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Pré-Publication, Document De Travail Année : 2022

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

Richard M. Höfer
  • Fonction : Auteur
Marta Leocata
  • Fonction : Auteur

Résumé

We consider a microscopic model of $n$ identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress that appears in so-called Doi models which couple a Fokker-Planck equation to the Stokes equations. We consider both Deborah numbers of order $1$ and very small Deborah numbers. Our microscopic model contains several simplifications, most importantly, we neglect the time evolution of the particle centers as well as hydrodynamic interaction for the evolution of the particle orientations. The microscopic fluid velocity is modeled by the Stokes equations with given torques at the particles in terms of Stratonovitch noise. We give a meaning to this PDE in terms of an infinite dimensional Stratonovitch integral. This requires the analysis of the shape derivatives of the Stokes equations in perforated domains, which we accomplish by the method of reflections.

Dates et versions

hal-03867256 , version 1 (23-11-2022)

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Richard M. Höfer, Marta Leocata, Amina Mecherbet. Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization. 2022. ⟨hal-03867256⟩
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