# Publications by Daiki Matsunaga

## 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>

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