The University of Illinois findings, to be published in the Proceedings of the National Academy of Sciences next week, "raise fundamental questions concerning the statistical nature of the diffusion process," critical to drug delivery, water purification and the normal operation of living cells, engineering professor Steve Granick said.
They also have real-world applications, including predicting stock market fluctuations.
Albert Einstein, best known for his theories of special relativity and general relativity, developed a statistical molecular theory of liquids that supported the bell-curve motion of particles -- known as Brownian motion, after 19th century Scottish botanist Robert Brown -- in his doctoral dissertation, submitted to Switzerland's University of Zurich in 1905.
But Einstein's theory, commonly cited in textbooks, is not true in certain important cases, Granick said.
"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," said Granick, whose experiments were conducted by tracking the motion of 100-nanometer colloidal beads using a fluorescence microscope.
A nanometer is equal to a billionth of a meter.
In two sets of experiments, many beads moved according to a bell-shaped curve, but others moved much farther than the common curve could predict, the study found.
The new findings "change the rules of the diffusion game," Granick said.
"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," he said. "And we can correct the textbooks."