On the volume oscillations of a tethered bubble

The behaviour of a gas bubble tethered to a rigid plane boundary in an oscillatory pressure field is investigated by means of image theory. The inversion method is utilised to obtain an exact solution. This method is based on invariance of the Laplace equation to conformal transformations. The modified Rayleigh equation for the volume pulsation has been derived. It follows directly from this equation that the fundamental — the so-called ‘Minnaert’ frequency — for the tethered bubble depends on the contact angle and this dependence is not monotonic.