Comptes Rendus
no. 2
Calculus of variations
Asymptotic formulas for perturbations in Stokes flow due to the presence of small immiscible liquid particles

Presented by: Haïm Brézis

Mohamed Abdelwahed1; Nejmeddine Chorfi1; Maatoug Hassine2
1 Department of Mathematics, College of Sciences, King Saud University, Saudi Arabia
2 Département de Mathématiques, Faculté des sciences de Monastir, Tunisia
Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 219-223.

The aim of this work is the design of an efficient method to obtain information about a finite number of small and well-separated liquid particles located in a viscous fluid from boundary measurements. The viscosity and density of particles are different from those of a background fluid governed by a Stokes flow. An asymptotic formula for the velocity perturbation is derived based on the concept of Viscous Moment Tensor analysis. This formula will be the principle for efficient computational algorithms of identification.

On considère l'écoulement d'un fluide visqueux incompressible décrit par les équations de Stokes. On démontre dans cette note des formules de représentations asymptotiques pour les perturbations de vitesse causées par la présence d'un nombre fini de particules liquides de faible volume. On suppose que les particules (la phase dispersée) sont distinctes et que leurs caractéristiques physiques (la viscosité et la densité) sont différentes de celle du fluide de référence (la phase continue). Nous avons introduit la notion des tenseurs visqueux. Ces formules de représentations peuvent être utilisées pour construire des algorithmes numériques très efficaces d'identification (ou d'optimisation d'emplacements) des particules à partir des données au bord sur-déterminées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.10.023

Mohamed Abdelwahed 1; Nejmeddine Chorfi 1; Maatoug Hassine 2

1 Department of Mathematics, College of Sciences, King Saud University, Saudi Arabia
2 Département de Mathématiques, Faculté des sciences de Monastir, Tunisia 
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     title = {Asymptotic formulas for perturbations in {Stokes} flow due to the presence of small immiscible liquid particles},
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Mohamed Abdelwahed; Nejmeddine Chorfi; Maatoug Hassine. Asymptotic formulas for perturbations in Stokes flow due to the presence of small immiscible liquid particles. Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 219-223. doi : 10.1016/j.crma.2015.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.023/

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