Rethinking Brownian motion with the 'Emperor's New Clothes'

July 27, 2009

In the classic fairy tale, "The Emperor's New Clothes," Hans Christian Andersen uses the eyes of a child to challenge conventional wisdom and help others to see more clearly. In similar fashion, researchers at the University of Illinois have now revealed the naked truth about a classic bell-shaped curve used to describe the motion of a liquid as it diffuses through another material.

"The new findings raise fundamental questions concerning the statistical nature of the diffusion process," says Steve Granick, Founder Professor of Engineering, and professor of materials science and engineering, of chemistry, of chemical and biomolecular engineering, and of physics at the U. of I.

Diffusion is critical to processes such as drug delivery, water purification, and the normal operation of living cells. Key to the diffusion process is the manner in which the motion of one molecule affects the motion of another.

"In high school science classes, students are often assigned the task of using a microscope to watch a particle of dust sitting in a drop of water," Granick said. "The dust particle seems alive, moving back and forth, never in the same way. The motion of the dust particle is caused by the random 'kicks' of surrounding ."

Called "Brownian motion" (after botanist Robert Brown, who noticed it in 1828), this phenomenon of fluids was described by in 1905, when he published his statistical molecular theory of liquids.

According to Einstein, if the motions of many particles were watched, and the distance each moved in a certain time were recorded, the distribution would resemble the familiar Gaussian, bell-shaped curve used to assign grades in a science class.

Einstein had it right - almost.

"Like Einstein, we used to think we could describe Brownian motion with a standard bell-shaped curve," Granick said. "But now, with the ability to measure very small distances much more precisely than was possible 100 years ago, we have found that we can have extremes much farther than previously imagined."

In a paper to be published in the Proceedings of the National Academy of Sciences Online Early Edition next week, the U. of I. researchers show that Einstein's explanation, commonly cited in textbooks, fails in certain important cases.

The experiments were conducted by precisely tracking the motion of 100-nanometer colloidal beads using fluorescence microscopy.

In one series of experiments, the researchers watched as the beads moved up and down tiny tubes of lipid molecules by Brownian motion. In a second series of experiments, the researchers watched as the beads diffused through a porous membrane of entangled macromolecule filaments, again by Brownian motion.

In both sets of experiments, there were many features in full agreement with Einstein and the bell-shaped curve; but there were also features in significant disagreement. In those cases, the beads moved much farther than the common curve could predict. In those extreme displacements, diffusion behavior was not Gaussian, the researchers report. The behavior was exponential.

"These large displacements happen less often, but when they do occur, they are much bigger than we previously thought possible," Granick said.

The new findings "change the rules of the diffusion game," Granick said. "Like the emperor's new clothes, now that we know the bell-shaped curve isn't always the right way to think about a particular problem, process, or operation, we can begin to design around it, and maybe take advantage of it. And, we can correct the textbooks."

Source: University of Illinois at Urbana-Champaign (news : web)

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3.7 / 5 (3) Jul 28, 2009
Why we should correct our textbooks?

Mr. Einstein has derived diffusion for bulk medium. If he asked him to derive it for porous medium, then his equations would be different. Diffusion through porous medium is just a special case of diffusion and original equations still remain valid.

Should we rewrite Navier-Stokes equations in textbooks just because liquid flows through capillars in laminar way only?
not rated yet Jul 28, 2009
The other aspect of Brownian Motion that Einstein observed was the mean distance a particle moved( in straightline from its starting point) is proportional to the square root of the time interval that had elapsed. For example if the particle moves at 1 m/sec then after 4 seconds it has moved 2 metres, after 9 seconds 3 metres etc
2.5 / 5 (2) Jul 28, 2009
Using statistics you can't guess the exact position or velocity of a dust particle on the surface of the water, but you can guess how 100 particles will move on average. The fact that some particles are off the chart that doesn't mean the chart is bad it just means the term "statistics" was missunderstood by those scientists.
1 / 5 (4) Jul 28, 2009


For several years we struggled with observations that clearly showed evidence of severe mass fractionation of isotopes and elements from diffusion in meteorites, in planets, in the solar wind, and in solar flares.

For example the elements that Donald V. Reames observed in a solar flare with the Wind spacecraft [Ap. J. 540 (2000) L111%u2013L114] http://epact2.gsf...0HiZ.pdf

Mass fractionated neon in meteorites was mistakenly labeled as Ne-A, Ne-B, Ne-C, Ne-D, Ne-E, Ne-A1, Ne-A2, Ne-E(l), Ne-E(h), Ne-O from 1967-1980 ["The Neon Alphabet Game" in Proceedings of the 11th Lunar Planet Sci. Conf. 15, Number 2 (1980) 879-899]

Recently it was finally realized that the Sun itself operates a plasma diffuser, selectively moving lightweight elements - like H and He - and lightweight isotopes of each element to its surface.

With kind regards,
Oliver K. Manuel
1 / 5 (3) Jul 28, 2009
There are far more interesting topics related to particle vibration and brownian motion than the mathamatics of any stupid curve bell shaped or otherwise. Observation and interpritation is the requirement not stupid maths
5 / 5 (1) Jul 28, 2009
Slotin: At each reprint of a text book, each topic should be updated to reflect new knowledge that could alter the validity of the original. There is no point in miseducating the next generation - they will not thank us for it, as we do not thank our teachers for the amount of old knowledge we have had to revise or dispense with.
not rated yet Jul 28, 2009
It shouldn't surprise anyone that in the small, Brownian motion is a subset of a scaling distribution. This is our old friend, the Levy Distribution, with exponents making it look like a Gaussian Distribution, or a close approximation.

Remember, Wall Street thought that Mandelbrot was insane when he suggested that fractal Brownian motion described the movements of markets better. We know better now, don't we.
1 / 5 (3) Jul 28, 2009
Over-due experiments include the movements of energy-active electrons through the membrane covering of a living cell to accelerate mitosis and result in the malfunction called "CANCER"!
1 / 5 (1) Jul 28, 2009 is no point in miseducating the next generation..
It's the point of scientific journalism, which is fighting for public attention and grant money support.
not rated yet Jul 29, 2009
Is any thought given to the possible effect of observation with regard to any Brownian motion testing?

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