Tank-treading of microcapsules in shear flow

We investigated experimentally the deformation of soft microcapsules and the dynamics of their membrane in simple shear flows. Firstly, the tank-treading motion, i.e. the rotation of the membrane, was visualized and quantified by tracking particles included in the membrane by a new protocol. The period of membrane rotation increased quadratically with the extension of the long axis. The tracking of the distance between two close microparticles showed membrane contraction at the tips and stretching on the sides, a specific property of soft particles such as capsules. The present experimental results are discussed in regard to previous numerical simulations. This analysis showed that the variation of the tank-treading period with the Taylor parameter (deformation) cannot be explained by purely elastic membrane models. It suggests a strong effect of membrane viscosity whose order of magnitude is determined. Secondly, two distinct shapes of sheared microcapsules were observed. For moderate deformations, the shape was a steady ellipsoid in the shear plane. For larger deformations, the capsule became asymmetric and presented an S-like shape. When the viscous shear stress increased by three orders of magnitude, the short axis decreased by 70% whereas the long axis increased by 100% before any break-up. The inclination angle decreased from 40 degrees to 8 degrees, almost aligned with the flow direction as expected by theory and numerics on capsules and from experiments, theory and numerics on drops and vesicles. Whatever the microcapsule size and the concentration of proteins, the characteristic lengths of the shape, the Taylor parameter and the inclination angle satisfy master curves versus the long axis or the normalized shear stress or the capillary number in agreement with theory for non-negligible membrane viscosity in the regime of moderate deformations. Finally, we observed that very small deviation from sphericity gave rise to swinging motion, i.e. shape oscillations, in the small-deformation regime. In conclusion, this study of tank-treading motion supports the role of membrane viscosity on the dynamics of microcapsules in shear flow by independent methods that compare experimental data both with numerical results in the regime of large deformations and with theory in the regime of moderate deformations.