A New Damping Mechanism in Non-linear Bubble Dynamics

Abstract

Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived including new terms resulted from consideration of the viscosity and compressibility not only at the bubble interface, but also in the bulk of liquid. The new equations are two non-linear coupled equations, which can not be merged into one equation unlike all previously derived equations. Numerical calculations have been performed considering effects of heat and mass transfer at the bubble interface. The results indicate that the new terms exhibit an important damping role at the collapse, so that their consideration dramatically weakens the bubble rebounds after the collapse. Dependence of this new damping mechanism to amplitude and frequency of the deriving pressure has been investigated.