## Saturday, December 01, 2018

### Late Thanksgiving physics: Split peas and sandcastles

Last week, when I was doing some cooking for the US Thanksgiving holiday, I was making a really good vegetarian side dish (seriously, try it), and I saw something that I thought was pretty remarkable, and it turns out that a Nature paper had been written about it.

The recipe involves green split peas, and the first step is to rinse these little dried lozenge-shaped particles (maybe 4 mm in diameter, maybe 2 mm thick) in water to remove any excess dust or starch.  So, I put the dried peas in a wire mesh strainer, rinsed them with running water, and dumped them into a saucepan.  Unsurprisingly, the wet split peas remained stuck together in a hemispherical shape that exactly mimicked the contours of the strainer.  This is a phenomenon familiar to anyone who has ever built a sandcastle - wet particulates adhere together.

The physics behind this adhesion is surface tension.  Because water molecules have an attractive interaction with each other, in the absence of any other interactions, liquid water will settle into a shape that minimizes the area of the water-vapor interface.  That's why water forms spherical blobs in microgravity.  It costs about 72 mJ/m2 to create some area of water-air interface.  It turns out that it is comparatively energetically favored to form a water-split pea interface, because of attractive interactions between the polar water molecules and the mostly cellulose split pea surface.

For a sense of scale, creating water-air interface with the area of one split pea (surface area roughly 2.5e-5 m2) would take about 2 microjoules of energy.  The mass of the split pea half I'm considering, assuming a density similar to water, is around 25 mg = 2.5e-5 kg.  So, lifting such a split pea by about it's own height requires an energy of $mgh \sim$ 2.5e-5*9.807*2e-4 = 0.5 microjoules.  The fact that this is comparable to (but smaller than) the surface energy of the water-air interface of a wet split pea tells you that you should not be surprised that water coatings can hold wet split peas up against the force of gravity.

What I then saw, which was surprising to me, was that even as I started adding the 3.5 cups of water mentioned in the recipe,  the hemispherical split pea "sandcastle" stayed together, even when I prodded it with a cooking spoon.  This surprised me.  A few minutes of internet search confirmed that this effect is surprising enough to merit its own Nature Materials paper, with its own News and Views article. The transition from cohering wet grains to a flowing slurry turns out to happen at really high water fractions.  Neat physics, and the richness of a system as simple as grains/beads, water, and air is impressive.