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Rheology of a confined vesicle suspension

Abdessamad Nait-Ouhra1,2, Alexander Farutin1, Hamid Ez-Zahraouy2, Abdelilah Benyoussef2,3, and Chaouqi Misbah1

  • 1Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
  • 2Laboratoire de Matière Condensée et Sciences Interdisciplinaires, Faculty of Sciences, Mohammed V University of Rabat, 1014 Morocco
  • 3Hassan II Academy of Science and Technology, Rabat, 10220 Morocco

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Phys. Rev. Fluids 4, 103602 – Published 14 October, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.103602

Abstract

Rheology of a confined suspension of vesicles (model for blood) is analyzed numerically in two dimensions as a function of the viscosity contrast λ (defined as the ratio between the inner and the outer viscosities, ηin and ηout). We consider both the dilute, semidilute, and more concentrated regimes up to about 35% of vesicle area fraction. This paper is a follow-up of our recent work [Phys. Rev. Fluids 3, 123601 (2018)], where we found that, depending on λ, the vesicle can either be centered or off-centered in a channel. Here we analyze in particular how the existence of the new attractor (off-centered solution) affects rheology. In the dilute regime, it is found that the effective viscosity corresponding to the off-centered solution may have a lower value than that of the centered solution. Moreover, the effective viscosity shows a discontinuity as a function of λ. This discontinuity is traced back to the existence of a saddle-node bifurcation of the lateral position. When the flow strength is increased, the viscosity behavior becomes continuous, owing to the evolution of the transition of the off-centered solution from a saddle-node to a pitchfork bifurcation. We analyze then rheology as a function of the suspension concentration φ for different values of λ. For large enough λ the viscosity may be lower or larger than that corresponding to small λ, depending on initial configuration. There is a critical concentration beyond which the initial configuration is irrelevant, but still the behavior of the suspension viscosity with φ for low and large λ are quite different both qualitatively and quantitatively. This is traced back to special spatial organization of the confined suspensions, which depends on λ.

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Phys. Rev. Fluids 4, 103602– Published 14 October, 2019
  • Received 8 April 2019
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