R(t) — bubble radius. Ṙ — signed wall velocity: positive for growth, negative for collapse. R̈ — wall acceleration.
R(t) 表示气泡半径。Ṙ 表示带符号的壁面速度：生长时为正，塌缩时为负。R̈ 表示壁面加速度。
pB — total pressure just inside the bubble, including gas and vapor contributions when present. p∞ — pressure in the liquid far from the bubble.
σ — surface tension of a clean liquid–gas interface. The static curvature pressure for one spherical interface is 2σ/R.
ρ — liquid density. It sets how much liquid inertia responds to a pressure drive.
D = pB − p∞ − 2σ/R — outward pressure surplus for the clean spherical model. For a wall initially at rest, positive D means outward acceleration.
Inception — formation or activation of a cavity. It is a separate question from the motion of a bubble that already exists.
Δp = pv(T) − p∞ — vapor-pressure advantage in the idealized nucleation example; positive Δp favors sufficiently large vapor embryos.
r* — critical embryo radius in that model, 2σ/Δp. An embryo below it tends to shrink; a larger one can grow while favorable conditions persist.
Pressure symbols are absolute unless labeled as a difference or gauge pressure. A nanodroplet shell or nearby wall requires a more specific model.