Sonochemistry Hot-Spot: Cavitation Bubble Collapse

Acoustic Driving

Pressure amplitude P_A 1.20 atm

Drive frequency f 26.5 kHz

Ambient bubble radius R₀ 4.5 µm

Polytropic index γ 1.40

Live Readouts

Radius R/R₀

1.00

Wall velocity

0 m/s

Hot-spot T_peak

300 K

Radical dose

0.00

How it works

The bubble wall radius R(t) obeys the Rayleigh–Plesset equation, a nonlinear ODE for a spherical gas/vapor cavity oscillating in a liquid under a sinusoidal acoustic drive p_∞(t):

ρ [ R R̈ + (3/2) Ṙ² ] = p_g(R) − p∞(t) − 2σ/R − 4μ Ṙ/R

p_g(R) = ( p₀ + 2σ/R₀ ) (R₀/R)^(3γ)     — polytropic gas core
p∞(t)  = p₀ − P_A sin(2π f t)            — driving acoustic field

ρ is liquid density, σ surface tension, μ viscosity, p₀ ambient pressure, γ the polytropic index of the trapped gas. The equation is integrated numerically every frame with small substeps (the collapse is extremely stiff — R can shrink by 10× in nanoseconds).

During the rarefaction half-cycle the bubble grows several times its resting radius R₀; during compression it collapses almost inertially. Because the gas inside is compressed far faster than heat can escape, the collapse is close to adiabatic, giving a hot-spot temperature:

T_peak ≈ T₀ · (R_max / R_min)^(3(γ−1))

Real collapses reach on the order of several thousand kelvin and hundreds of atmospheres for a few nanoseconds — the "hot spot theory" of sonochemistry (Suslick et al.). Above roughly 2000 K, water vapor trapped in the bubble pyrolyzes into reactive radicals — mainly •OH and •H, which recombine outside the bubble into H₂O₂ and drive oxidation chemistry in the surrounding liquid. Each violent collapse in this simulation releases a burst of radical markers whose brightness scales with that event's peak temperature, and the readout accumulates a running "radical dose" that decays between collapses, mirroring the intermittent, pulsed nature of real sonochemical radical production.

P_A — acoustic pressure amplitude; higher amplitude drives larger expansion and a more violent, hotter collapse.
f — drive frequency; sets how often the bubble is forced through an oscillation cycle.
R₀ — ambient (resting) bubble radius, set by the dissolved-gas nucleus the bubble grew from.
γ — polytropic index of the enclosed gas (1.0 = isothermal, up to ~1.67 for a monatomic adiabatic gas); higher γ means a hotter, sharper collapse.

Bubble wall •OH / •H radicals

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