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Rheology of a dense suspension of spherical capsules under simple shear flow

Published online by Cambridge University Press:  30 November 2015

D. Matsunaga ,
Y. Imai ,
T. Yamaguchi  and
T. Ishikawa
D. Matsunaga
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
Y. Imai*
Affiliation:
School of Engineering, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
T. Yamaguchi
Affiliation:
Department of Biomedical Engineering, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
T. Ishikawa
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan Department of Biomedical Engineering, Tohoku University, 6-6-01 Aoba, Aoba, Sendai 980-8579, Japan
*
†Email address for correspondence: [email protected]
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Abstract

We present a numerical analysis of the rheology of a dense suspension of spherical capsules in simple shear flow in the Stokes flow regime. The behaviour of neo-Hookean capsules is simulated for a volume fraction up to ${\it\phi}=0.4$ by graphics processing unit computing based on the boundary element method with a multipole expansion. To describe the specific viscosity using a polynomial equation of the volume fraction, the coefficients of the equation are calculated by least-squares fitting. The results suggest that the effect of higher-order terms is much smaller for capsule suspensions than rigid sphere suspensions; for example, $O({\it\phi}^{3})$ terms account for only 8 % of the specific viscosity even at ${\it\phi}=0.4$ for capillary numbers $Ca\geqslant 0.1$. We also investigate the relationship between the deformation and orientation of the capsules and the suspension rheology. When the volume fraction increases, the deformation of the capsules increases while the orientation angle of the capsules with respect to the flow direction decreases. Therefore, both the specific viscosity and the normal stress difference increase with volume fraction due to the increased deformation, whereas the decreased orientation angle suppresses the specific viscosity, but amplifies the normal stress difference.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 110 - 127
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Copyright
© 2015 Cambridge University Press 

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