Abstract

When a microscopic particle moves through a low Reynolds number fluid, it creates a flow-field which exerts hydrodynamic forces on surrounding particles. In this work we study the ‘Lissajous-like’ trajectories of an optically trapped ‘probe’ microsphere as it is subjected to time-varying oscillatory hydrodynamic flow-fields created by a nearby moving particle (the ‘actuator’). We show a breaking of time-reversal symmetry in the motion of the probe when the driving motion of the actuator is itself time-reversal symmetric. This symmetry breaking results in a fluid-pumping effect, which arises due to the action of both a time-dependent hydrodynamic flow and a position-dependent optical restoring force, which together determine the trajectory of the probe particle. We study this situation experimentally, and show that the form of the trajectories observed is in good agreement with Stokesian dynamics simulations. Our results are related to the techniques of active micro-rheology and flow measurement, and also highlight how the mere presence of an optical trap can perturb the environment it is in place to measure.

© 2015 Optical Society of America

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References

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    [Crossref]
  24. M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
    [Crossref]
  25. D. L. Ermak and J. McCammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
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    [Crossref]
  28. H. Nagar and Y. Roichman, “Collective excitations of hydrodynamically coupled driven colloidal particles,” Phys. Rev. E 90, 042302 (2014).
    [Crossref]
  29. S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
    [Crossref]
  30. B. A. Nemet and M. Cronin-Golomb, “Microscopic flow measurements with optically trapped microprobes,” Opt. Lett. 27, 1357–1359 (2002).
    [Crossref]
  31. A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
    [Crossref]
  32. Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
    [Crossref] [PubMed]
  33. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
    [Crossref]
  34. G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
    [Crossref] [PubMed]
  35. J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
    [Crossref]
  36. R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
    [Crossref]

2015 (3)

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers: single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78, 056601 (2015).
[Crossref]

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

2014 (6)

H. Nagar and Y. Roichman, “Collective excitations of hydrodynamically coupled driven colloidal particles,” Phys. Rev. E 90, 042302 (2014).
[Crossref]

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

2013 (1)

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

2012 (1)

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

2011 (1)

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

2010 (1)

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

2008 (4)

T. Niedermayer, B. Eckhardt, and P. Lenz, “Synchronization, phase locking, and metachronal wave formation in ciliary chains,” Chaos 18, 037128 (2008).
[Crossref] [PubMed]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[Crossref] [PubMed]

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

2006 (2)

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

2005 (1)

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

2004 (1)

A. Najafi and R. Golestanian, “Simple swimmer at low reynolds number: Three linked spheres,” Phys. Rev. E 69, 062901 (2004).
[Crossref]

2002 (3)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

L. Hough and H. Ou-Yang, “Correlated motions of two hydrodynamically coupled particles confined in separate quadratic potential wells,” Phys. Rev. E 65, 021906 (2002).
[Crossref]

B. A. Nemet and M. Cronin-Golomb, “Microscopic flow measurements with optically trapped microprobes,” Opt. Lett. 27, 1357–1359 (2002).
[Crossref]

2000 (1)

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

1999 (1)

J.-C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211 (1999).
[Crossref]

1993 (1)

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[Crossref] [PubMed]

1992 (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569 (1992).
[Crossref] [PubMed]

1989 (1)

A. Shapere and F. Wilczek, “Geometry of self-propulsion at low reynolds number,” J. Fluid Mech 198, 557–585 (1989).
[Crossref]

1986 (1)

1978 (1)

D. L. Ermak and J. McCammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[Crossref]

1977 (1)

E. M. Purcell, “Life at low reynolds number,” Am. J. Phys 45, 3–11 (1977).
[Crossref]

1969 (1)

J. Rotne and S. Prager, “Variational treatment of hydrodynamic interaction in polymers,” J. Chem. Phys. 50, 4831–4837 (1969).
[Crossref]

Ashkin, A.

Atakhorrami, M.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Bain, C. D.

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

Bassetti, B.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Bérut, A.

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

Bjorkholm, J.

Bowman, R. W.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Box, S.

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Brenner, H.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media (Springer Science & Business Media, 2012) vol. 1.

Brumley, D. R.

D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, “Metachronal waves in the flagellar beating of volvox and their hydrodynamic origin,” arXiv preprint arXiv:1505.02423 (2015).

Bruot, N.

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Carberry, D.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

Carberry, D. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Carretero-Palacios, S.

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

Chu, S.

Cicuta, P.

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Ciliberto, S.

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

Cooper, J.

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

Cooper, J. M.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

Cronin-Golomb, M.

Curran, A.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Debono, L.

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Di Leonardo, R.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

Diamant, H.

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

Dziedzic, J.

Eckhardt, B.

T. Niedermayer, B. Eckhardt, and P. Lenz, “Synchronization, phase locking, and metachronal wave formation in ciliary chains,” Chaos 18, 037128 (2008).
[Crossref] [PubMed]

Elgeti, J.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers: single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78, 056601 (2015).
[Crossref]

Ermak, D. L.

D. L. Ermak and J. McCammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[Crossref]

Feldmann, J.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

Frydel, D.

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

Gibson, G. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[Crossref] [PubMed]

Goldstein, R. E.

D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, “Metachronal waves in the flagellar beating of volvox and their hydrodynamic origin,” arXiv preprint arXiv:1505.02423 (2015).

Golestanian, R.

A. Najafi and R. Golestanian, “Simple swimmer at low reynolds number: Three linked spheres,” Phys. Rev. E 69, 062901 (2004).
[Crossref]

Gompper, G.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers: single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78, 056601 (2015).
[Crossref]

Grier, D. G.

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Grieve, J. A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

Hanna, S.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Happel, J.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media (Springer Science & Business Media, 2012) vol. 1.

Ho, Y.-L.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

Hough, L.

L. Hough and H. Ou-Yang, “Correlated motions of two hydrodynamically coupled particles confined in separate quadratic potential wells,” Phys. Rev. E 65, 021906 (2002).
[Crossref]

Inoue, H.

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Am. Inst. Phys. (2006).

Jäckel, F.

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

Keen, S.

Kirchner, S.

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

Kirchner, S. R.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

Koenderink, G.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Kotar, J.

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Kuo, S. C.

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[Crossref] [PubMed]

Lagomarsino, M. C.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Leach, J.

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[Crossref] [PubMed]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

Lee, M. P.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

Lenz, P.

T. Niedermayer, B. Eckhardt, and P. Lenz, “Synchronization, phase locking, and metachronal wave formation in ciliary chains,” Chaos 18, 037128 (2008).
[Crossref] [PubMed]

Leoni, M.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

Linnenberger, A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Liverpool, T.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Lohmüller, T.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

MacKintosh, F.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Mader, A.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

Maruo, S.

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Am. Inst. Phys. (2006).

McCammon, J.

D. L. Ermak and J. McCammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[Crossref]

Meiners, J.-C.

J.-C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211 (1999).
[Crossref]

Mellor, C. D.

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

Miles, M.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

Miles, M. J.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Mizuno, D.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Mushfique, H.

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

Nagar, H.

H. Nagar and Y. Roichman, “Collective excitations of hydrodynamically coupled driven colloidal particles,” Phys. Rev. E 90, 042302 (2014).
[Crossref]

Najafi, A.

A. Najafi and R. Golestanian, “Simple swimmer at low reynolds number: Three linked spheres,” Phys. Rev. E 69, 062901 (2004).
[Crossref]

Nedev, S.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

Nemet, B. A.

Niedermayer, T.

T. Niedermayer, B. Eckhardt, and P. Lenz, “Synchronization, phase locking, and metachronal wave formation in ciliary chains,” Chaos 18, 037128 (2008).
[Crossref] [PubMed]

Opitz, M.

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

Ou-Yang, H.

L. Hough and H. Ou-Yang, “Correlated motions of two hydrodynamically coupled particles confined in separate quadratic potential wells,” Phys. Rev. E 65, 021906 (2002).
[Crossref]

Padgett, M.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

Padgett, M. J.

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[Crossref] [PubMed]

Pedley, T. J.

D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, “Metachronal waves in the flagellar beating of volvox and their hydrodynamic origin,” arXiv preprint arXiv:1505.02423 (2015).

Petrosyan, A.

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

Phillips, D.

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Phillips, D. B.

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Polin, M.

D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, “Metachronal waves in the flagellar beating of volvox and their hydrodynamic origin,” arXiv preprint arXiv:1505.02423 (2015).

Prager, S.

J. Rotne and S. Prager, “Variational treatment of hydrodynamic interaction in polymers,” J. Chem. Phys. 50, 4831–4837 (1969).
[Crossref]

Purcell, E. M.

E. M. Purcell, “Life at low reynolds number,” Am. J. Phys 45, 3–11 (1977).
[Crossref]

Quake, S. R.

J.-C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211 (1999).
[Crossref]

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

Roichman, Y.

H. Nagar and Y. Roichman, “Collective excitations of hydrodynamically coupled driven colloidal particles,” Phys. Rev. E 90, 042302 (2014).
[Crossref]

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Rotne, J.

J. Rotne and S. Prager, “Variational treatment of hydrodynamic interaction in polymers,” J. Chem. Phys. 50, 4831–4837 (1969).
[Crossref]

Ruocco, G.

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

Schmidt, C.

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

Serati, S.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Shapere, A.

A. Shapere and F. Wilczek, “Geometry of self-propulsion at low reynolds number,” J. Fluid Mech 198, 557–585 (1989).
[Crossref]

Sharp, M. A.

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

Sheetz, M. P.

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[Crossref] [PubMed]

Simpson, S.

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Simpson, S. H.

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

Sokolov, Y.

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

Stolarski, A.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Sun, B.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Tiziani, H.

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

Ward, A. D.

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

Wilczek, F.

A. Shapere and F. Wilczek, “Geometry of self-propulsion at low reynolds number,” J. Fluid Mech 198, 557–585 (1989).
[Crossref]

Winkler, R. G.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers: single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78, 056601 (2015).
[Crossref]

Wright, A. J.

Am. J. Phys (1)

E. M. Purcell, “Life at low reynolds number,” Am. J. Phys 45, 3–11 (1977).
[Crossref]

Appl. Phys. Lett. (2)

S. R. Kirchner, S. Nedev, S. Carretero-Palacios, A. Mader, M. Opitz, T. Lohmüller, and J. Feldmann, “Direct optical monitoring of flow generated by bacterial flagellar rotation,” Appl. Phys. Lett. 104, 093701 (2014).
[Crossref]

S. Nedev, S. Carretero-Palacios, S. Kirchner, F. Jäckel, and J. Feldmann, “Microscale mapping of oscillatory flows,” Appl. Phys. Lett. 105, 161113 (2014).
[Crossref]

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569 (1992).
[Crossref] [PubMed]

Chaos (1)

T. Niedermayer, B. Eckhardt, and P. Lenz, “Synchronization, phase locking, and metachronal wave formation in ciliary chains,” Chaos 18, 037128 (2008).
[Crossref] [PubMed]

Comput. Phys. Commun. (1)

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “‘Red tweezers’: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Europhys. Lett. (1)

A. Bérut, A. Petrosyan, and S. Ciliberto, “Energy flow between two hydrodynamically coupled particles kept at different effective temperatures,” Europhys. Lett. 107, 60004 (2014).
[Crossref]

J. Appl. Phys. (1)

C. D. Mellor, M. A. Sharp, C. D. Bain, and A. D. Ward, “Probing interactions between colloidal particles with oscillating optical tweezers,” J. Appl. Phys. 97, 103114 (2005).
[Crossref]

J. Chem. Phys. (2)

D. L. Ermak and J. McCammon, “Brownian dynamics with hydrodynamic interactions,” J. Chem. Phys. 69, 1352–1360 (1978).
[Crossref]

J. Rotne and S. Prager, “Variational treatment of hydrodynamic interaction in polymers,” J. Chem. Phys. 50, 4831–4837 (1969).
[Crossref]

J. Fluid Mech (1)

A. Shapere and F. Wilczek, “Geometry of self-propulsion at low reynolds number,” J. Fluid Mech 198, 557–585 (1989).
[Crossref]

Lab Chip (1)

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006).
[Crossref] [PubMed]

Nat. Photon. (1)

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nat. Photon. 8, 400–405 (2014).
[Crossref]

Opt. Commun. (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185, 77–82 (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E (5)

A. Najafi and R. Golestanian, “Simple swimmer at low reynolds number: Three linked spheres,” Phys. Rev. E 69, 062901 (2004).
[Crossref]

H. Nagar and Y. Roichman, “Collective excitations of hydrodynamically coupled driven colloidal particles,” Phys. Rev. E 90, 042302 (2014).
[Crossref]

S. Box, L. Debono, D. Phillips, and S. Simpson, “Transitional behavior in hydrodynamically coupled oscillators,” Phys. Rev. E 91, 022916 (2015).
[Crossref]

M. Atakhorrami, D. Mizuno, G. Koenderink, T. Liverpool, F. MacKintosh, and C. Schmidt, “Short-time inertial response of viscoelastic fluids measured with brownian motion and with active probes,” Phys. Rev. E 77, 061508 (2008).
[Crossref]

L. Hough and H. Ou-Yang, “Correlated motions of two hydrodynamically coupled particles confined in separate quadratic potential wells,” Phys. Rev. E 65, 021906 (2002).
[Crossref]

Phys. Rev. Lett. (6)

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Y. Sokolov, D. Frydel, D. G. Grier, H. Diamant, and Y. Roichman, “Hydrodynamic pair attractions between driven colloidal particles,” Phys. Rev. Lett. 107, 158302 (2011).
[Crossref] [PubMed]

R. Di Leonardo, J. Leach, H. Mushfique, J. Cooper, G. Ruocco, and M. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[Crossref] [PubMed]

J.-C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211 (1999).
[Crossref]

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, “Partial synchronization of stochastic oscillators through hydrodynamic coupling,” Phys. Rev. Lett. 108, 240601 (2012).
[Crossref] [PubMed]

J. Kotar, L. Debono, N. Bruot, S. Box, D. Phillips, S. Simpson, S. Hanna, and P. Cicuta, “Optimal hydrodynamic synchronization of colloidal rotors,” Phys. Rev. Lett. 111, 228103 (2013).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, “Hydrodynamic synchronization of colloidal oscillators,” Proc. Natl. Acad. Sci. U.S.A. 107, 7669–7673 (2010).
[Crossref] [PubMed]

Proc. SPIE (1)

D. B. Phillips, L. Debono, S. H. Simpson, and M. J. Padgett, “Optically controlled hydrodynamic micro-manipulation,” Proc. SPIE 9548, 95481A (2015).
[Crossref]

Rep. Prog. Phys. (1)

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers: single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78, 056601 (2015).
[Crossref]

Science (1)

S. C. Kuo and M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993).
[Crossref] [PubMed]

Other (3)

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Am. Inst. Phys. (2006).

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media (Springer Science & Business Media, 2012) vol. 1.

D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, “Metachronal waves in the flagellar beating of volvox and their hydrodynamic origin,” arXiv preprint arXiv:1505.02423 (2015).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic showing how the trajectory of a microsphere is calculated at each simulation time-step from the balance of external forces, Fext (such as hydrodynamic and stochastic thermal forces), optical forces, Fopt, and frictional forces, Ffriction. (b) A map of the flow-field (relative to the velocity of the microsphere) around an isolated microsphere of 5 μm in diameter, as it is translated left. Arrows indicate the amplitude and direction of the flow. The white scale bar represents 10 μm.
Fig. 2
Fig. 2 Simulations of the system with a non time-reversal symmetric actuator trajectory. (a) Trajectory of a free-floating probe microsphere as it is driven by the rotary motion of the actuator in the absence of thermal forces. (b) Velocity of the free-floating probe along its trajectory. (c) Trajectory and velocity of the probe when it is constrained by an optical trap. (d) Schematic of the relative positions of the actuator and probe microspheres during one actuator cycle. The relative size of the probe trajectory has been exaggerated compared to both the probe’s size, and the actuator trajectory, for clarity. (e) Cycle averaged flow-field around an isolated actuator. (f) Cycle averaged flow-field around the actuator while the probe is held in a stationary optical trap. (g) Difference in the flow-field between (e) and (f). In each case the white scale bars represent 10μm.
Fig. 3
Fig. 3 Simulations of the system with a time-reversal symmetric actuator trajectory. (a) The time-reversal symmetric trajectory and velocity of the free-floating probe. (b) The motion of the probe with the introduction of a second stationary optical trap constraining its motion. Here time-reversal symmetry is broken as the probe follows a particular direction around the ‘figure of 8’ trajectory. (c) The cycle averaged flow-field of the system in a plane through the centre of both the actuator and probe microsphere. The white scale bar represents 10 μm. (d) A schematic showing the relative positions of the actuator and probe microspheres through one actuator cycle. Once again the relative size of the probe trajectory has been exaggerated compared to both the probe size, and the actuator trajectory, for clarity.
Fig. 4
Fig. 4 Simulation of the work done on the probe microsphere in the absence of Brownian motion. (a) non time-reversal symmetric case. (b) time-reversal symmetric case. Each case shows the evolution of the energy stored in the system when the probe is initially positioned at rest at the centre of the trap. In (a), the probe orbits the centre of the trap, and at no point in its cycle does it revisit the trap centre, and consequently the curve never returns to zero as the stored energy is never fully released. The insets show the points in the trajectory where energy is released. Full schematics of the trajectories are shown in Fig. 2(d) and Fig. 3(d).
Fig. 5
Fig. 5 Schematic of the dual beam holographic optical tweezers system. Our optical tweezers system is built around a custom-made inverted microscope with a Zeiss halogen illumination module (100 Watt). The holographic actuator trap is created by expanding a diode pumped solid state (DPSS) infra-red 1064 nm wavelength laser beam to overfill a nematic liquid crystal spatial light modulator (SLM) (BNS XY series, 512 × 512 pixels, 200Hz frame-rate). The SLM is placed in the Fourier plane of the sample and telescopically re-imaged onto and overfilling the back aperture of the objective lens (Nikon 100 × oil immersion, 1.3 NA) using a Fourier lens (L1) of 250 mm focal length and a tube lens of focal length 100 mm. The single beam trap is provided by a green DPSS 532 nm wavelength laser. Its position can be manually controlled using a steering mirror, and it also overfills the back aperture of the objective lens. The sample is viewed using a high-speed CMOS camera (Dalsa Genie gigabit ethernet), and any reflected infra-red and green laser light is filtered out. The top left inset shows a schematic of the relative optical trap positions and trajectories within the sample.
Fig. 6
Fig. 6 Experimentally measured probe microsphere trajectories when subjected to a non-time-reversible flow-field. (a) The trajectory of the probe over a single non time-reversal symmetric actuator cycle. (b) A 2D occupancy histogram showing the number of visits the probe made to each 10 nm wide bin over the course of 100 actuator cycles. The white scale bar represents 100 nm. (c) The average drift velocity of the probe as it passes through each 10 nm × 10 nm histogram bin. (d) The magnitude and direction of the drift velocity of the probe bead.
Fig. 7
Fig. 7 Experimentally measured probe microsphere trajectories when subjected to a time-reversible flow-field. (a) The trajectory of the probe over a single time-reversal symmetric actuator cycle. (b) and (e) 2D occupancy histograms showing the number of visits the probe made to each 10 nm wide bin over the course of 100 actuator cycles. The white scale bars represent 100 nm. (b) is the first half of the cycle, (e) is the second half of the cycle. (c) and (f) The average drift velocity of the probe as it passes through each 10 nm × 10 nm histogram bin. (d) and (g) The magnitude and direction of the drift velocity of the probe bead.

Equations (2)

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m i d 2 x i d t 2 = j = 1 3 N ( ξ i j d x j d t + κ j ( δ x j ) ) + j = 1 3 N α i j f j ,
W = C F hydro ( r ) d r = C F hydro ( r ( t ) ) d r d t d t ,

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