Non-modal Floquet analysis for stabilizing soft particles in large-amplitude oscillatory extension
We analyzed the stability of a capsule in large-amplitude oscillatory extensional (LAOE) flow, as often used to study the rheology and dynamics of suspensions. Such a flow is typically established in a cross-slot configuration, with the particle (or particles) of interest observed in the stagnation region. However, controlling this configuration is challenging because the flow is unstable. We quantify such an instability for spherical elastic capsules suspended near the stagnation point using a non-modal global Floquet analysis, which is formulated to include full coupling of the capsule-viscous-flow dynamics. The flow is shown to be transiently, though not asymptotically, unstable. For each case considered, two predominant transient instabilities are identified: intra-period growth for translational capsule perturbations and period-to-period growth for certain capsule distortions. The amplitude of the intra-period instability depends linearly on the flow strength and oscillation period, and the period-to-period growth saturates over several periods, commensurate with the asymptotic stability of the flow.
S. H. Bryngelson and J. B. Freund, “Non-modal Floquet stability of capsules in large-amplitude oscillatory extensional ﬂow,” submitted