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Floquet stability analysis of capsules in viscous shear flow

Published online by Cambridge University Press:  13 August 2018

Spencer H. Bryngelson  and
Jonathan B. Freund Open the ORCID record for Jonathan B. Freund [Opens in a new window]
Spencer H. Bryngelson
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
Jonathan B. Freund*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
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Abstract

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 develop 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 yields Floquet multipliers that classify the stability of the capsule motion for elastic capillary numbers $Ca$ ranging from $Ca=0.01$ to 5. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon $Ca$, over many periods of the rotation. The transitions in this stability behaviour correspond to the different classes of rotating motion observed in previous studies.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Capsule/cell dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 663 - 677
Copyright
© 2018 Cambridge University Press 

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