Cavitation Cloud Field: Standing-Wave Bubble Collapse (2D)

Acoustic Driving

Pressure amplitude P_A 1.20 atm

Drive frequency f 26.5 kHz

Mean bubble radius R₀ 4.5 µm

Polytropic index γ 1.40

Live Readouts

Mean R/R₀

1.00

Antinodes across gap

Hottest hot-spot

300 K

Collapse rate

0.0 /s

Field radical dose

0.00

Active bubbles

–

How this 2D field model works

The 3D version of this simulator follows a single spherical bubble in isolation. This 2D companion instead models a cavitation cloud: a scattered field of ~40 bubbles sitting between an ultrasonic transducer (bottom) and a reflector (top) a fixed 5 cm apart, each independently integrating its own Rayleigh–Plesset equation —

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

p_g(R) = ( p₀ + 2σ/R₀ ) (R₀/R)^(3γ)
p∞(y,t) = p₀ − P_A·|sin(k·y)|·sin(2π f t),   k = 2π f / c

The key difference from the 3D single-bubble model: the drive amplitude here is not uniform — it is scaled by the local antinode factor |sin(k·y)| of a real standing wave, where k = 2πf/c (c = 1481 m/s, speed of sound in water) and y is each bubble's height in the 5 cm gap. Raising the drive frequency shortens the wavelength and packs more antinodes into the same physical gap — exactly why real sonochemical reactors show layered "cavitation cloud" structures rather than uniform bubbling. Bubbles sitting near a pressure node barely oscillate; bubbles at an antinode collapse violently.

Each bubble also gets its own ambient radius, drawn ±40% around R₀, making the cloud polydisperse like a real cavitation field — some sizes couple to the drive far better than others. On a violent collapse (R falling well below R₀ then rebounding), each bubble's own compression ratio gives a local hot-spot estimate:

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

and above ~1500 K it fires a small radical burst, exactly as in the 3D model's single-bubble readout — but here summed and rate-tracked across the whole field, which is the quantity that actually matters for bulk sonochemical yield.

P_A — global acoustic pressure amplitude at the antinodes; local drive amplitude for a given bubble is this times its position's standing-wave factor.
f — drive frequency; also sets the standing-wave spacing (wavelength = c/f), changing how many antinode bands fit across the fixed 5 cm gap.
R₀ — mean ambient bubble radius of the size distribution (each bubble varies ±40% around it).
γ — polytropic index of the enclosed gas; higher γ gives hotter, sharper collapses.

Bubble (size ∝ R) Hot-spot / radical burst