The motion of an initially spherical capsule in a wall-bounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neo-Hookean model is used as the constitutive law of the capsule membrane. The maximum wall-normal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of high-frequency oscillation. The migration velocity decreases monotonically with the frequency of the applied shear and the capsule-wall distance. We report a significant correlation between the capsule lateral migration and the normal stress difference induced in the flow. The periodic variation of the capsule deformation is roughly in phase with that of the migration velocity and normal stress difference, with twice the frequency of the imposed shear. The maximum deformation increases linearly with the membrane elasticity before reaching a plateau at higher capillary numbers when the deformation is limited by the time over which shear is applied in the same direction and not by the membrane deformability. The maximum membrane deformation scales as the distance to the wall to the power 1/3 as observed for capsules and droplets in near-wall steady shear flows.
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July 2015
Research Article|
July 16 2015
The dynamics of a capsule in a wall-bounded oscillating shear flow Available to Purchase
LaiLai Zhu;
LaiLai Zhu
a)
1
Linné Flow Center and SeRC
, KTH Mechanics, S-100 44 Stockholm, Sweden
2
Laboratory of Fluid Mechanics and Instabilities
, Station 9, EPFL, 1105 Lausanne, Switzerland
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Jean Rabault
;
Jean Rabault
b)
1
Linné Flow Center and SeRC
, KTH Mechanics, S-100 44 Stockholm, Sweden
3
École Polytechnique
, 91128 Palaiseau Cedex, France
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Luca Brandt
Luca Brandt
1
Linné Flow Center and SeRC
, KTH Mechanics, S-100 44 Stockholm, Sweden
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1
Linné Flow Center and SeRC
, KTH Mechanics, S-100 44 Stockholm, Sweden
2
Laboratory of Fluid Mechanics and Instabilities
, Station 9, EPFL, 1105 Lausanne, Switzerland
3
École Polytechnique
, 91128 Palaiseau Cedex, France
a)
Electronic mail: [email protected]
b)
Current address: Mechanics Division, Department of Mathematics, University of Oslo, 0316 Oslo, Norway.
Physics of Fluids 27, 071902 (2015)
Article history
Received:
November 18 2014
Accepted:
June 26 2015
Citation
LaiLai Zhu, Jean Rabault, Luca Brandt; The dynamics of a capsule in a wall-bounded oscillating shear flow. Physics of Fluids 1 July 2015; 27 (7): 071902. https://doi.org/10.1063/1.4926675
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