Rayleigh's Collapse

Plate 8 speaks for itself: “Empty space, crushed in 91 microseconds.”

The Physics

Rayleigh solved the collapse of an empty spherical cavity in an incompressible liquid under a constant pressure difference. The collapse time scales with the radius and the square root of density over pressure.

t_c ≈ 0.915 R₀ √(ρ / Δp)

• t_c: collapse time, s
• R₀: initial cavity radius, m
• ρ: liquid density, kg m⁻³
• Δp: pressure difference driving collapse, Pa

R₀ = 1 mm, Δp = 101 325 Pa in water: t_c ≈ 91 µs (Rayleigh, 1917).

Honest caveat: Real bubbles hold gas and vapour, so they rebound rather than collapse to a point.

Sources

• Lord Rayleigh, Phil. Mag. 34, 94 (1917).

On the poster

Plate 008, “Rayleigh's Collapse”: the pixel-art plate with its slogan “Empty space, crushed in 91 microseconds.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.