A recent article in Physical Review Letters reports on “self-propelled droplet removal” from fibers — the authors designed hydrophobic fibers with the property that when water droplets grow and coalesce on them, the energy released by the coalescence flings the drops off the fibers. The underlying phenomenon is one we’ve all seen: two water droplets, on a window for example, will rapidly merge into one when they come into contact since the one large droplet has less surface area, and therefore less interfacial energy, than two small droplets. The merger is very fast, driven by the large amount of energy associated with an air-water interface being transformed into the kinetic energy of the water. Here, this kinetic energy is sufficient to fling the drop away.
The paper is neat. As noted in the synopsis in Physics, the effect of droplet removal has been seen before in other material contexts, such as planar surfaces. Zhang & colleagues show with experiments and simulation that the high curvature of the fibers causes droplets to fling themselves much more easily than is possible on flat surfaces.
The reason I’m writing about this, though, is that there’s a very nice biophysical connection that isn’t mentioned in the paper. A practical use for surface-tension-mediated launching of droplets has been around for much, much longer than any man-made technology: it’s a mechanism by which many fungi scatter their spores.
In these “basidiomycete” fungi, fluid accumulates at the base of the hydrophobic fungal spores. When the growing droplet reaches the more hydrophilic “sterigma,” it suddenly wets it; this flings the droplet off and the spore goes along for the ride. (It’s somewhat surprising that the droplet doesn’t de-wet the spore, I suppose.) There’s a discussion of this, along with impressive images from high-speed video, in a 2005 paper from Anne Pringle and colleagues , from whom I learned of this remarkable phenomenon. (See the references there for citations of earlier papers, especially work from JCR Turner in the 1990s, on the physics of how the ballistospores work, and decades-old papers on fungal behaviors. There’s also more recent work on this, e.g. here, which looks neat, but which I haven’t read.) The droplets, by the way, are small: a few microns in radius.
The fungi launch their spores at a few meters per second. Can we make sense of this speed? It’s a great candidate for dimensional analysis. (I’ll pause while you think about what the relevant variables that determine the velocity are likely to be…)
We’d expect that the launch speed of a droplet depends on its radius, the density of the liquid, and the interfacial energy, or surface tension. (Surface tension has dimensions of Force / Length.) There’s only one combination of these variables that gives dimensions of velocity; I’ll leave it to the reader to work it out, since dimensional analysis is wonderfully entertaining. (If you’re rusty on dimensional analysis, see here.) You should find that the speed is greater for smaller drops (as you might have expected). If you imagine, as is usually the case, that dimensionless constants are roughly 1, and use “typical” numbers of 1000 kg/m^3 for the density of water, 0.07 N/m for the surface tension of an air-water interface, and 10 microns for the drop radius, you should estimate a speed on the order of 1 meter per second — perfect!
The Eighteenth Elephant 