RayleighPlessettype

Rayleigh-Plesset type refers to a class of models used to describe the radial dynamics of a gas bubble in a liquid under time-varying pressure. These models are based on the balance of inertial, viscous, surface-tension, and pressure forces acting on a spherical bubble and are widely used in cavitation and acoustics research.

The original Rayleigh–Plesset equation governs the radius R(t) of a spherical bubble in an infinite liquid with density ρ and dynamic viscosity μ. A common incompressible form is

ρ (R d^2R/dt^2 + (3/2)(dR/dt)^2) = P_g(R) − P∞(t) − 4 μ (dR/dt)/R − 2 σ/R,

where P∞(t) is the far-field pressure, σ is surface tension, and P_g(R) is the gas pressure inside the bubble, often modeled by a polytropic relation P_g(R) = P_g0 (R0/R)^{3γ} with equilibrium radius R0 and polytropic exponent γ.

Rayleigh-Plesset type models are extended to include compressibility, heat and mass transfer, and external driving pressures. Notable variants include the Keller–Miksis equation and the Gilmore equation, which incorporate liquid compressibility and acoustic driving; other forms like the Herring equation address related regimes. These models are used to study cavitation thresholds, bubble collapse dynamics, sonoluminescence, and bubble behavior under ultrasound.

Limitations include the assumption of a single isolated, perfectly spherical bubble, neglect of non-spherical modes, inter-bubble interactions, phase-change kinetics, and detailed thermal diffusion. Consequently, while providing valuable insight, these models are approximations best applied under controlled conditions or as components within more comprehensive multiphase simulations.