A Floquet stability analysis for capsules in shear flow
Observations in experiments and simulations show that the kinematic behaviour of an elastic capsule, suspended and rotating in shear flow, depends upon the flow strength, the capsule membrane material properties and its at-rest shape. We developed a linear stability description of the periodically rotating base state of this coupled system, as represented by a boundary integral flow formulation with spherical harmonic basis functions describing the elastic capsule geometry. This gave Floquet multipliers that classified the stability of the capsule motion for varying elastic capillary numbers. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon the flow strength, over many periods of the rotation. The transitions in this stability behavior correspond to the different classes of rotating motion observed in previous studies.
S. H. Bryngelson and J. B. Freund, “Floquet stability analysis of capsules in viscous shear ﬂow,” J. Fluid Mech. 852, 663–677 (2018)