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Controlling rotation and migration of rings in a simple shear flow through geometric modifications

Published online by Cambridge University Press:  12 February 2018

Neeraj S. Borker Open the ORCID record for Neeraj S. Borker [Opens in a new window] ,
Abraham D. Stroock  and
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]
Neeraj S. Borker
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Abraham D. Stroock
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Donald L. Koch*
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: dlk15@cornell.edu
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Abstract

A ring with a cross-section that has a blunt inner and sharper outer edge can attain an equilibrium orientation in a Newtonian fluid subject to a low Reynolds number simple shear flow. This may be contrasted with the continuous rotation exhibited by most rigid bodies. Such rings align along an orientation when the rotation due to fluid vorticity balances the counter-rotation due to the extensional component of the simple shear flow. While the viscous stress on the particle tries to rotate it, the pressure can generate a counter-vorticity torque that aligns the particle. Using boundary integral computations, we demonstrate ways to effectively control this pressure by altering the geometry of the ring cross-section, thus leading to alignment at moderate particle aspect ratios. Aligning rings that lack fore–aft symmetry can migrate indefinitely along the gradient direction. This differs from the periodic spatial trajectories of fore–aft asymmetric axisymmetric particles that rotate in periodic orbits. The mechanism for migration of aligned rings along the gradient direction is elucidated in this work. The migration speed can be controlled by varying the cross-sectional shape and size of the ring. Our results provide new insights into controlling motion of individual particles and thereby open new pathways towards manipulating macroscopic properties of a suspension.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 379 - 407
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Copyright
© 2018 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions: with Formulas, Graphs and Mathematical Tables. Courier.Google Scholar
Anczurowski, E. & Mason, S. G. 1967 The kinetics of flowing dispersions. Part III. Equilibrium orientations of rods and discs (experimental). J. Colloid Interface Sci. 23 (4), 533–546.CrossRefGoogle Scholar
Bao, G., Hutchinson, J. W. & McMeeking, R. M. 1991 Particle reinforcement of ductile matrices against plastic flow and creep. Acta Metall. Mater. 39 (8), 1871–1882.CrossRefGoogle Scholar
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44 (3), 419–440.CrossRefGoogle Scholar
Brenner, H. 1964 The Stokes resistance of an arbitrary particle. Part III: Shear fields. Chem. Engng Sci. 19 (9), 631–651.CrossRefGoogle Scholar
Bretherton, F. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14 (2), 284–304.CrossRefGoogle Scholar
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 324 (2), 289–306.CrossRefGoogle Scholar
Foulds, I. G. & Parameswaran, M. 2006 A planar self-sacrificial multilayer SU-8-based MEMS process utilizing a UV-blocking layer for the creation of freely moving parts. J. Micromech. Microengng 16 (10), 2109–2115.CrossRefGoogle Scholar
Isla, A., Brostow, W., Bujard, B., Esteves, M., Rodriguez, J. R., Vargas, S. & Castano, V. M. 2003 Nanohybrid scratch resistant coatings for teeth and bone viscoelasticity manifested in tribology. Mat. Res. Innovat. 7, 110–114.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Kim, S. & Karilla, S. J. 1991 Microhydrodynamics. Dover.Google Scholar
Kim, Y. J. & Rae, W. J. 1991 Separation of screw-sensed particles in a homogeneous shear field. Intl J. Multiphase Flow 17 (6), 717–744.CrossRefGoogle Scholar
Leal, L. & Hinch, E. 1971 The effect of weak Brownian rotations on particles in shear flow. J. Fluid Mech. 46 (4), 685–703.CrossRefGoogle Scholar
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59 (2), 209–223.CrossRefGoogle Scholar
Paulsen, K. S., Di Carlo, D. & Chung, A. J. 2015 Optofluidic fabrication for 3D-shaped particles. Nat. Commun. 6, 6976.CrossRefGoogle ScholarPubMed
Rahnama, M., Koch, D. L. & Shaqfeh, E. S. G. 1995 The effect of hydrodynamic interactions on the orientation distribution in a fiber suspension subject to simple shear flow. Phys. Fluids 7 (3), 487–506.CrossRefGoogle Scholar
Raney, J. R. & Lewis, J. A. 2015 Printing mesoscale architectures. MRS Bull. 40 (11), 943–950.CrossRefGoogle Scholar
Singh, V., Koch, D. L. & Stroock, A. D. 2013 Rigid ring-shaped particles that align in simple shear flow. J. Fluid Mech. 722, 121–158.CrossRefGoogle Scholar
Stover, C. A. & Cohen, C. 1990 The motion of rodlike particles in the pressure-driven flow between two flat plates. Rheol. Acta 29 (3), 192–203.CrossRefGoogle Scholar
Trevelyan, B. J. & Mason, S. G. 1951 Particle motions in sheared suspensions. I. Rotations. J. Colloid Sci. 6 (4), 354–367.CrossRefGoogle Scholar
Wang, J., Tozzi, E. J., Graham, M. D. & Klingenberg, D. J. 2012 Flipping, scooping, and spinning: drift of rigid curved nonchiral fibers in simple shear flow. Phys. Fluids 24 (12), 123304.CrossRefGoogle Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69 (02), 377–403.CrossRefGoogle Scholar
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