This formulation allows the study of the motions and the effects of heat conduction, shear viscosity, compressibility, and surface tension on small cavitation bubbles in liquids that are set into motion by an acoustic pressure field. The effect of vapor pressure on the cavitation bubble can also be determined using the interfacial temperature. The formulation is specifically designed to describe the motion of a bubble that expands to a maximum radius and then violently collapses or contracts.  This set of equations was solved using an improved Euler method.
where  is the radius of the bubble, the dots indicate first and second time derivatives,  is the density of the liquid,  is the speed of sound through the liquid,  is the pressure on the liquid side of the bubble's interface,  is time, and  is the driving pressure.