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Ultrafast viscosity measurement with ballistic optical tweezers


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.

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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.

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.


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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




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.

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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.

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Madsen, L.S., Waleed, M., Casacio, C.A. et al. Ultrafast viscosity measurement with ballistic optical tweezers. Nat. Photonics 15, 386–392 (2021).

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