# 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

<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>

## Deformation of a micro-torque swimmer

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences The Royal Society **472** (2016) 20150604-20150604

## A numerical model of a red blood cell infected by Plasmodium falciparum malaria: coupling cell mechanics with ligand-receptor interactions

Science and Technology of Advanced Materials Informa UK Limited **17** (2016) 454-461

## Reorientation of a single red blood cell during sedimentation

Journal of Fluid Mechanics Cambridge University Press (CUP) **806** (2016) 102-128

<jats:p>The reorientation phenomenon of a single red blood cell during sedimentation is simulated using the boundary element method. The cell settles downwards due to a density difference between the internal and external fluids, and it changes orientation toward a vertical orientation regardless of Bond number or viscosity ratio. The reorientation phenomenon is explained by a shape asymmetry caused by the gravitational driving force, and the shape asymmetry increases almost linearly with the Bond number. When velocities are normalised by the driving force, settling/drifting velocities are weak functions of the Bond number and the viscosity ratio, while the angular velocity of the reorientation drastically changes with these parameters: the angular velocity is smaller for lower Bond number or higher viscosity ratio. As a consequence, trajectories of the sedimentation are also affected by the angular velocity, and blood cells with slower reorientation travel longer distances in the drifting direction. We also explain the mechanism of the reorientation using an asymmetric dumbbell. From the analysis, we show that the magnitude of the angular velocity is explained by two main factors: the shape asymmetry and the instantaneous orientation angle.</jats:p>

## Deformation of a spherical capsule under oscillating shear flow

Journal of Fluid Mechanics Cambridge University Press (CUP) **762** (2015) 288-301

<jats:title>Abstract</jats:title><jats:p>The deformation of a spherical capsule in oscillating shear flow is presented. The boundary element method is used to simulate the capsule motion under Stokes flow. We show that a capsule at high frequencies follows the deformation given by a leading-order prediction, which is derived from an assumption of small deformation limit. At low frequencies, on the other hand, a capsule shows an overshoot phenomenon where the maximum deformation is larger than that in steady shear flow. A larger overshoot is observed for larger capillary number or viscosity ratio. Using the maximum deformation in start-up shear flow, we evaluate the upper limit of deformation in oscillating shear flow. We also show that the overshoot phenomenon may appear when the quasi-steady orientation angle under steady shear flow is less than <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112014006491_inline1" /><jats:tex-math>$9.0^{\circ }$</jats:tex-math></jats:alternatives></jats:inline-formula>. We propose an equation to estimate the threshold frequency between the low-frequency range, where the capsule may have an overshoot, and the high-frequency range, where the deformation is given by the leading-order prediction. The equation only includes the viscosity ratio and the Taylor parameter under simple shear flow, so it can be extended to other deformable particles, such as bubbles and drops.</jats:p>

## A full GPU implementation of a numerical method for simulating capsule suspensions

Journal of Biomechanical Science and Engineering Japan Society of Mechanical Engineers **9** (2014)

## Lateral migration of a spherical capsule near a plane wall in Stokes flow

Physical Review E American Physical Society (APS) **90** (0) 043009