Rayleigh–Plesset equation

The Rayleigh–Plesset equation describes the radial motion of a spherical bubble in a liquid. It relates bubble acceleration to pressure differences, liquid inertia, viscosity, and surface tension.

Bubble dynamics: The study of how gas or vapor bubbles form, move, grow, and collapse in fluids. The equation is a central model for the radial motion of a bubble.
Spherical symmetry: A condition in which a system is unchanged by rotations about its center. It reduces the bubble and surrounding flow to a single radius-dependent motion.
Lord Rayleigh: John William Strutt, the third Baron Rayleigh, was a British physicist known for work in acoustics, optics, and fluid mechanics. His 1917 analysis of cavity collapse in an incompressible liquid underlies the equation's inertial foundation.
Ultrasonic cleaning: A cleaning method that uses high-frequency sound to produce cavitation bubbles in a liquid. Bubble oscillations predicted by the equation help explain cleaning forces and operating conditions.
Gilmore equation: A compressible-liquid bubble model using the liquid enthalpy and a pressure-dependent sound speed. It handles strong collapses more fully than the classical equation's incompressible assumption.
Young–Laplace equation: An equation relating pressure difference across a curved interface to surface tension and curvature. It supplies the surface-tension pressure term opposing changes in bubble radius.
Incompressible flow: Fluid flow in which density remains constant along the motion. The classical equation assumes liquid incompressibility, limiting its validity during rapid collapse.
Milton Plesset: Milton S. Plesset was an American physicist who studied bubble dynamics and cavitation. His 1949 formulation incorporated effects including surface tension and liquid viscosity.
Shock wave lithotripsy: A medical treatment that uses focused acoustic pulses to fragment kidney or urinary stones. The equation models cavitation bubbles generated by intense treatment pulses near stones.
Shape instability: The growth of deviations from a system's initially symmetric shape under perturbations. A single-radius equation cannot describe the nonspherical distortions that arise during unstable motion.

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