What is cavitation?

Bubbles, collapse, and the sound of imploding water.

The sound book closed at the edge of its own linear theory. Push the amplitude of an acoustic wave high enough — say, the focus of a medical ultrasound transducer, or the surface of a fast-spinning ship propeller — and the small-perturbation expansion stops being small. Pressure swings into the negative, and a liquid that has been politely transmitting waves suddenly tears: a bubble appears where there was no bubble before. The bubble grows for a few microseconds, then collapses inward at supersonic wall velocities and emits a shock, a flash of light, and an audible click.

This is cavitation. The phenomenon is the regime in which a liquid’s continuum behaviour breaks down and a new set of objects — vapour bubbles, gas bubbles, bubble clouds — takes over as the dominant carriers of the dynamics. The mathematics is the same fluid mechanics the sound book built up, applied at a scale and amplitude where linearisation fails.

Ten chapters develop the field. The book is independent of the sound book — it can be read on its own — but its natural entry point is Sound 10.6 — Bridge to Cavitation, which states the questions this volume answers.

Chapters

1. Chapter 1The liquid stateWhat a liquid is, and why it can in principle hold tension
   1. 1.1What a liquid is
   2. 1.2Tensile strength in principle
   3. 1.3Why the measured strength is pathetic
2. Chapter 2NucleationHow the liquid finds a hole to break through
   1. 2.1Homogeneous nucleation theory
   2. 2.2Heterogeneous nucleation and the Harvey crevice model
   3. 2.3Nucleation site populations and dissolved gas
   4. 2.4Nucleation in flowing liquids and cavitation inception
3. Chapter 3The Rayleigh–Plesset equationA momentum balance on a spherical bubble
   1. 3.1Derivation from momentum balance
   2. 3.2Bubble contents: gas, vapour, polytropic exponent
   3. 3.3Static equilibrium and the Blake threshold
   4. 3.4Solving the Rayleigh–Plesset equation

Working notes

• Anchor reference. Christopher Brennen, Cavitation and Bubble Dynamics (Oxford University Press, 1995). The planned spine maps to Brennen’s eight chapters with a few modifications; for now the book ends at Chapter 3 (Rayleigh–Plesset) and the remaining chapters — growth, collapse, noise & luminescence, oscillating bubbles, translation, bubbly flows, cavitating flows — are deferred.
• Voice. Same as the other books — graduate-notebook texture, math taught on the page, derivations not hidden when insight requires them.
• Status. Drafting. Chapters 1–3 (the liquid state, nucleation, the Rayleigh–Plesset equation) are in place. The book pauses here for now.