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Shape curvature effects in viscous streaming

Published online by Cambridge University Press:  03 July 2020

Yashraj Bhosale ,
Tejaswin Parthasarathy  and
Mattia Gazzola Open the ORCID record for Mattia Gazzola [Opens in a new window]
Yashraj Bhosale
Affiliation:
Mechanical Sciences and Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Tejaswin Parthasarathy
Affiliation:
Mechanical Sciences and Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Mattia Gazzola*
Affiliation:
Mechanical Sciences and Engineering, National Center for Supercomputing Applications and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
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Abstract

Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length scales are involved has not been looked into in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analysing the system through the lens of bifurcation theory. Our set-up consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system, and in particular the role of bifurcations in determining the local flow topology, can be then generalized to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Nonlinear Dynamical Systems: Bifurcation Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Aydin, O., Zhang, X., Nuethong, S., Pagan-Diaz, G. J., Bashir, R., Gazzola, M. & Saif, M. T. A. 2019 Neuromuscular actuation of biohybrid motile bots. Proc. Natl Acad. Sci. USA 116, 201907051.Google ScholarPubMed
Badr, H. M. 1994 Oscillating viscous flow over an inclined elliptic cylinder. Ocean Engng 21 (4), 401–426.CrossRefGoogle Scholar
Batchelor, G. K. 2000 An introduction to fluid dynamics. In An Introduction to Fluid Dynamics, by GK Batchelor. Cambridge University Press, 2000, 635 pp. ISBN 0521663962.CrossRefGoogle Scholar
Bertelsen, A., Svardal, A. & Tjøtta, S. 1973 Nonlinear streaming effects associated with oscillating cylinders. J. Fluid Mech. 59 (3), 493–511.CrossRefGoogle Scholar
Bertelsen, A. F. 1974 An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders. J. Fluid Mech. 64 (3), 589–598.CrossRefGoogle Scholar
Bosschaert, M. & Hanßmann, H. 2013 Bifurcations in Hamiltonian systems with a reflecting symmetry. Qual. Theory Dyn. Sys. 12 (1), 67–87.CrossRefGoogle Scholar
Buono, P.-L., Laurent-Polz, F. & Montaldi, J. 2005 Symmetric Hamiltonian bifurcations. In Geometric Mechanics and Symmetry: The Peyresq Lectures, pp. 357–402. Cambridge University Press.CrossRefGoogle Scholar
Ceylan, H., Giltinan, J., Kozielski, K. & Sitti, M. 2017 Mobile microrobots for bioengineering applications. Lab on a Chip 17 (10), 1705–1724.CrossRefGoogle ScholarPubMed
Chong, K., Kelly, S. D., Smith, S. & Eldredge, J. D. 2013 Inertial particle trapping in viscous streaming. Phys. Fluids 25 (3), 033602.CrossRefGoogle Scholar
Chung, S. K. & Cho, S. K. 2009 3-D manipulation of millimeter-and micro-sized objects using an acoustically excited oscillating bubble. Microfluid. Nanofluid. 6 (2), 261–265.CrossRefGoogle Scholar
Coenen, W. 2013 Oscillatory flow about a cylinder pair with unequal radii. Fluid Dyn. Res. 45 (5), 055511.Google Scholar
Coenen, W. 2016 Steady streaming around a cylinder pair. Proc. R. Soc. Lond. A 472 (2195), 20160522.CrossRefGoogle Scholar
Dam, M., Juul Rasmussen, J., Naulin, V. & Brøns, M. 2017 Topological bifurcations in the evolution of coherent structures in a convection model. Phys. Plasmas 24 (8), 082301.CrossRefGoogle Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53 (2), 287–303.CrossRefGoogle Scholar
Gazzola, M., Chatelain, P., van Rees, W. M. & Koumoutsakos, P. 2011 Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 7093–7114.CrossRefGoogle Scholar
Gazzola, M., Hejazialhosseini, B. & Koumoutsakos, P. 2014 Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36 (3), B622–B639.CrossRefGoogle Scholar
Gazzola, M., Mimeau, C., Tchieu, A. A. & Koumoutsakos, P. 2012a Flow mediated interactions between two cylinders at finite Re numbers. Phys. Fluids 24 (4), 043103.CrossRefGoogle Scholar
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A. & Koumoutsakos, P. 2016 Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726–749.CrossRefGoogle Scholar
Gazzola, M., Van Rees, W. M. & Koumoutsakos, P. 2012b C-start: optimal start of larval fish. J. Fluid Mech. 698, 5–18.CrossRefGoogle Scholar
Glauert, M. B. 1956 The laminar boundary layer on oscillating plates and cylinders. J. Fluid Mech. 1 (1), 97–110.CrossRefGoogle Scholar
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am. 26 (1), 26–39.CrossRefGoogle Scholar
Huang, H.-W., Uslu, F. E., Katsamba, P., Lauga, E., Sakar, M. S. & Nelson, B. J. 2019 Adaptive locomotion of artificial microswimmers. Sci. Adv. 5 (1), eaau1532.CrossRefGoogle ScholarPubMed
Klotsa, D., Baldwin, K. A., Hill, R. J. A., Bowley, R. M. & Swift, M. R. 2015 Propulsion of a two-sphere swimmer. Phys. Rev. Lett. 115 (24), 248102.CrossRefGoogle ScholarPubMed
Kotas, C. W., Yoda, M. & Rogers, P. H. 2007 Visualization of steady streaming near oscillating spheroids. Exp. Fluids 42 (1), 111–121.CrossRefGoogle Scholar
Kuznetsov, Y. A. 2013 Elements of Applied Bifurcation Theory, vol. 112, pp. 178–213. Springer.CrossRefGoogle Scholar
Lane, C. A. 1955 Acoustical streaming in the vicinity of a sphere. J. Acoust. Soc. Am. 27 (6), 1082–1086.CrossRefGoogle Scholar
Liu, R. H., Yang, J., Pindera, M. Z., Athavale, M. & Grodzinski, P. 2002 Bubble-induced acoustic micromixing. Lab on a Chip 2 (3), 151–157.CrossRefGoogle ScholarPubMed
Lutz, B. R., Chen, J. & Schwartz, D. T. 2003 Microfluidics without microfabrication. Proc. Natl Acad. Sci. USA 100 (8), 4395–4398.CrossRefGoogle ScholarPubMed
Lutz, B. R., Chen, J. & Schwartz, D. T. 2005 Microscopic steady streaming eddies created around short cylinders in a channel: flow visualization and Stokes layer scaling. Phys. Fluids 17 (2), 023601.CrossRefGoogle Scholar
Marmottant, P. & Hilgenfeldt, S. 2004 A bubble-driven microfluidic transport element for bioengineering. Proc. Natl Acad. Sci. USA 101 (26), 9523–9527.CrossRefGoogle ScholarPubMed
Murdock, J. 2006 Unfoldings. Scholarpedia 1 (12), 1904.CrossRefGoogle Scholar
Nair, S. & Kanso, E. 2007 Hydrodynamically coupled rigid bodies. J. Fluid Mech. 592, 393–411.CrossRefGoogle Scholar
Nama, N., Huang, P.-H., Huang, T. J. & Costanzo, F. 2014 Investigation of acoustic streaming patterns around oscillating sharp edges. Lab on a Chip 14 (15), 2824–2836.CrossRefGoogle ScholarPubMed
Ovchinnikov, M., Zhou, J. & Yalamanchili, S. 2014 Acoustic streaming of a sharp edge. J. Acoust. Soc. Am. 136 (1), 22–29.CrossRefGoogle ScholarPubMed
Park, S.-J., Gazzola, M., Park, K. S., Park, S., Di Santo, V., Blevins, E. L., Lind, J. U., Campbell, P. H., Dauth, S., Capulli, A. K. et al. 2016 Phototactic guidance of a tissue-engineered soft-robotic ray. Science 353 (6295), 158–162.CrossRefGoogle ScholarPubMed
Parthasarathy, T.2018 Viscous streaming-enhanced inertial particle transport. Master’s thesis, available at https://www.ideals.illinois.edu/handle/2142/102963.Google Scholar
Parthasarathy, T., Chan, F. K. & Gazzola, M. 2019 Streaming-enhanced flow-mediated transport. J. Fluid Mech. 878, 647–662.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19 (1), 125–155.CrossRefGoogle Scholar
Riley, N. 1966 On a sphere oscillating in a viscous fluid. Q. J. Mech. Appl. Maths 19 (4), 461–472.CrossRefGoogle Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33 (1), 43–65.CrossRefGoogle Scholar
Strogatz, S. H. 2018 Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, pp. 159–173. CRC Press.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24 (4), 673–687.CrossRefGoogle Scholar
Tatsuno, M. 1974 Circulatory streaming in the vicinity of an oscillating square cylinder. J. Phys. Soc. Japan 36 (4), 1185–1191.CrossRefGoogle Scholar
Tatsuno, M. 1975 Circulatory streaming in the vicinity of an oscillating triangular cylinder. J. Phys. Soc. Japan 38 (1), 257–264.CrossRefGoogle Scholar
Tchieu, A. A., Crowdy, D. & Leonard, A. 2010 Fluid–structure interaction of two bodies in an inviscid fluid. Phys. Fluids 22 (10), 107101.CrossRefGoogle Scholar
Thameem, R., Rallabandi, B. & Hilgenfeldt, S. 2016 Particle migration and sorting in microbubble streaming flows. Biomicrofluidics 10 (1), 014124.CrossRefGoogle ScholarPubMed
Thameem, R., Rallabandi, B. & Hilgenfeldt, S. 2017 Fast inertial particle manipulation in oscillating flows. Phys. Rev. F 2 (5), 052001.Google Scholar
Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., Hazlewood, V., Lathrop, S., Lifka, D., Peterson, G. D. et al. 2014 XSEDE: accelerating scientific discovery. Comput. Sci. Engng 16 (5), 62–74.CrossRefGoogle Scholar
Vishwanathan, G. & Juarez, G.2019 Steady streaming flows in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 271, 104143.Google Scholar
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2011 Size-sensitive sorting of microparticles through control of flow geometry. Appl. Phys. Lett. 99 (3), 034101.Google Scholar
Williams, B. J., Anand, S. V., Rajagopalan, J. & Saif, M. T. A. 2014 A self-propelled biohybrid swimmer at low Reynolds number. Nat. Commun. 5, 3081.CrossRefGoogle ScholarPubMed
Yan, B., Ingham, D. B. & Morton, B. R. 1994 The streaming flow initiated by oscillating cascades of cylinders and their stability. Phys. Fluids 6 (4), 1472–1481.CrossRefGoogle Scholar
Yoshizawa, A. 1974 Steady streaming induced by an oscillating flat plate in a viscous fluid. J. Phys. Soc. Japan 37 (2), 524–528.CrossRefGoogle Scholar
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