. The discrete system itself is characterized by in general time-dependent quantities, the basic variables, belonging to the whole system [2]. This is of course a reduced model of a thermodynamical system. For a more detailed depiction of the system, it has to be described as a composite (or compound) system or by field formulation. The exchanges between the system and the environment depend on both their basic variables. Because naturally no gradients appear in the description of discrete systems, this concept is used in thermostatics. But also complex machines in engineering sciences are described by discrete systems, if mainly exchange quantities are of interest. Thus, for a reduced description of complex situations, the concept of a discrete system is a very useful one.

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“…The mesoscopic distribution function (MDF) satisfies a balance equation because of the definition (4) and of the mesoscopic mass balance (9). A straight forward calculation results in [12].…”

Section: Balance Of the Mdfmentioning

confidence: 99%

“…The fifth concept describing liquid crystals introduces the above-mentioned microscopic director related to the orientation of a single rigid uniaxial molecule. The anisotropic fluid is formally treated as a mixture by regarding all particles of a volume element of the same orientation as one component of the fluid [9][10][11][12][13]. Thus the orientation distribution function results from the fraction of the mass density of one component by the mass density of the mixture.…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic Theory of Liquid Crystals

Muschik

Papenfuß

Ehrentraut

Entropy and Entropy Generation

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Liquid crystals of uniaxial and biaxial molecules are considered in the framework of the mesoscopic description which is a general tool of continuum theory. A mesoscopic theory introduces the fields beyond hydrodynamics as additional variables of a configuration space, called mesoscopic space, on which the fields appearing in balances are defined. Besides the mesoscopic space, a mesoscopic distribution function is introduced which describes the distribution of the additional variables at each time and position. It is demonstrated, how the mesoscopic theory can be applied to liquid crystals, and how the Ericksen-Leslie theory and the alignment tensor theory of liquid crystals fit into the mesoscopic framework. general case in constitutive theory. As the following examples show, the additional fields describing complex materials are of various kinds: internal variables ! memory alloys order parameters ! phase transitions damage parameters ! fatigue problems Cosserat triads ! steel, microcrystallites, granular media conformation tensors ! polymers fabric tensors ! composite materials directors, alignment tensors ! liquid crystals.The orientational order in liquid crystals can be di¤erently characterized. Because of thermal fluctuations the molecules are not totally aligned, but have a certain distribution around a ''mean orientation'' which can be described by a normalized macroscopic director field. The name ''macroscopic'' originates from the fact that the macroscopic director field belongs to all molecules of a volume element, whereas a special molecule may be aligned di¤erently. So it is obvious to introduce a microscopic director which describes the alignment of a single molecule and which is different from the local macroscopic director in general.Besides the microscopic and the macroscopic director, other descriptions for alignment are in use which can be found in the following synopsis. Up to now there are five di¤erent phenomenological concepts suitable to describe liquid crystals nonmicroscopically. The first one is the well known Ericksen-Leslie theory [1, 2] whose balance equations are formulated by use of the macroscopic director mentioned above. But in fact this theory is not able to represent a change in the degree of orientational order [3]. In general we need at each point and time a distribution function for describing the macroscopic orientation of the fluid. Therefore the macroscopic director has to be redefined statistically.The second concept describes liquid crystals as micropolar media in the frame of a 3-director theory [4]. Instead of a balance equation for the macroscopic director, the spin balance is taken into account, but no microscopic concepts are introduced.The third concept [5] introduces besides the balance equations of a micropolar medium an additional field, called microinertia tensor field. This field, satisfying its own balance equation, is coupled to the spin balance. The form of this coupling causes all needle-shaped molecules of a volume element to always have the same angul...

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Mesoscopic theory of liquid crystals

Cited by 17 publications

References 38 publications

Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Mesoscopic Modeling for Continua with Pores: Application in Biological Soft Tissue

Remarks on thermodynamical terminology

Mesoscopic Theory of Liquid Crystals

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