Geodesic
Dynamics and Rheology of highly deflated vesicles
Giovanni Ghigliotti1 ; Hassib Selmi2 ; Badr Kaoui1 ; George Biros3 ; Chaouqi Misbah1
1 Laboratoire de Spectrométrie Physique, CNRS - Université Joseph Fourier / UMR 5588, BP 87, 38402 Saint Martin d'Hères, France.
2 Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie B.P. 743 - 2078 La Marsa, Tunisia
3 Georgia Institute of Technology, 1324 Klaus Advanced Computing Building, 266 Ferst Drive, Atlanta GA 30332-0765
ESAIM. Proceedings, Tome 28 (2009), pp. 211-226.

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We study the dynamics and rheology of a single two-dimensional vesicle embedded in a linear shear flow by means of numerical simulations based on the boundary integral method. The viscosities inside and outside the vesicle are supposed to be identical. We explore the rheology by varying the reduced area, i.e. we consider more and more deflated vesicles. Effective viscosity and normal stress differences are computed and discussed in detail, together with the inclination angle and the lateral membrane velocity (tank-treading velocity). The angle is found, surprisingly, to reach a zero value (flow alignment) at a critical reduced area even in the absence of viscosity contrast. A Fast Multipole Method is presented that enables to run efficiently simulations with a large number of vesicles. This method prevails over the direct summation for a number of mesh points beyond a value of about 103. This offers an interesting perspective for simulation of semi-dilute and concentrated suspensions.
DOI : 10.1051/proc/2009048

Giovanni Ghigliotti 1 ; Hassib Selmi 2 ; Badr Kaoui 1 ; George Biros 3 ; Chaouqi Misbah 1

1 Laboratoire de Spectrométrie Physique, CNRS - Université Joseph Fourier / UMR 5588, BP 87, 38402 Saint Martin d'Hères, France.
2 Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie B.P. 743 - 2078 La Marsa, Tunisia
3 Georgia Institute of Technology, 1324 Klaus Advanced Computing Building, 266 Ferst Drive, Atlanta GA 30332-0765 
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     author = {Giovanni Ghigliotti and Hassib Selmi and Badr Kaoui and George Biros and Chaouqi Misbah},
     title = {Dynamics and {Rheology} of highly deflated vesicles},
     journal = {ESAIM. Proceedings},
     pages = {211--226},
     publisher = {mathdoc},
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     year = {2009},
     doi = {10.1051/proc/2009048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009048/}
}
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Giovanni Ghigliotti; Hassib Selmi; Badr Kaoui; George Biros; Chaouqi Misbah. Dynamics and Rheology of highly deflated vesicles. ESAIM. Proceedings, Tome 28 (2009), pp. 211-226. doi : 10.1051/proc/2009048. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009048/

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