Mesoscopic continuum thermodynamics for mixtures of particles with orientation

Florindo, Caio César Ferreira; Papenfuß, Christina; Bassi, Adalberto Bono Maurizio Sacchi

doi:10.1007/s10910-017-0778-0

Cited by 3 publications

(7 citation statements)

References 31 publications

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“…The orientational balances for the mesophase pitch (microdomains and ambient mesophase) are shown in Table 1. Their mathematical deduction is not displayed here, but it is similar to those deduced in [15] and [28].…”

Section: Orientational Balancessupporting

confidence: 72%

“…The orientational balance equations for the mesophase pitch are similar to those used in the theory of liquid crystals [16-18, 21-23, 26, 27] and in the thermodynamic investigation of mixtures with orientation [15]. These balance equations on the mesoscopic level are obtained from the general expression of balance equations [16] for an arbitrary extensive quantity:…”

Section: Orientational Balancesmentioning

confidence: 99%

“…Starting from Eq. ( 4) and the mesoscopic mass balance (see Table 1 and reference [15]), an evolution equation for the MDF of microdomain α is obtained,…”

Section: Orientation Distribution Function For the Microdomainsmentioning

confidence: 99%

“…In addition, evolution equations for the density and orientation of the crystalline microdomains are also deduced. The employed approach is based on the continuum mesoscopic thermodynamics [15], developed originally for liquid crystals [16][17][18][19][20]. The idea is to take into account the mesoscopic distribution function for molecular aggregates.…”

Section: Introductionmentioning

confidence: 99%

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On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach

Florindo¹,

Papenfuß

Bassi

2022

J Math Chem

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The present paper proposes a mesoscopic continuum approach in order to describe the behavior of microdomains within carbon fiber precursory mesophase pitch. The microdomains are assumed to have an orientation, which is determined by the average orientation of the particles that form it. On the mesoscopic space, balance equations for the microdomains are presented. Evolution equations for the density and for the orientation of the crystalline microdomains are proposed. In order to determine the temporal variation of the microdomain density, it was deduced a quite simple relation between mass production, critical density of microdomains and a mesoscopic operator acting on the orientation distribution function. As presented in the present work, the mass production can be determined by the crystallization kinetics theory via the steady-state nucleation rate. Specific forms for the mesoscopic operator are proposed in this work, although they may be extended to other models that describe oriented microstructures. There are not yet enough experimental data to test the mesoscopic model deduced here, but in turn, it is presented as a new tool for experimental studies, since it can estimate the time rate of microdomain property changes. Possible extensions of this model could be applied to describe mechanical and rheological properties of carbon fibers.

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Section: Orientational Balancessupporting

confidence: 72%

Section: Orientational Balancesmentioning

confidence: 99%

“…Starting from Eq. ( 4) and the mesoscopic mass balance (see Table 1 and reference [15]), an evolution equation for the MDF of microdomain α is obtained,…”

Section: Orientation Distribution Function For the Microdomainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach

Florindo¹,

Papenfuß

Bassi

2022

J Math Chem

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“…The mesoscopic concept has been applied to various kinds of materials with an internal structure, like solids damaged by micro-cracks [56][57][58][59][60][61][62][63], dipolar media [64], mixtures [65,66], granular materials [67], magnetorheological fluids [68] and fiber reinforced concrete [69,70]. Three different applications will be sketched in the following.…”

Section: Further Applications Of Mesoscopic Theorymentioning

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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Benchmarking solutions of the Folgar–Tucker-Equation and its reduction to a linear problem for non-linear closure forms

Winters¹,

Papenfuß²,

Karow³

2022

Journal of Non-Newtonian Fluid Mechanics

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Mesoscopic continuum thermodynamics for mixtures of particles with orientation

Cited by 3 publications

References 31 publications

On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach

On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach

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

Benchmarking solutions of the Folgar–Tucker-Equation and its reduction to a linear problem for non-linear closure forms

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