Dynamics of a Spherical Capsule in a Planar Hyperbolic flow: Influence of bending Resistance

We consider an initially spherical capsule freely suspended in a planar hyperbolic flow and study the influence of the wall bending resistance on the capsule dynamics. The capsule wall is assumed to be made of a three-dimensional homogeneous elastic material. The fluid-structure interaction between the capsule and the external flow is modeled numerically by coupling a boundary integral method with a shell finite element method. It is found that, for given three-dimensional wall mechanical properties, the capsule deformability is drastically reduced as the bending resistance is increased. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the shape and deformation: the capsule main deformation mode is thus solely a function of the elastic stretching of the mid-surface. The wall bending resistance still plays a role locally in the regions where buckling occurs. Its influence is studied in the low flow strength regime, for which wrinkling of the wall is observed to persist at steady state. We show that the wrinkle wavelength only depends on the bending number, which compares the relative importance of bending and shearing phenomena, and provide the correlation law. This result is interesting as it allows bending resistance to be estimated from experiments on capsules in a planar hyperbolic flow at low flow strength.