text: The Rayleigh–Plesset equation can be derived entirely from first principles using the bubble radius as the dynamic parameter.  Consider a spherical bubble with time-dependent radius , where  is time.  Assume that the bubble contains a homogeneously distributed vapor/gas with a uniform temperature  and pressure . Outside the bubble is an infinite domain of liquid with constant density  and dynamic viscosity .  Let the temperature and pressure far from the bubble be  and .  The temperature  is assumed to be constant.  At a radial distance  from the center of the bubble, the varying liquid properties are pressure , temperature , and radially outward velocity .  Note that these liquid properties are only defined outside the bubble, for .