Eddies in Einstein's formula

Oct 07, 2011 By Nicolas Guérin
Credit: 2011 Alain Doyon

(PhysOrg.com) -- How does a microscopic particle behave in a liquid? New results published in the journal Nature show that Einstein’s formula for describing this situation needs a little adjustment. This will in turn open up possibilities for new applications, particularly in biology.

A pollen grain suspended in water appears to move about randomly; this is what is known as “.” The grain is hit on all sides by water molecules, which make it quiver. At the human scale, on the contrary, a swimmer plows forward in the water by continuing to move in the direction of her propulsion; her motion is aided by the eddies that she leaves in her wake. For the first time, physicists have observed and measured the effect of these eddies at the microscopic scale. They have found that the viscosity of the water doesn’t completely inhibit the momentum that the water molecules transfer to the pollen grain. As Einstein suspected back in 1905, his formula describing Brownian motion needs to be adjusted.

By observing at very high speeds the shadow cast by a the particle on a detector, researchers in EPFL’s Laboratory of Complex Matter Physics were able to show, and measure, the existence of eddies formed by a particle in motion in a liquid. These tiny vortices dissipate after just five microseconds. “The rate at which the vortex dissipates depends on the size of the particle that creates it and the density and viscosity of the liquid,” explains Sylvia Jeney.

Optical tweezers

The challenge was to measure the characteristics of these vortices. To do this, the physicists used what they refer to as “optical tweezers.” Using a laser, they are able to hold very small objects, such as a particle in a liquid, as if the particle was attached to the end of a spring. By measuring the vibration of the particle against the spring, they can demonstrate that the vortex increases the particle’s fluctuations. And, inversely, it is possible to determine certain properties of the particle, such as its size or shape, from the characteristics of the vortex. It’s as if one could deduce the size or shape of a swimmer’s body from the wake she leaves in the water.

From biology to sensors

These developments hold promise for making improvements in many areas. “In biology, exchanges between the cell and its surroundings take place in a liquid medium; proteins or viruses that pass through the membrane are one example,” notes Jeney. Elsewhere, micro-sensors used in viscous media currently lack precision. They are used to test interactions in a between a drug and various molecules attached to a microscaffolding. These results could help scientists improve these interactions.

Explore further: Boron-based atomic clusters mimic rare-earth metals

More information: Resonances arising from hydrodynamic memory in Brownian motion, Thomas Franosch, et al., Nature, 05.10.2011, DOI:10.1038/nature10498

Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid, Rongxin Huang, et al., NaturePhysics, 27.03.2011, DOI:10.1038/NPHYS1953

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1 / 5 (2) Oct 07, 2011
You can observe the Brownian motion inside of nonpolar system easily even with naked eye (for example in sulphur dispersion in carbondisulphide, naphthalene in benzene, etc.). Such motion can serve as a tangible evidence of atoms, molecular motion, quantum phenomena or even extradimensions.

At the water and another polar fluid the suspended particles are surrounded with polar molecules, which are forming invisible "coat" around them, and they slow down the Brownian motion of particles in such a way, it can be observed under microscope only.
not rated yet Oct 07, 2011
Fascinating. Since Brownian motion is used in stellar dynamics to model how a massive body responds to background gravitational influences, doesn't this have implications for current cosmological models ?
not rated yet Oct 07, 2011
Brownian motion works well if there are no defects in space. In other case it differs from random walk finally constructed accordingly to thermodynamical principles (Maximal Entropy Random Walk), which for example agrees with quantum mechanics that stationary probability distribution of electrons on semiconductor lattice should be the quantum ground state:
1 / 5 (2) Oct 19, 2011
In dense aether model the above observation could be applied even to the observable Universe as a whole. While it's interior appears driven with entropic phenomena (gravity or pressure of radiation) nearly exclusively, its outer areas (at both quantum, both cosmological scales) have symmetry of Brownian motion broken and they exhibit various spin fields, polarization of CMBR field, axis of rotation and dark matter flow.
not rated yet Oct 19, 2011
BTW This recent study analyses the above insight in semi-quantitative way for dark matter flow.... http://physics.ap...5.095005

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