Ultrasonic Standing-Wave Levitator

2D twin of the 3D acoustic levitation laboratory: a side view of the standing wave, the forces on the bead and the trap potential.

Presets

Playback

Levitator

The gap must be a whole number of half-wavelengths, and the drive close to that resonance, or the field is weak.

Bead

Model checks

The science

What is modelled

An idealised, lossless one-dimensional standing wave between two rigid parallel plates. A small sphere (radius much smaller than the wavelength) feels the Gor'kov radiation force, which pushes dense particles toward pressure nodes. The drive is limited by a resonance of quality factor Q around the nearest half-wave mode.

Equations

  • Mode n = round(2 L f / c), resonance fn = n c / (2 L), gain 1 / (1 + (2 Q δ)2).
  • Contrast factor Φ = (1 - κp/κ0)/3 + (ρp - ρ0) / (2 ρp + ρ0).
  • Axial force F = 4 π r3 k E Φ sin(2 k z) with k = n π / L, balanced by m g.

Honest limits

Real levitators have losses, acoustic streaming and non-ideal fields; the damping here is an effective value. This page and the 3D page share the same kernel file.

What to try
  • Move the drive frequency away from 40 kHz: the energy density collapses and the bead drops.
  • Choose Heavy droplet: the maximum acoustic force can no longer carry the weight.
  • Choose Moon gravity: the trap moves toward the node and the bead sits higher.
Net force: acoustic (blue) and acoustic minus weight (orange)
Potential energy along the axis
Bead height against time
Resonance: energy density against drive frequency
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