Researchers measured the viscosity, or stickiness, of liquids, which could have applications in biology. [Image: University of Queensland]

Most examples of viscosity come from everyday macroscopic substances, from motor oil to honey. However, on the level of living cells and other biological materials, viscosity measurements can provide key information about phase transitions and dynamics on time scales of milliseconds or microseconds.

Previous methods of measuring viscosity on these short time and length scales required integration times of multiple seconds, so that they could not capture the rapidly changing dynamics of particle–liquid interactions. A research team at an Australian university has measured small-scale fluid viscosity with temporal resolution on a few tens of microseconds by tracking a particle inside an optical trapping field with high precision (Nat. Photonics, doi: 10.1038/s41566-021-00798-8).

Beating Einstein’s prediction

Early in the 20th century, Albert Einstein provided a thermodynamic explanation of Brownian motion—the random motions of microparticles suspended in a fluid. “However, Einstein also realized that with fast enough measurements a different sort of behavior should emerge, where particles move in smooth trajectories, much like the ballistic trajectories of a ball when thrown,” says Warwick P. Bowen, a professor in the quantum optics laboratory at the University of Queensland, Australia.

Back then, Einstein predicted that it would be impossible to take measurements fast enough to reach this “ballistic regime,” but in the past decade, experimenters led by OSA Fellow Mark G. Raizen at the University of Texas at Austin, USA, showed that Einstein’s conjecture was inaccurate.

Bowen and his Queensland collaborators reasoned that if they could reach this regime where they could see the smooth trajectories of the microparticles in an optical trap, then they could measure the velocities of the particles, not just their positions, and calculate their kinetic energy and thus their viscosity.

“So, velocity measurement allows a direct measurement of viscosity, rather than the statistical inference that one is able to do with position measurement,” Bowen says. “It is this key fact that allowed us to increase the speed of viscosity measurement by several orders of magnitude. It also removes calibration requirements for other viscosity measurement techniques, since the kinetic energy is so closely connected to viscosity. This is important for making measurements in complex environments such as cells.”

Better detection with structured light

Key to the outcome of the Queensland group’s research was the development of a different technique for detecting the light passing through the optical tweezers. Bowen and his colleagues compared the standard method, called split detection, with their new approach, called structured-light detection.

When the laser light passing through optical tweezers hits a trapped particle, like a tiny silica sphere floating in water, some small fraction of the light is scattered. “The interference between the scattered and transmitted field results in a deflection of the light,” Bowen says. “In split detection, this deflection is directly measured by taking the different photocurrent from the two sides of the detector.” However, the disadvantage of this simple, robust technique is that it places limits on the total amount of scattered field that can be detected due to saturation or damage of the photodiode from the bright transmitted light.

“A significant challenge with building a precision optical tweezer is that the transmitted optical trapping field is typically very much larger than the scattered light signal that you wish to detect (maybe a billion times larger),” Bowen says. Structured-light detection permits full suppression of the trap field, together with nearly perfect detection of the information-carrying field. Thus, the researchers could crank up the intensity of the optical trapping field, pick up the scattered light signal and not be blinded by the transmission.

In the new technique of structured-light detection, the Queensland team suppressed the transmitted field by using a spatial filter—specifically, a phase-plate that imparts a π phase shift on half of the output field from the tweezers, while leaving the other half unchanged. “This converts the transmitted trapping field from a symmetric Gaussian beam shape to an anti-symmetric shape,” Bowen says.

“On the other hand, the component of the scattered field that contains information about the position of the trapped particle is anti-symmetric to begin with,” Bowen says. The phase plate reverses that component so that it can enter the single-mode fiber leading to the detector.

“Our detection system is therefore able to collect most of the information carrying field while rejecting most of the transmitted trapping field,” Bowen adds. “Thus it resolves the power-handling problem of split detectors.”

Biological applications

Bowen believes that the viscosity-measurement technique is ready to move into the biology laboratory, and the team plans to demonstrate the method with measurements of “the fast out-of-equilibrium dynamics” of viscosity within living cells. The Queensland researchers hope that the technique will provide a new level of detail about the inner dynamics of cells.