Abstract
We present a three-dimensional numerical study on the dynamics of deformable capsules in sinusoidally oscillating shear flow. We consider capsules of spherical and oblate spheroid resting shapes. For spherical resting shapes, we find an identical deformation response during positive and negative vorticities. However, the deformation response becomes unequal and shows complex behavior for nonspherical resting shapes. The average elongation is higher in the retarding phase of the shear flow than in the accelerating phase. Primarily two types of dynamics are observed for nonspherical shapes: a clockwise/counter-clockwise swinging motion in response to the altering flow direction that occurs at both high and low values of shear rate amplitudes, and a continuous/unidirectional tumbling motion that occurs at intermediate values. The unidirectional tumbling motion occurs despite the fact that the time-average vorticity is zero. Such a tumbling motion is accompanied by a continuous tank-treading motion of the membrane in the opposite direction. We obtain phase diagram that shows existence of two critical shear rates and two oscillation frequencies. The unidirectional tumbling motion occurs in the intermediate range, and the clockwise/counter-clockwise swinging motion occurs otherwise. We also find that the dynamics is highly sensitive to the initial condition. A swinging is generally observed when the capsule is released aligned with the extensional or compressional axis of the shear flow, and a tumbling is observed otherwise. These results suggest the possibility of chaotic behavior of cells in time-dependent flows. We provide explanations of such complex dynamics by analyzing the coupling between the shape and angular oscillation and the imposed flow oscillation.