Heterogeneous hard-sphere interactions for equilibrium transport processes beyond perforated domain formulations

Markus Schmuck

Research output: Contribution to journalArticle

Abstract

We consider transport of neutral species interacting under a potential of mean force with randomly placed, rigid spherical obstacles. Generally, this kind of transport problems are studied as so-called perforated domain problems, where one imposes no-flux or reaction boundary conditions on the pore walls forming the interface between the pore and the solid phase. Here, we advocate a general framework that replaces the perforated domain formulation with interaction energies as well as with characteristic and scale-dependent randomness of materials. Our framework provides both well-posed effective macroscopic equations for highly heterogeneous situations and a full scale description for weakly heterogeneous materials for which we present first computational results.
Original languageEnglish
Pages (from-to)78-83
Number of pages6
JournalApplied Mathematics Letters
Volume49
DOIs
Publication statusPublished - Nov 2015

Fingerprint

macroscopic equations
porosity
formulations
solid phases
interactions
boundary conditions
energy

Keywords

  • Composites
  • Hard-sphere potential
  • Homogenization
  • Potential of mean force
  • Random materials
  • Smoluchowski equation
  • Stochastic two-scale convergence in the mean

Cite this

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abstract = "We consider transport of neutral species interacting under a potential of mean force with randomly placed, rigid spherical obstacles. Generally, this kind of transport problems are studied as so-called perforated domain problems, where one imposes no-flux or reaction boundary conditions on the pore walls forming the interface between the pore and the solid phase. Here, we advocate a general framework that replaces the perforated domain formulation with interaction energies as well as with characteristic and scale-dependent randomness of materials. Our framework provides both well-posed effective macroscopic equations for highly heterogeneous situations and a full scale description for weakly heterogeneous materials for which we present first computational results.",
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Heterogeneous hard-sphere interactions for equilibrium transport processes beyond perforated domain formulations. / Schmuck, Markus.

In: Applied Mathematics Letters, Vol. 49, 11.2015, p. 78-83.

Research output: Contribution to journalArticle

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KW - Random materials

KW - Smoluchowski equation

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