🔊 Acoustic Levitation: Standing Waves & Radiation Force

No — simple radiation pressure alone can't produce a stable trap. What traps the bead is the acoustic radiation force, a small nonlinear (second-order) effect described by the Gor'kov potential, which depends on the spatial gradient of both the time-averaged pressure and velocity fields, not on the instantaneous push of the wave.

For a particle denser and less compressible than the surrounding air — true for polystyrene beads and water droplets — the Gor'kov potential has its minimum energy at the pressure node (which is also the velocity antinode), so that location is where the bead is stable. Very light, highly compressible objects like bubbles in a liquid can behave the opposite way.

Two coherent waves travelling in opposite directions interfere to form a standing wave whose pressure amplitude is zero every half wavelength (λ/2) — that spacing falls directly out of the interference condition and doesn't depend on transducer separation, only on frequency.

Higher frequency means shorter wavelength, so node planes pack closer together and more of them fit in the same transducer gap — more node planes means more independent stable trapping sites between the arrays.

The Gor'kov radiation force scales with the particle's volume, i.e. with the cube of its radius, while gravity (its weight) also scales with volume — but the acoustic term additionally carries an extra factor from the size-to-wavelength ratio, so trap stiffness falls off fast for beads that aren't small compared to the wavelength.

Acoustic levitation enables containerless processing of materials that would be contaminated by touching a container, contactless manipulation of cells and droplets in biomedical research, and — via open-source rigs like TinyLev — hobbyist experiments floating small water drops, foam beads and insects.

Real transducers oscillate 20,000-60,000 times per second — far too fast for any screen to render frame by frame. The pulsing here is deliberately slowed down purely to make the standing-wave shape visible; the actual trapping force depends only on the time-averaged field, which doesn't care how fast we animate it.

Real levitators (including TinyLev) use curved or phased arrays that focus the beam and create a true 3-D potential well. This simulation uses flat opposing arrays, so lateral confinement is approximated with a simplified restoring term rather than a fully derived 3-D Gor'kov field — noted here for transparency.