Force Balance in a Developing Sessile Bubble

With the consideration of extended base of contact, the attachment force for a bubble, f, can be given by 

The force which resists against the expansion of bubble attachment base or the force for bubble closing, f 2, can be given by 

The expansion force of a bubble is the component of the internal pressure of air in the bubble acting at this point, and therefore at the edge of the bubble attaching 

When the value of 0 exceeds 90 degrees, f 2 and exchange their roles and /2 becomes the bubble expansion force and the resisting force. The internal force of pressure, which acts perpendicular to the surface of the bubble, is balanced by the hydrostatic pressure of water acting on the opposite side of the bubble surface for each point, except at the three-phase contact point where 0 is observed. 

At 0 = 90 degrees, the internal force due to gas pressure is balanced against the hydrostatic pressure of water because the interfacial tension has no component in the direction of the solid surface. In this case, the interfacial tension is directly balanced against the buoyancy of a bubble. Such a direct balance between the interfacial tension and the buoyancy can be justified for only this special case of 0 = 90 degrees. 

---