Single Cavitation Bubble Collapse: Phenomena, Theoretical Models, and Thermodynamic Effects

Nomenclature

The following nomenclature defines the symbols and abbreviations used in this article. Unless otherwise stated, quantities are expressed in SI units.

Symbol	Definition	SI unit or status
c	Small signal sound speed in the liquid	m s⁻¹
C	Local sound speed at the bubble wall in the Gilmore model	m s⁻¹
$E_0$	Initial bubble potential energy	J
$E_{jet}$	Energy in the liquid jet and directed flow	J
$E_{rebound}$	Rebound bubble energy	J
$E_{shock}$	Radiated shock wave energy	J
$E_{thermal}$	Energy transferred by heat and phase change	J
$E_{visc}$	Viscous and vortical energy loss	J
h	Distance from the bubble center to a nearby wall	m
H	Liquid enthalpy difference	m² s⁻²
j	Interfacial vapor mass flux, positive into the bubble	kg m⁻² s⁻¹
Ja	Jakob number	dimensionless
$L_v$	Latent heat of vaporization	J kg⁻¹
Ma	Mach number	dimensionless
$p_B$	Total pressure inside the bubble	Pa
$p_g$	Noncondensable gas partial pressure	Pa
$p_{sat}$	Saturation vapor pressure	Pa
$p_{\infty }$	Far field liquid pressure	Pa
Pe	Thermal Peclet number	dimensionless
R	Equivalent bubble radius	m
$R_0$	Reference or equilibrium radius	m
$R_{\max }$	Maximum bubble radius	m
$R_{\min }$	Minimum bubble radius	m
r	Radial coordinate from the bubble center	m
$t_R$	Rayleigh collapse time	s
$T_i$	Interfacial temperature	K
$T_{\infty }$	Ambient liquid temperature	K
$U_j$	Microjet velocity	m s⁻¹
$U_R$	Rayleigh velocity scale	m s⁻¹
$V_b$	Bubble volume	m³

Greek Letters

Symbol	Letter name	Meaning in this chapter
${\alpha }_l$	Alpha	Liquid thermal diffusivity
γ	Gamma	Surface tension
${\gamma }_s$	Gamma	Bubble standoff parameter relative to a wall
κ	Kappa	Polytropic exponent of the bubble gas
μ	Mu	Dynamic viscosity
ρ	Rho	Liquid density
ζ	Zeta	Collapse anisotropy parameter
φ	Phi	Velocity potential in potential flow models
τ	Tau	Viscous stress tensor in multiphase flow equations
Δ	Delta	Collapse driving pressure difference