# Publications by Daiki Matsunaga

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

Journal of Fluid Mechanics Cambridge University Press (CUP) 786 (2016) 110-127

D Matsunaga, Y Imai, T Yamaguchi, T Ishikawa

<jats:p>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 <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015006667_inline1" /><jats:tex-math>${\it\phi}=0.4$</jats:tex-math></jats:alternatives></jats:inline-formula> 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, <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015006667_inline2" /><jats:tex-math>$O({\it\phi}^{3})$</jats:tex-math></jats:alternatives></jats:inline-formula> terms account for only 8 % of the specific viscosity even at <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015006667_inline3" /><jats:tex-math>${\it\phi}=0.4$</jats:tex-math></jats:alternatives></jats:inline-formula> for capillary numbers <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112015006667_inline4" /><jats:tex-math>$Ca\geqslant 0.1$</jats:tex-math></jats:alternatives></jats:inline-formula>. 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.</jats:p>

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