Partitioning by collision

February 5, 2016, Ludwig Maximilian University of Munich
Biophysics: Partitioning by collision
Shaking a can of mixed nuts sorts them according to size. Mixtures of self-propelling particles of equal size can also undergo demixing, provided they differ in their diffusivities.

An ensemble consisting of a binary mixture of particles of equal size can partition itself into its component fractions - provided that the two species differ in their diffusion constants.

If you shake a can of mixed nuts before opening it, you can count on finding the walnuts on top and the peanuts at the bottom. This is an everyday example of the "spontaneous", demixing of heterogeneously sized particles, popularly known as the Brazil Nut effect. The phenomenon is observed in all granular systems consisting of particles of unequal sizes, where the imposition of an undirected force results in random active movements of its constituents. However, computer simulations performed by a group led by Ludwig-Maximilans-Universitaet (LMU) in Munich physicist Erwin Frey have now shown that mixtures of equally sized particles in solution will sort themselves out, provided that the components differ in diffusivity. "Based on the results of our simulations, we now provide a theoretical explanation for this phenomenon, which has never been investigated before. Our model indicates that the random motions of the particles involved play an important role in the demixing process," says Frey. The new study appears in the journal Physical Review Letters.

Soluble substances normally become evenly distributed throughout the solvent medium, thanks to passive molecular diffusion. The rate at which this occurs depends on the diffusion constant of the molecule concerned, whose magnitude increases with the temperature. In mixtures that have attained thermal equilibrium, particles of equal size normally exhibit the same diffusion constant. "We were interested in what happens when particles of equal size differ in their diffusion constants," says Simon Weber, first author on the new paper. Since such a situation can only arise in non-equilibrium systems which contain actively driven particles, we chose a system in which some of the particles exhibit irregular active motion. These motions are characterized by their so-called persistence length, which describes the average path length traversed by a particle in a given direction before it careers off in a different direction."

Simulations of particle motions in such a system indicate that a binary mixture consisting of rapidly moving 'hot' particles and passively diffusing 'cold' particles will undergo spontaneous partitioning if the persistence length for the self-propelled particles is very short. This is the case for motile bacterial cells, for example, for which the persistence length is less than the cell diameter. "Demixing occurs because the passive particles are constantly being buffeted by the active species," Frey explains. "This results in an effective attraction between the passive particles, such that, in the long term, they congregate into a single cluster. The active particles become distributed uniformly around the cluster, essentially acting as a cage within which the cluster is confined.

However, the fractionation effect is only observed if both the total number of particles and the difference between the diffusion constants of the particle species are sufficiently large - and even then, demixing is a slow process. "It takes a long time for a population of particles to be distributed uniformly in a given volume of space by means of diffusive motion. And the fact that the diffusive motions of the passive particles are primarily driven by collisions with the active particles makes the process even slower," Weber says. "We believe that the reason why this sort of cluster formation by the passive has never been reported before is that the relevant simulations were broken off too early." The next chapter in this story will be concerned with the experimental verification of the effect predicted by the simulations described in the new paper.

Explore further: Model system used to illustrate phase transition of a mixture of active and passive particles

More information: Simon N. Weber et al. Binary Mixtures of Particles with Different Diffusivities Demix, Physical Review Letters (2016). DOI: 10.1103/PhysRevLett.116.058301

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Whydening Gyre
5 / 5 (1) Feb 05, 2016
Same size - different shape/properties - it's still the "Brazil Nut Effect".
The REAL experiment is to see if particles ALL exactly alike do this.
(over an even longer length of time, of course)
I'll bet they do...
RealScience
5 / 5 (2) Feb 06, 2016
@wg - umm - if the particles are "ALL exactly alike", how can you tell if they have de-mixed?
Whydening Gyre
5 / 5 (1) Feb 07, 2016
Well, a paint mark maybe? Different colors?
WAs wonderin' how long it would take someone to catch on...:-)
RealScience
5 / 5 (2) Feb 07, 2016
Nature runs similar experiments all the time - my favorite is beach sand with repeated agitation by waves. It is interesting how well sorted out the darker sand often seems to be, but then it has a different composition (and thus density) and a different grain size as well. I'll try to remember to bring a microscope next time to check the grain shape.

But even the color can make a big difference - under sunlight the dark grains will become warmer, and dry faster, becoming sticky with salt before the lighter grains do.

In a lab one could make them pretty darned close to identical physically, yet distinguishable (e.g. tagging one type of sand grains with a different isotopic mixture of silicon that still had the same average number of neutrons).

But you are a philosopher, and from a philosophical point of view: if we can distinguish them then nature could be distinguishing them, too...
(Hence my (partially humorous) question on 'exactly alike').
Whydening Gyre
5 / 5 (2) Feb 07, 2016
But you are a philosopher, and from a philosophical point of view: if we can distinguish them then nature could be distinguishing them, too...

MOST definitely...
(Hence my (partially humorous) question on 'exactly alike').

I found it humorous...:-) I may not have any science education, but I know it when I see it...:-)
I also found your "sciency" breakdown full of, well - real science...:-)
As to "philosopher"..? I think I'm more of a "1+1=a new 1" kind of guy...
No problems, only solutions is my philosophy...
Oh, and - "there no ordinary moments." (but not really applicable here, so....)
TehDog
5 / 5 (3) Feb 07, 2016
High fives to both of you, reminds me of what these forums could be :)

"If you shake a can of mixed nuts before opening it, you can count on finding the walnuts on top and the peanuts at the bottom."

I'm imagining a woofer full of nuts and can see how either lighter nuts could by virtue of moving more would layer around the heavier, or the heavier would be bounced to the top, or that the heavier would migrate to the edges, and damn I've given myself something else to think about while falling asleep :)
(I'm allergic to nuts, so not an experiment I'm likely to try :)
Whydening Gyre
not rated yet Feb 08, 2016
High fives to both of you, reminds me of what these forums could be :)

"If you shake a can of mixed nuts before opening it, you can count on finding the walnuts on top and the peanuts at the bottom."

I'm imagining a woofer full of nuts and can see how either lighter nuts could by virtue of moving more would layer around the heavier, or the heavier would be bounced to the top, or that the heavier would migrate to the edges, and damn I've given myself something else to think about while falling asleep :)
(I'm allergic to nuts, so not an experiment I'm likely to try :)

Sounds like more fun than counting sheep.... or thinkin' bout massive credit card debt...
Gigel
5 / 5 (2) Feb 08, 2016
Well, a paint mark maybe? Different colors?

You say that if you have identical particles but you paint some red ans some other blue and then you shake them, the red ones will separate from the blue ones? But how do particles know what colour they are? And what if you wrongly painted a blue-wannabe particle in red? Would the wrongly red particle go into the blue stack because it knows better? Or would it be fooled into running into the red stack?
Whydening Gyre
not rated yet Feb 09, 2016

You say that if you have identical particles but you paint some red ans some other blue and then you shake them, the red ones will separate from the blue ones? But how do particles know what colour they are? And what if you wrongly painted a blue-wannabe particle in red? Would the wrongly red particle go into the blue stack because it knows better? Or would it be fooled into running into the red stack?

put them in a flat round surface with a rim to prevent any falling off. Paint the left half red, leave the other half plain. start rotating the plate quickly. In an indeterminate period of time they will assemble into discernable patterns.

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