Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Ultrafast viscosity measurement with ballistic optical tweezers

Nature Photonics volume 15, pages 386–392 (2021)Cite this article

Subjects

Abstract

Viscosity is an important property of out-of-equilibrium systems such as active biological materials and driven non-Newtonian fluids, and for fields ranging from biomaterials to geology, energy technologies and medicine. Non-invasive viscosity measurements typically require integration times of seconds. Here, we demonstrate measurement speeds reaching 20 μs, with uncertainty dominated by thermal molecular collisions for the first time. We achieve this using the instantaneous velocity of a trapped particle in an optical tweezer. To resolve the instantaneous velocity we develop a structured-light detection system that allows particle tracking over femtometre length scales and 16-ns timescales. Our results translate viscosity from a static averaged property to one that may be dynamically tracked on the timescales of active dynamics. This opens a pathway to new discoveries in out-of-equilibrium systems, from the fast dynamics of phase transitions to energy dissipation in motor molecule stepping and to violations of fluctuation laws of equilibrium thermodynamics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Fast velocity thermalization increases the speed of viscosity measurements.
Fig. 2: Optical tweezers with structured-light detection.
Fig. 3: Absolute viscosity estimation.
Fig. 4: Orders-of-magnitude faster viscosity measurement in the ballistic regime.

Similar content being viewed by others

Data availability

Supplementary Information is available for this paper. Further data that supports the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code used to estimate viscosity from the measured power spectral densities is available from the corresponding author upon reasonable request.

References

  1. Ashkin, A. History of optical trapping and manipulation of small-neutral particle, atoms and molecules. IEEE J. Select. Topics Quantum Electron. 6, 841–856 (2000).

    Article  ADS  Google Scholar 

  2. Carney, S. P. et al. Direct measurement of stepping dynamics of E. coli UvrD helicase. Biophys. J. 118, 71a (2020).

    Article  ADS  MathSciNet  Google Scholar 

  3. Nishizawa, K. et al. Feedback-tracking microrheology in living cells. Sci. Adv. 3, e1700318 (2017).

    Article  ADS  Google Scholar 

  4. Killian, J. L., Ye, F. & Wang, M. D. Optical tweezers: a force to be reckoned with. Cell 175, 1445–1448 (2018).

    Article  Google Scholar 

  5. Tassieri, M. Microrheology with optical tweezers: peaks & troughs. Curr. Opin. Colloid Interface Sci. 43, 39–51 (2019).

    Article  Google Scholar 

  6. Grimm, M., Franosch, T. & Jeney, S. High-resolution detection of Brownian motion for quantitative optical tweezers experiments. Phys. Rev. E 86, 021912 (2012).

    Article  ADS  Google Scholar 

  7. Kheifets, S., Simha, A., Melin, K., Li, T. & Raizen, M. G. Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss. Science 343, 1493–1496 (2014).

    Article  ADS  Google Scholar 

  8. Gnesotto, F., Mura, F., Gladrow, J. & Broedersz, C. Broken detailed balance and non-equilibrium dynamics in living systems: a review. Rep. Prog. Phys. 81, 066601 (2018).

    Article  ADS  Google Scholar 

  9. Dogterom, M. & Koenderink, G. H. Actin–microtubule crosstalk in cell biology. Nat. Rev. Mol. Cell Biol. 20, 38–54 (2019).

    Article  Google Scholar 

  10. Rathee, V., Blair, D. L. & Urbach, J. S. Localized stress fluctuations drive shear thickening in dense suspensions. Proc. Natl Acad. Sci. 114, 8740–8745 (2017).

    Article  ADS  Google Scholar 

  11. Waitukaitis, S. R. & Jaeger, H. M. Impact-activated solidification of dense suspensions via dynamic jamming fronts. Nature 487, 205–209 (2012).

    Article  ADS  Google Scholar 

  12. Han, E., Peters, I. R. & Jaeger, H. M. High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming. Nat. Commun. 7, 12243 (2016).

    Article  ADS  Google Scholar 

  13. Saint-Michel, B., Gibaud, T. & Manneville, S. Uncovering instabilities in the spatiotemporal dynamics of a shear-thickening cornstarch suspension. Phys. Rev. X 8, 031006 (2018).

    Google Scholar 

  14. Capitanio, M. et al. Ultrafast force-clamp spectroscopy of single molecules reveals load dependence of myosin working stroke. Nat. Methods 9, 1013–1019 (2012).

    Article  Google Scholar 

  15. Tassieri, M. Linear microrheology with optical tweezers of living cells ‘is not an option’! Soft Matter 11, 5792–5798 (2015).

    Article  ADS  Google Scholar 

  16. Ariga, T., Tomishige, M. & Mizuno, D. Nonequilibrium energetics of molecular motor kinesin. Phys. Rev. Lett. 121, 218101 (2018).

    Article  ADS  Google Scholar 

  17. Battle, C. et al. Broken detailed balance at mesoscopic scales in active biological systems. Science 352, 604–607 (2016).

    Article  ADS  Google Scholar 

  18. Oyama, N., Kawasaki, T., Mizuno, H. & Ikeda, A. Glassy dynamics of a model of bacterial cytoplasm with metabolic activities. Phys. Rev. Res. 1, 032038 (2019).

    Article  Google Scholar 

  19. Nishizawa, K. et al. Universal glass-forming behavior of in vitro and living cytoplasm. Sci. Rep. 7, 15143 (2017).

    Article  ADS  Google Scholar 

  20. Grob, M., Zippelius, A. & Heussinger, C. Rheological chaos of frictional grains. Phys. Rev. E 93, 030901 (2016).

    Article  ADS  Google Scholar 

  21. Jünger, F. et al. Measuring local viscosities near plasma membranes of living cells with photonic force microscopy. Biophys. J. 109, 869–882 (2015).

    Article  ADS  Google Scholar 

  22. Chavez, I., Huang, R., Henderson, K., Florin, E.-L. & Raizen, M. G. Development of a fast position-sensitive laser beam detector. Rev. Sci. Instrum. 79, 105104 (2008).

    Article  ADS  Google Scholar 

  23. Pralle, A., Florin, E.-L., Stelzer, E. & Hörber, J. Local viscosity probed by photonic force microscopy. Appl. Phys. A 66, S71–S73 (1998).

    Article  Google Scholar 

  24. Tolić-Nørrelykke, S. F. et al. Calibration of optical tweezers with positional detection in the back focal plane. Rev. Sci. Instrum. 77, 103101 (2006).

    Article  ADS  Google Scholar 

  25. Bishop, A. I., Nieminen, T. A., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Optical microrheology using rotating laser-trapped particles. Phys. Rev. Lett. 92, 198104 (2004).

    Article  ADS  Google Scholar 

  26. Guzmán, C. et al. In situ viscometry by optical trapping interferometry. Appl. Phys. Lett. 93, 184102 (2008).

    Article  ADS  Google Scholar 

  27. Lukić, B. et al. Direct observation of nondiffusive motion of a Brownian particle. Phys. Rev. Lett. 95, 160601 (2005).

    Article  ADS  Google Scholar 

  28. Rouan, D., Riaud, P., Boccaletti, A., Clénet, Y. & Labeyrie, A. The four-quadrant phase-mask coronagraph. I. Principle. Publ. Astron. Soc. Pacific 112, 1479–1486 (2000).

    Article  ADS  Google Scholar 

  29. Jia, S., Vaughan, J. C. & Zhuang, X. Isotropic three-dimensional super-resolution imaging with a self-bending point spread function. Nat. Photon. 8, 302–306 (2014).

    Article  ADS  Google Scholar 

  30. Shechtman, Y., Weiss, L. E., Backer, A. S., Lee, M. Y. & Moerner, W. Multicolour localization microscopy by point-spread-function engineering. Nat. Photon. 10, 590–594 (2016).

    Article  ADS  Google Scholar 

  31. Treps, N. et al. A quantum laser pointer. Science 301, 940–943 (2003).

    Article  ADS  Google Scholar 

  32. Taylor, M. A. et al. Biological measurement beyond the quantum limit. Nat. Photon. 7, 229–233 (2013).

    Article  ADS  Google Scholar 

  33. Meers, B. J. Recycling in laser-interferometric gravitational-wave detectors. Phys. Rev. D 38, 2317–2326 (1988).

    Article  ADS  Google Scholar 

  34. Huang, R. et al. Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid. Nat. Phys. 7, 576–580 (2011).

    Article  Google Scholar 

  35. Berg-Sørensen, K. & Flyvbjerg, H. Power spectrum analysis for optical tweezers. Rev. Sci. Instrum. 75, 594–612 (2004).

    Article  ADS  Google Scholar 

  36. Viswanath, D. S., Ghosh, T. K., Prasad, D. H., Dutt, N. V. & Rani, K. Y. Viscosity of Liquids: Theory, Estimation, Experiment and Data (Springer Science & Business Media, 2007).

  37. Peterman, E. J., Gittes, F. & Schmidt, C. F. Laser-induced heating in optical traps. Biophys. J. 84, 1308–1316 (2003).

    Article  ADS  Google Scholar 

  38. Hammond, A. P. & Corwin, E. I. Direct measurement of the ballistic motion of a freely floating colloid in Newtonian and viscoelastic fluids. Phys. Rev. E 96, 042606 (2017).

    Article  ADS  Google Scholar 

  39. Milovanovic, D., Wu, Y., Bian, X. & De Camilli, P. A liquid phase of synapsin and lipid vesicles. Science 361, 604–607 (2018).

    Article  ADS  Google Scholar 

  40. Parry, B. R. et al. The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity. Cell 156, 183–194 (2014).

    Article  Google Scholar 

  41. Chacko, R. N., Mari, R., Cates, M. E. & Fielding, S. M. Dynamic vorticity banding in discontinuously shear thickening suspensions. Phys. Rev. Lett. 121, 108003 (2018).

    Article  ADS  Google Scholar 

  42. Doostmohammadi, A., Shendruk, T. N., Thijssen, K. & Yeomans, J. M. Onset of meso-scale turbulence in active nematics. Nat. Commun. 8, 15326 (2017).

    Article  ADS  Google Scholar 

  43. Arbore, C., Perego, L., Sergides, M. & Capitanio, M. Probing force in living cells with optical tweezers: from single-molecule mechanics to cell mechanotransduction. Biophys. Rev. 11, 765–782 (2019).

    Article  Google Scholar 

  44. Rohrbach, A., Meyer, T., Stelzer, E. H. & Kress, H. Measuring stepwise binding of thermally fluctuating particles to cell membranes without fluorescence. Biophys. J. 118, 1850–1860 (2020).

    Article  ADS  Google Scholar 

  45. Comtet, J. et al. Pairwise frictional profile between particles determines discontinuous shear thickening transition in non-colloidal suspensions. Nat. Commun. 8, 15633 (2017).

    Article  ADS  Google Scholar 

  46. Geiß, D. & Kroy, K. Brownian thermometry beyond equilibrium. ChemSystemsChem 2, e1900041 (2020).

    Article  Google Scholar 

  47. Brown, E. & Jaeger, H. M. Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Rep. Prog. Phys. 77, 046602 (2014).

    Article  ADS  Google Scholar 

  48. Joly, L., Merabia, S. & Barrat, J.-L. Effective temperatures of a heated Brownian particle. Europhys. Lett. 94, 50007 (2011).

    Article  ADS  Google Scholar 

  49. Sanchez, T., Chen, D. T., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    Article  ADS  Google Scholar 

  50. Ovarlez, G. et al. Density waves in shear-thickening suspensions. Sci. Adv. 6, eaay5589 (2020).

    Article  ADS  Google Scholar 

  51. Doostmohammadi, A., Adamer, M. F., Thampi, S. P. & Yeomans, J. M. Stabilization of active matter by flow-vortex lattices and defect ordering. Nat. Commun. 7, 10557 (2016).

    Article  ADS  Google Scholar 

  52. Vliegenthart, G. A., Ravichandran, A., Ripoll, M., Auth, T. & Gompper, G. Filamentous active matter: band formation, bending, buckling and defects. Sci. Adv. 6, eaaw9975 (2020).

    Article  ADS  Google Scholar 

  53. Jünger, F. & Rohrbach, A. Strong cytoskeleton activity on millisecond timescales upon particle binding revealed by ROCS microscopy. Cytoskeleton 75, 410–424 (2018).

    Article  Google Scholar 

  54. Ghosh, P. K. et al. Membrane microviscosity regulates endothelial cell motility. Nat. Cell Biol. 4, 894–900 (2002).

    Article  Google Scholar 

  55. Sani, E. & Dell’Oro, A. Spectral optical constants of ethanol and isopropanol from ultraviolet to far infrared. Opt. Mater. 60, 137–141 (2016).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank P.K. Lam for providing the split-waveplate used to implement structured detection and N. Mauranyapin for taking scanning electron microscope images of the microparticles. We also thank N. Mauranyapin for useful discussions, along with H. Rubinsztein-Dunlop and I. Lenton. This work was supported primarily by the Air Force Office of Scientific Research (AFOSR) grant no. FA2386-14-1-4046. It was also supported by the Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS, CE170100009). W.P.B. acknowledges support from the Australian Research Council Future Fellowship FT140100650. M.A.T. acknowledges support from the Australian Research Council Discovery Early Career Research Award DE190100641.

Author information

Author notes

  1. These authors contributed equally. Lars S. Madsen, Muhammad Waleed.

Authors and Affiliations

  1. ARC Centre of Excellence for Engineered Quantum Systems, University of Queensland, St Lucia, Queensland, Australia

    Lars S. Madsen, Muhammad Waleed, Catxere A. Casacio, Alex Terrasson & Warwick P. Bowen

  2. School of Mathematics and Physics, University of Queensland, St Lucia, Queensland, Australia

    Alexander B. Stilgoe

  3. Australian Institute for Bioengineering and Nanotechnology, University of Queensland, St Lucia, Queensland, Australia

    Michael A. Taylor

Authors
  1. Lars S. Madsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Waleed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Catxere A. Casacio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alex Terrasson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alexander B. Stilgoe
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Michael A. Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Warwick P. Bowen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

L.S.M., M.W. and C.A.C. collected the data, with trouble-shooting provided by A.B.S. and W.P.B. M.W. and L.S.M. constructed the optical tweezers with contributions from M.A.T. M.W., L.S.M. and C.A.C. constructed the structured-light detector. L.S.M. performed the data analysis, with contributions from M.A.T., A.T., M.W. and W.P.B. L.S.M. and A.T. performed the simulations, with contributions from A.B.S., M.A.T. and W.P.B. L.S.M., M.A.T. and W.P.B. conceived the idea and designed the experiment. W.P.B. and L.S.M. wrote the manuscript with contributions from M.A.T. and assistance from the other authors. W.P.B. led the project with contributions from M.A.T. and L.S.M.

Corresponding author

Correspondence to Warwick P. Bowen.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks Donald Sirbuly and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Microparticle tracking in the ballistic regime.

a, Position trajectory of a 0.59 μm radius silica microsphere in water taken with conventional split-detection over a time spanning 10τt. b, High resolution trajectory taken simultaneously with structured-light detection, shown here over a time of 10τi. c, Particle velocity calculated from the data in b. Error bars: one-sigma uncertainty due to laser noise obtained from simulations. d, Velocity autocorrelation function calculated from data in c, (blue points) compared to theory (grey line). Note: the oscillations are an artefact arising from highpass filtering. e & f, Position and velocity power spectral densities, calculated as described in Section 1 of the Supplementary Information. The low frequency components (red traces) were obtained with split-detection, and the high frequency components (blue traces) were obtained with structured-light detection. Grey shading: theoretically predicted power spectra from thermal motion alone. Blue shading: noise floor of structured-light detection. Dashed line: 1/2πτt. Dot-dashed line: 1/2πτ.

Supplementary information

Supplementary Information

Supplementary Figs. 1–11, theory, simulations, experiments and discussion.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Madsen, L.S., Waleed, M., Casacio, C.A. et al. Ultrafast viscosity measurement with ballistic optical tweezers. Nat. Photonics 15, 386–392 (2021). https://doi.org/10.1038/s41566-021-00798-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-021-00798-8

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing