Research: Dynamics of Floating Particles

Figure 1: Animated GIF of the zippering up process for a train of six rods. The rods are each 4 cm in length and are floating on a 4:1 mixture of water and golden syrup (hence the slightly yellow tinge). The snapshots are taken roughly every 10 seconds, although there is a delay of around 1 minute between the last two frames. (Thanks to Julia Wolf for help in manufacturing this train.)

Objects floating at an interface move together because of the mutual attraction, or 'Cheerios effect'. What interests us the most about this problem is questions about how fast this all happens. If the particles are spheres, then they move together along a line joining their centres but if they are long and thin, for example, then much more interesting effects can be observed. In the animated GIF above, you see a train consisting of six rods joined together by very thin fibres. The fibres act as a hinge that ensures the rods stay attached while they are attracted to a nearby wall, leading to an interesting motion.

You can find some movies of the interesting things that happen as the train "zips up" against the wall on Ho-Young's website. These show that we sometimes observe a flicking of the rods (caused by the inextensibility of the train) as they zip up so that the motion involves rotations as well as the translations that are observed in the simpler situation when bubbles or breakfast cereal interact. You can also see this in the sequence of snap-shots in figure 1, with the train starting from rest but being pulled through a whole host of different positions by the anisotropy of the forces it experiences before finally coming to rest next to the wall.

If you've seen the movies then I hope that you're convinced that this is, if nothing else, a cute problem. However, the importance of understanding of motion of particles at interfaces, and particularly that due to surface tension, should not be underestimated. In fact, much work is being conducted at Harvard (by the Whitesides Group) and elsewhere to use these "self-assembly" techniques to make microchips more quickly and easily than can be achieved using conventional means.

Reference:

D. Vella, H.-Y. Kim and L. Mahadevan, "The wall-induced motion of a floating, flexible train", J. Fluid Mech. 502, 89 (2004). PDF File (276 KB)

Abstract:

We consider the dynamics of capillary attraction between an articulated train of rigid rods floating at a liquid-gas interface and a nearby wall. We then explain some of the phenomena that are a result of the strong anisotropy and the extended nature of the system, such as the lining up next to the walling in a 'zippering' motion that is observed and compare our results qualitatively with those of experiments

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