Shape of a sliding capillary contact

We consider a classical problem of a capillary neck between a parabolic body and a plane with a small amount of liquid in between. In the state of thermodynamic equilibrium, the contact area between the bodies and the liquid layer has a circular shape. However, if the bodies are forced to slowly move in the tangential direction, the shape will change due to the hysteresis of the contact angle. We discuss the form of the contact area under two limiting assumptions about the friction law in the boundary line.