Soft matter / 03
Why jelly wobbles (and steel doesn't)
Steel rings. Jelly wobbles. Both are vibrating. Steel just does it far too fast for you to see.
Squash it or slide it
You can squeeze something, which changes its volume. Or you can shear it: slide one layer past another without changing the volume at all. Materials fight these two very differently, and gels are about as extreme as it gets.
A gel is mostly water, and water barely compresses. Squeezing jelly means forcing water through pores so fine it won't go. So its resistance to squashing, the bulk modulus, is basically water's: a couple of gigapascals, like lots of hard materials.
Shearing is a totally different story. Sliding layers only stretches the loose chains between junction zones, and they stretch easily. A soft gel's shear modulus is measured in kilopascals. Published values vary a lot with the recipe, but a few kilopascals is a fair picture for a soft dessert jelly.
Jelly is about a million times easier to shear than to squash. That one ratio is the whole story.
A wave at walking pace
A wobble is a shear wave running through the jelly, bouncing off its sides and coming back. Its speed depends on the shear modulus G and the density ρ:
c = √(G / ρ)Try it for a soft gel. G is a few kilopascals, and ρ is close to water's, 1,000 kg per cubic metre. The square root of a few thousand over a thousand is between one and two. So the wave moves at 1 to 2 metres a second. Walking pace.
Now steel: G is about 80 gigapascals and ρ about 7,800. The square root of that is a bit over 3,000 metres a second.
So the wave crosses a 10 cm jelly in about a tenth of a second, and a 10 cm steel bar in 30 microseconds. The jelly shakes a few times a second, which your eyes easily follow. The steel shakes tens of thousands of times a second. Your eyes can't keep up, so your ears hear it as a ring.
Jelly isn't doing anything weird. It's doing the same thing as steel, slowly enough to watch.
Bigger jelly, slower wobble
How often the main wobble repeats (the fundamental mode) depends on how long the wave takes to cross and come back. So it scales with wave speed divided by size L:
f ∝ c / L = √(G / ρ) / LIn plain words: double the size of a jelly, same recipe, and it wobbles about half as fast. A huge party jelly heaves. A teaspoon of the same mix quivers fast. The stuff didn't change. Only the distance the wave travels did.
Same rule, other way round: a firmer recipe wobbles faster. More gelatin means a bigger shear modulus, a faster wave, and a higher frequency at the same size.
Why it stops wobbling
Something perfectly springy would wobble forever. Jelly doesn't, because it's viscoelastic: part spring, part damper.
Rheologists (scientists who study how stuff flows) split it in two. The storage modulus, G′, is the springy part: energy stored and given back each wobble. The loss modulus, G″, is the gooey part: energy turned into heat and never returned. If G′ beats G″, it acts like a solid. The moment they're equal is used to define when a cooling liquid becomes a gel.
Divide G″ by G′ and you get tan delta: a direct measure of how fast the wobble dies. Small tan delta: it rings on for seconds. Large tan delta: it stops almost at once and feels more like paste.
On our jelly, the damping slider is exactly this knob. Turn it down and it wobbles for ages. Turn it up and it settles almost at once. The softness slider changes the other thing, stiffness, which changes how fast it wobbles, not how long.
It changes shape, never size
Watch closely: the jelly changes shape all the time, but its volume stays put. That's the no-squash rule again, and it's why the wobble is a shear wave, not a pressure wave. Stuff that can't change volume has only one way to move, and every wobble you see is that one move, on repeat.
It's also the hardest thing to fake in a simulation. Let the volume drift and the model slowly sags into a bag, however good it looks. That's why our jelly holds its volume on purpose, every single step.