Skip to main content Accessibility help

Streaming-enhanced flow-mediated transport

  • Tejaswin Parthasarathy (a1), Fan Kiat Chan (a1) and Mattia Gazzola (a1) (a2)


We investigate the ability of an active body (master) to manipulate a passive object (slave) purely via contactless flow-mediated mechanisms, motivated by potential applications in microfluidic devices and medicine (drug delivery purposes). We extend prior works on active–passive cylinder pairs by superimposing periodic oscillations to the master’s linear motion. In a viscous fluid, such oscillations produce an additional viscous streaming field, which is leveraged for enhancing slave transport. We see that superimposing oscillations robustly improves transport across a range of Reynolds numbers. Comparison with results without oscillations highlights the flow mechanisms at work, which we capitalize on to design (master) geometries for augmented transport. These principles are found to extend to three-dimensional active–passive shapes as well.


Corresponding author

Email address for correspondence:


Hide All
Ahmed, D., Mao, X., Juluri, B. K. & Huang, T. J. 2009 A fast microfluidic mixer based on acoustically driven sidewall-trapped microbubbles. Microfluid Nanofluid 7 (5), 727731.
Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489496.
Bergmann, M. & Iollo, A. 2011 Modeling and simulation of fish-like swimming. J. Comput. Phys. 230 (2), 329348.
Bertelsen, A., Svardal, A. & Tjotta, S. 1973 Nonlinear streaming effects associated with oscillating cylinders. J. Fluid Mech. 59 (03), 493511.
Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211 (10), 15411558.
Boschitsch, B. M., Dewey, P. A. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26 (5), 051901.
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111157.
Ceylan, H., Giltinan, J., Kozielski, K. & Sitti, M. 2017 Mobile microrobots for bioengineering applications. Lab on a Chip 17 (10), 17051724.
Chang, E. J. & Maxey, M. R. 1994 Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion. J. Fluid Mech. 277, 347379.
Chong, K., Kelly, S. D., Smith, S. & Eldredge, J. D. 2013 Inertial particle trapping in viscous streaming. Phys. Fluids 25 (3), 033602.
Chong, K., Kelly, S. D., Smith, S. T. & Eldredge, J. D. 2016 Transport of inertial particles by viscous streaming in arrays of oscillating probes. Phys. Rev. E 93 (1), 013109.
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53 (02), 287303.
Dombrowski, T., Jones, S. K., Katsikis, G., Bhalla, A. P. S., Griffith, B. E. & Klotsa, D. 2019 Transition in swimming direction in a model self-propelled inertial swimmer. Phys. Rev. Fluids 4 (2), 021101.
Eldredge, J. 2010 A reconciliation of viscous and inviscid approaches to computing locomotion of deforming bodies. Exp. Mech. 50, 13491353.
Gazzola, M., Chatelain, P., van Rees, W. M. & Koumoutsakos, P. 2011a Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 70937114.
Gazzola, M., Dudte, L. H., McCormick, A. G. & Mahadevan, L. 2018 Forward and inverse problems in the mechanics of soft filaments. R. Soc. Open Sci. 5 (6), 171628.
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), B622B639.
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.
Gazzola, M., van Rees, W. M. & Koumoutsakos, P. 2012b C-start: optimal start of larval fish. J. Fluid Mech. 698, 518.
Gazzola, M., Tchieu, A. A., Alexeev, D., de Brauer, A. & Koumoutsakos, P. 2015 Learning to school in the presence of hydrodynamic interactions. J. Fluid Mech. 789, 726749.
Gazzola, M., Vasilyev, O. V. & Koumoutsakos, P. 2011b Shape optimization for drag reduction in linked bodies using evolution strategies. Comput. Struct. 89 (11–12), 12241231.
He, Y., Bi, Y., Hua, Y., Liu, D., Wen, S., Wang, Q., Li, M., Zhu, J., Lin, T., He, D. et al. 2011 Ultrasound microbubble-mediated delivery of the siRNAs targeting MDR1 reduces drug resistance of yolk sac carcinoma L2 cells. J. Expl Clinical Cancer Res. 30 (1), 104.
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), 2639.
House, T. A., Lieu, V. H. & Schwartz, D. T. 2014 A model for inertial particle trapping locations in hydrodynamic tweezers arrays. J. Micromech. Microengng 24 (4), 045019.
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization. J. Fluid Mech. 86 (1), 179200.
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119160.
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.
Koch, D. L. & Subramanian, G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637659.
Kotas, C. W., Yoda, M. & Rogers, P. H. 2007 Visualization of steady streaming near oscillating spheroids. Exp. Fluids 42 (1), 111121.
Kotas, C. W., Yoda, M. & Rogers, P. H. 2008 Steady streaming flows near spheroids oscillated at multiple frequencies. Exp. Fluids 45 (2), 295307.
Kubo, S. & Kitano, Y. 1980 Secondary flow induced by a circular cylinder oscillating in two directions. J. Phys. Soc. Japan 49 (5), 20262037.
Lane, C. A. 1955 Acoustical streaming in the vicinity of a sphere. J. Acoust. Soc. Am. 27 (6), 10821086.
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.
Liao, J. C. 2007 A review of fish swimming mechanics and behaviour in altered flows. Phil. Trans. R. Soc. Lond. B 362 (1487), 19731993.
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302 (5650), 15661569.
Lieu, V. H., House, T. A. & Schwartz, D. T. 2012 Hydrodynamic tweezers: impact of design geometry on flow and microparticle trapping. Analyt. Chem. 84 (4), 19631968.
Lin, Z., Liang, D. & Zhao, M. 2018 Effects of damping on flow-mediated interaction between two cylinders. J. Fluids Engng 140 (9), 091106.
Liu, R. H., Yang, J., Pindera, M. Z., Athavale, M. & Grodzinski, P. 2002 Bubble-induced acoustic micromixing. Lab on a Chip 2 (3), 151157.
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.
Lutz, B. R., Chen, J. & Schwartz, D. T. 2006 Hydrodynamic tweezers: 1. Noncontact trapping of single cells using steady streaming microeddies. Analyt. Chem. 78 (15), 54295435.
Marmottant, P. & Hilgenfeldt, S. 2003 Controlled vesicle deformation and lysis by single oscillating bubbles. Nature 423 (6936), 153156.
Marmottant, P. & Hilgenfeldt, S. 2004 A bubble-driven microfluidic transport element for bioengineering. Proc. Natl Acad. Sci. USA 101 (26), 95239527.
Metzger, B., Nicolas, M. & Guazzelli, E. 2007 Falling clouds of particles in viscous fluids. J. Fluid Mech. 580, 283301.
Nair, S. & Kanso, E. 2007 Hydrodynamically coupled rigid bodies. J. Fluid Mech. 592, 393411.
Pagan-Diaz, G. J., Zhang, X., Grant, L., Kim, Y., Aydin, O., Cvetkovic, C., Ko, E., Solomon, E., Hollis, J., Kong, H. et al. 2018 Simulation and fabrication of stronger, larger, and faster walking biohybrid machines. Adv. Funct. Mater 28 (23), 1801145.
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), 158162.
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), 125155.
Rallabandi, B., Wang, C. & Hilgenfeldt, S. 2017 Analysis of optimal mixing in open-flow mixers with time-modulated vortex arrays. Phys. Rev. Fluids 2 (6), 064501.
Riley, N. 1966 On a sphere oscillating in a viscous fluid. Q. J. Mech. Appl. Maths 19 (4), 461472.
Riley, N. 1967 Oscillatory viscous flows. Review and extension. IMA J. Appl. Maths 3 (4), 419434.
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33 (1), 4365.
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.
Ryu, K., Chung, S. K. & Cho, S. K. 2010 Micropumping by an acoustically excited oscillating bubble for automated implantable microfluidic devices. J. Assoc. Lab. Autom. 15 (3), 163171.
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24 (04), 673687.
Subramanian, G. & Koch, D. L. 2008 Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions. J. Fluid Mech. 603, 63100.
Tabakova, S. S. & Zapryanov, Z. D. 1982a On the hydrodynamic interaction of two spheres oscillating in a viscous fluid. i. Axisymmetrical case. Z. Angew. Math. Phys. 33 (3), 344357.
Tabakova, SS. & Zapryanov, ZD. 1982b On the hydrodynamic interaction of two spheres oscillating in a viscous fluid. ii. Three dimensional case. Z. Angew. Math. Phys. 33 (4), 487502.
Tatsuno, M. 1975 Circulatory streaming in the vicinity of an oscillating triangular cylinder. J. Phys. Soc. Japan 38 (1), 257264.
Tchieu, A. A., Crowdy, D. & Leonard, A. 2010 Fluid–structure interaction of two bodies in an inviscid fluid. Phys. Fluids 22 (10), 107101.
Tchieu, A. A., Kanso, E. & Newton, P. K. 2012 The finite-dipole dynamical system. Proc. R. Soc. Lond. A 468 (2146), 30063026.
Thameem, R., Rallabandi, B. & Hilgenfeldt, S. 2016 Particle migration and sorting in microbubble streaming flows. Biomicrofluidics 10 (1), 014124.
Tovar, A. R., Patel, M. V. & Lee, A. P. 2011 Lateral air cavities for microfluidic pumping with the use of acoustic energy. Microfluid Nanofluid 10 (6), 12691278.
Van Dyke, M. 1982 An Album of Fluid Motion, vol. 176. Parabolic.
Voth, G. A., Bigger, B., Buckley, M. R., Losert, W., Brenner, M. P., Stone, H. A. & Gollub, J. P. 2002 Ordered clusters and dynamical states of particles in a vibrated fluid. Phys. Rev. Lett. 88 (23), 234301.
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2011 Size-sensitive sorting of microparticles through control of flow geometry. Appl. Phys. Lett. 99 (3), 034101.
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241 (5387), 290291.
Williams, B. J., Anand, S. V., Rajagopalan, J. & Saif, M. A. 2014 A self-propelled biohybrid swimmer at low Reynolds number. Nat. Commun. 5, 3081.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Type Description Title
Supplementary materials

Parthasarathy et al. supplementary material
Parthasarathy et al. supplementary material

 Unknown (35.5 MB)
35.5 MB

Streaming-enhanced flow-mediated transport

  • Tejaswin Parthasarathy (a1), Fan Kiat Chan (a1) and Mattia Gazzola (a1) (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed