Physicists track the random walks of ellipsoids, test 'lost' theory of Brownian motion

Oct 26, 2006
Physicists track the random walks of ellipsoids
Twenty seconds of a measured random walk trajectory for a micrometer-sized ellipsoid undergoing Brownian motion in water. The ellipsoid orientation, labeled with rainbow colors, illustrates the coupling of orientation and displacement and shows clearly that the ellipsoid diffuses faster along its long axis compared to its short axis.

Research carried out at the University of Pennsylvania has definitively measured and described the Brownian motion of an isolated ellipsoidal particle, completing a path laid out by Einstein 100 years ago when he first described rotational Brownian motion for spheres in water.

Brownian motion, the tiny random movements of small objects suspended in a fluid, has served as a paradigm for concepts of randomness ranging from noise in light detectors to fluctuations in the stock market. Using digital video microscopy, the researchers directly observed the twisty "random walks" arising from the combined effects of random rotations and displacements of ellipsoids in water.

"Brownian motion arises from the aggregate effect of the random collisions of many molecules with suspended objects. It is such a profound and fundamental phenomena that, as a physicist, I want to learn everything about it," said Arjun Yodh, professor in Penn's Department of Physics and Astronomy in the School of Arts and Sciences. "Our work explored the movement of rod-like particles in order to understand how their spinning motion affects the displacement or translation of their centers."

As Einstein predicted in his 1906 paper, the rotation of spherical particles does not affect their translation. On the other hand, the rotation of non-spherical particles affects their translation, and, since most Brownian particles are not spherical, they experience cross-talk between translation and rotation.

The findings of the Penn group, reported in the journal Science, rediscovered ideas about rotational-translational coupling first published by French physicist Francis Perrin in the 1930s, ideas that were apparently "forgotten" by the science community. Perrin's father, Jean Perrin won the Nobel Prize in 1926 for the first experimental observations confirming Einstein's theories about Brownian motion.

"One of the exciting aspects of this work is the precise agreement between a relatively simple theory and experiments. We developed the theory at Penn but later found many of our results in the forgotten French papers by Perrin," said Tom Lubensky, professor and chair of Penn's Department of Physics and Astronomy and co-author of the Science paper. "Perrin's work is largely unknown today, at least in part because experiments to verify it could not be done in his time."

The Penn researchers employed state-of-art digital imaging technology and computer image analysis for their experiments. Using a charge-couple device camera, they recorded the orientations and positions of a single, micrometer-sized plastic ellipsoid particle suspended in water at a sequence of times.

The experiments confirmed the theory's curious description of how an ellipsoid's random motions are different from those of spherical particles. On average, particles undergoing Brownian motion do not move very far. For example, in one second, the largest number of particles will stay very close, say within one micron, of their starting point; a smaller number will move between one micron and two microns; a still smaller number will move between two microns and three microns, and so on. A plot of the number of particles traveling specific distances yields the famous bell-shaped or Gaussian curve from statistics. The Penn researchers found that the same experiment, carried out on ellipsoidal particles, produces a curve that is not Gaussian.

"Since ellipsoids are longer than they are wide, they experience more water resistance going in one direction than the other," said Yilong Han, a post-doc in Yodh's research group. "These effects are larger in two-dimensions than in three, and the coupling of the rotational movement –- spinning –- with the translational movement –- the distance traveled -– give rise to the weirdly non-Gaussian behavior we observed."

Source: University of Pennsylvania

Explore further: New 'topological insulator' could lead to superfast computers

add to favorites email to friend print save as pdf

Related Stories

Inside the cell, an ocean of buffeting waves

Aug 14, 2014

Conventional wisdom holds that the cytoplasm of mammalian cells is a viscous fluid, with organelles and proteins suspended within it, jiggling against one another and drifting at random. However, a new biophysical ...

Stressed yeast paint a picture of Dorian Gray

Jul 02, 2014

We all pass unwanted stuff on to our children—emotional baggage, peculiar habits, unfashionable furniture. Cells do the same thing when they divide; along with their newly replicated genomes and the vital ...

Eddies in Einstein's formula

Oct 07, 2011

(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 w ...

The dance of hot nanoparticles

Sep 08, 2010

(PhysOrg.com) -- "Brownian motion is a very old concept," Klaus Kroy tells PhysOrg.com. "The laws explaining it were formulated more than a century ago by Albert Einstein. However, we are finding some intere ...

Recommended for you

Uncovering the forbidden side of molecules

Sep 21, 2014

Researchers at the University of Basel in Switzerland have succeeded in observing the "forbidden" infrared spectrum of a charged molecule for the first time. These extremely weak spectra offer perspectives ...

How Paramecium protozoa claw their way to the top

Sep 19, 2014

The ability to swim upwards – towards the sun and food supplies – is vital for many aquatic microorganisms. Exactly how they are able to differentiate between above and below in often murky waters is ...

User comments : 0