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Swinging and tumbling of multicomponent vesicles in flow

Published online by Cambridge University Press:  03 February 2022

Prerna Gera
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53711, USA
David Salac
Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260, USA
Saverio E. Spagnolie*
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53711, USA Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53711, USA
Email address for correspondence:


Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations and a two-dimensional system, we develop a reduced-order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid-body tumbling behaviour. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.

JFM Papers
© The Author(s), 2022. Published by Cambridge University Press

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Gera et al. supplementary movie 1

Movie M1: Vesicle dynamics with bending stiffness variation in spatial mode M=2. Beyond a critical magnitude of variation the elongated axis transitions from swinging to tumbling.

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Gera et al. supplementary movie 2

Movie M2: As in Movie M1, but with a smaller enclosed area.

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Gera et al. supplementary movie 3

Movie M3: As in Movies M1-M2, with yet smaller enclosed area.

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Gera et al. supplementary movie 4

Movie M4: Vesicles in a shear flow with different spatial modes of material property variation. The M=2 mode most strongly interacts with the deformation imposed by the background shear flow. The magnitude of the variation is just large enough for the case with two domains (M=2) to tumble.

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Gera et al. supplementary movie 5

Movie M5: As in Movie M3, but with increased variation in the bending stiffnesses. The swinging amplitudes of vesicles with even numbers of domains (M even) are increasing.

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Gera et al. supplementary movie 6

Movie M6: As in Movies M3-M4, with yet greater magnitude of bending stiffness variation, now showing tumbling in the vesicle with four domains (M=4).

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Supplementary material: PDF

Gera et al. supplementary material

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