..., and the increase of the surface energy of the substrate outside the contact zone is calculated based on the elastic foundation model. The total potential energy of the droplet-substrate system is given in terms of four geometrical parameters: the contact radius, the contact angle of the droplet, the deflection...

... by the bubble and applying the separation-of-variables method. The stream function can be expressed in terms of a difference in Legendre functions of the first kind. The effects of impinging velocity and contact angle of the bubble on the flow pattern and pressure distribution are provided. creeping flow...