Dynamics of a tethered bubble

Small gas bubbles adhering to solids occur in a range of manufacturing processes, including printing, casting, coating and electroplating. The behavior of a gas bubbles tethered to a rigid plane boundary in an oscillatory pressure field is investigated by use conformal symmetry of the problem. The dynamics of the tethered bubble differ from those of the free bubble. The inertial (or added) mass depends on the contact angle and this variation is not monotonic. As a result, the natural frequency depends on the contact angle. Viscous damping of the tethered bubble is increased by more than two orders of magnitude, firstly, owing to the greater dissipation near rigid wall in comparison with free air/water bubble interface and secondly, because of a contact line dissipation effect.