Soft matter / 04
Round blobs, flat puddles
Small drops are round. Big ones are flat. The switch isn't random: it happens at a size you can work out from two properties of the liquid.
Tug of war
Surface tension wants the least surface possible, and for a given volume that's a sphere. Gravity wants the centre of mass as low as possible, and that means spreading out flat.
Who wins depends on size, because the two grow at different rates. Surface energy grows with area: length squared. Gravitational energy grows with volume times height: length to the fourth. Make a drop bigger and gravity gains faster. So there has to be a size where they're equal.
The magic size: capillary length
Put the two against each other and you get a length made from surface tension γ, density ρ and gravity g:
ℓc = √( γ / (ρ g) )For room-temperature water, γ is about 0.072 newtons per metre, ρ is 1,000 kg per cubic metre and g is about 9.81. That gives roughly 2.5 to 3 millimetres.
Remember that number: you've been seeing it all your life. Dew drops, a few millimetres across, are properly round. A spilt glass of water is a flat film. Mercury has a much higher surface tension, so its capillary length is bigger, and it stays in round beads at sizes where water would spread out.
Nothing about the water changes between dew drop and puddle. Only which of the two energies is bigger at that size.
Why a tap stream turns into drops
The same love of less surface explains something you can watch at any tap. A smooth column of falling water doesn't stay a column. A wobble appears along it, grows, and pinches the stream into separate drops.
This is the Plateau-Rayleigh instability. A cylinder of liquid has more surface than the same liquid split into spheres, so surface tension actively breaks it up. The wobble grows fastest at one wavelength, set by the jet's width, which is why the drops come out fairly even, not random.
It's also why a thin stream breaks up sooner than a thick one, and why the neck between two drops thins to nothing instead of stopping halfway.
Jelly doesn't play by these rules
Jelly isn't a liquid, so none of this works the same way.
A liquid drop fights gravity only with its surface. A gel fights with its whole body, because its net has a shear modulus. At anything but tiny sizes, that's massively stronger. That's why a jelly out of its mould keeps its corners, while the same amount of water wouldn't keep any shape at all.
Compare surface tension with elasticity and you get another length, sometimes called the elastocapillary length: roughly surface tension divided by shear modulus. For a centimetre-sized jelly with a shear modulus in kilopascals, it comes out in micrometres. So surface tension does nothing to a dessert jelly's shape. Elasticity does it all.
That's why our jelly has no surface tension at all. At its size it would change nothing you could see. What matters is the net resisting shear and refusing to change volume, and those are the two rules it follows.
Where solid meets liquid
Super-soft gels at super-small sizes sit in between, and scientists are still working them out. Surface tension can round off the sharp corners of a very soft gel, and the softer and smaller it is, the more liquid-like its shape. Turns out the line between a soft solid and a liquid depends on the size you're looking at.