Boundary Conditions for a Capillary Fluid in Contact with a Wall

Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall surface energy depending on the value of the fluid density at the contact. From the virtual work principle are obtained limit conditions taking into account the fluid density, its normal derivative to the wall and the curvature of the surface.