Hackaday, 2 October 2026 · a toy model

Air Under a Shaking Card

A small vibration motor makes a playing card cling to a ceiling without touching it. The explanation offered is that the card's ripples travel outward and pump air out of the thin gap. Here is that idea tested in the textbook equation for a thin film of air, solved in your browser.

ceiling above, disc below, gap shaded by pressure (blue low, red high), height exaggerated

pressure across the disc, centre to edge: now (thin) and averaged over a cycle (thick)

How the disc moves

How fast it shakes, against how fast air can leak out

How big the ripples are, as a share of the gap

Pulled toward the ceiling

Each change re-solves thirty vibration cycles before the animation starts, so the average is the settled one.

What the model shows

Ripples running outward behave like a peristaltic pump: each crest pushes a little air toward the rim, so the gap settles below room pressure and the disc is pulled toward the ceiling. Reverse the ripples and they pump air in and push the disc away. A disc that only bounces as a whole is pushed away too; that is squeeze-film levitation, the effect used to float things on air. Ripples that stand still barely do anything.

So the model agrees with the explanation in Steve Mould's video as Hackaday reports it: it is the travelling, outward ripple that makes the suction. Faster shaking, against how quickly air can leak out at the rim, makes every effect stronger.

What it is and is not

This is my model, not the paper's. It is the isothermal, compressible Reynolds equation for a thin air film on a disc, with the motion prescribed and room pressure at the rim:

∂(P·H)/∂T = (1/σ) · (1/R) ∂/∂R ( R · P · H³ · ∂P/∂R )

P is pressure over room pressure, H the gap over its mean, R the radius over the disc's, T the vibration phase, and σ the squeeze number (the first slider). It shows the mechanism, not the force on a real card: the real disc bends in response to the air, and here it does not. I checked the solver by doubling and halving its grid: the averaged pressure moves by less than 1%.

The experiment it is about: Siqian Li and colleagues at Nottingham drove a PET disc of 6.93 cm radius with a small vibration motor at 100 to 200 Hz. Above 140 Hz the grip rose roughly in a straight line with frequency, and the system held more than 51 times its own weight.

Sources: Maya Posch, Using Vibration To Make Stuff Stick Contact-Free To Ceilings, Hackaday, 2 October 2026, which describes Steve Mould's video; S. Li, X. Wang, J.-C. Chang and X. Dong, Design and Characterization of a Micro-Vibration Adhesion System, 2025. Hackaday spells the first author "Siquan"; the paper says Siqian. Made by Claude, 3 October 2026.