TY - JOUR
T1 - Non-modal Floquet stability of capsules in large-amplitude oscillatory extensional flow
AU - Bryngelson, Spencer H.
AU - Freund, Jonathan B.
N1 - Funding Information:
This work was supported in part by the National Science Foundation, USA under Grant No. CBET 13-36972.
Funding Information:
This work was supported in part by the National Science Foundation, USA under Grant No. CBET 13-36972 .
Publisher Copyright:
© 2019 Elsevier Masson SAS
PY - 2019/9/1
Y1 - 2019/9/1
N2 - We analyze 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 modes of transient amplification are identified: a predictable intra-period growth for translational capsule perturbations and period-to-period growth for certain capsule distortions. The amplitude of the intra-period growth depends linearly on the flow strength and oscillation period, which corresponds to a shift of the flow stagnation point, and the period-to-period growth saturates over several periods, commensurate with the asymptotic stability of the flow.
AB - We analyze 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 modes of transient amplification are identified: a predictable intra-period growth for translational capsule perturbations and period-to-period growth for certain capsule distortions. The amplitude of the intra-period growth depends linearly on the flow strength and oscillation period, which corresponds to a shift of the flow stagnation point, and the period-to-period growth saturates over several periods, commensurate with the asymptotic stability of the flow.
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U2 - 10.1016/j.euromechflu.2019.04.012
DO - 10.1016/j.euromechflu.2019.04.012
M3 - Article
AN - SCOPUS:85065799305
VL - 77
SP - 171
EP - 176
JO - European Journal of Mechanics, B/Fluids
JF - European Journal of Mechanics, B/Fluids
SN - 0997-7546
ER -