Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis

We consider a sessile hemispherical bubble sitting on the transversally oscillating bottom of a deep liquid layer and focus on the interplay of the compressibility of the bubble and the contact angle hysteresis. In the presence of contact angle hysteresis, the compressible bubble exhibits two kinds of terminal oscillations: either with the stick-slip motion of the contact line or with the completely immobile contact line. For the stick-slip oscillations, we detect a double resonance, when the external frequency is close to eigenfrequencies of both the breathing mode and shape oscillations. For the regimes evolving to terminal oscillations with the fixed contact line, we find an unusual transient resembling modulated oscillations.