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The motion of a deforming capsule through a corner

Published online by Cambridge University Press:  08 April 2015

Lailai Zhu  and
Luca Brandt
Lailai Zhu*
Affiliation:
Swedish e-Science Research Centre and Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden Laboratory of Fluid Mechanics and Instabilities, Station 9, EPFL, 1105 Lausanne, Switzerland
Luca Brandt
Affiliation:
Swedish e-Science Research Centre and Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner, as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Boundary integral methods Biological Fluid Dynamics: Capsule/cell dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , pp. 374 - 397
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Copyright
© 2015 Cambridge University Press 

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Zhu and Brandt supplementary movie

The motion of a stiff capsule (Ca=0.0375) convected in a square duct with a 90 degree sharp corner. Half of the fluid domain is shown.

Download Zhu and Brandt supplementary movie(Video)
Video 5.5 MB

Zhu and Brandt supplementary movie

The motion of a floppy capsule (Ca=0.3) convected in a square duct with a 90 degree sharp corner. Half of the fluid domain is shown.

Download Zhu and Brandt supplementary movie(Video)
Video 6.6 MB