RayleighPlesset equation 1 Rayleigh–Plesset equation The Rayleigh–Plesset equation is often applied to the study of cavitation bubbles, shown here forming behind a propeller. In fluid mechanics, the Rayleigh–Plesset equation is an ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of liquid. [][] Its general form is usually written as where is the pressure within the bubble, assumed to be uniform is the external pressure infinitely far from the bubble is the density of the surrounding liquid, assumed to be constant is the radius of the bubble is the kinematic viscosity of the surrounding liquid, assumed to be constant is the surface tension of the bubble Provided that is known and is given, the Rayleigh–Plesset equation can be used to solve for the time-varying bubble radius . The Rayleigh–Plesset equation is derived from the Navier–Stokes equations under the assumption of spherical symmetry. [] Neglecting surface tension and viscosity, the equation was first derived by John Strutt, 3rd Baron Rayleigh in 1917. The equation was first applied to traveling cavitation bubbles by Milton S. Plesset in 1949. [] Derivation 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 temperate 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 . Mass conservation By conservation of mass, the inverse-square law requires that the radially outward velocity must be inversely proportional to the square of the distance from the origin (the center of the bubble). [] Therefore, letting be some function of time, In the case of zero mass transport across the bubble surface, the velocity at the interface must be which gives that