Rayleigh–Plesset equation
Ordinary differential equation / From Wikipedia, the free encyclopedia
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In fluid mechanics, the Rayleigh–Plesset equation or Besant–Rayleigh–Plesset equation is a nonlinear ordinary differential equation which governs the dynamics of a spherical bubble in an infinite body of incompressible fluid.[1][2][3][4] Its general form is usually written as
where
- 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-liquid interface
- , in which, is the pressure within the bubble, assumed to be uniform and is the external pressure infinitely far from 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.[4]