title: Effect of Disjoining Pressure on Surface Nanobubbles.
abstract: In gas-oversaturated solutions, stable surface nanobubbles can exist thanks to a balance between the Laplace pressure and the gas overpressure, provided the contact line of the bubble is pinned. In this article, we analyze how the disjoining pressure originating from the van der Waals interactions of the liquid and the gas with the surface affects the properties of the surface nanobubbles. From a functional minimization of the Gibbs free energy in the sharp-interface approximation, we find the bubble shape that takes into account the attracting van der Waals potential and gas compressibility effects. Although the bubble shape slightly deviates from the classical one (defined by the Young contact angle), it preserves a nearly spherical-cap shape. We also find that the disjoining pressure restricts the aspect ratio (size/height) of the bubble and derive the maximal possible aspect ratio, which is expressed via the Young angle.
authors.affiliation: Physics of Fluids Group, Department of Science and Technology and MESA+ Institute for Nanotechnology, and JM Burgers Center for Fluid Dynamics, University of Twente , P.O. Box 217, 7500 AE Enschede, The Netherlands.|Institute of Physics and Technology, Yaroslavl Branch, Russian Academy of Sciences , 150007 Yaroslavl, Russia.
authors.forename: Vitaly B
authors.initials: VB
authors.lastname: Svetovoy
authors.affiliation: Physics of Fluids Group, Department of Science and Technology and MESA+ Institute for Nanotechnology, and JM Burgers Center for Fluid Dynamics, University of Twente , P.O. Box 217, 7500 AE Enschede, The Netherlands.
authors.forename: Ivan
authors.initials: I
authors.lastname: Dević
authors.affiliation: Physics of Fluids Group, Department of Science and Technology and MESA+ Institute for Nanotechnology, and JM Burgers Center for Fluid Dynamics, University of Twente , P.O. Box 217, 7500 AE Enschede, The Netherlands.|Department of Applied Physics, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
authors.forename: Jacco H
authors.initials: JH
authors.lastname: Snoeijer
authors.affiliation: Physics of Fluids Group, Department of Science and Technology and MESA+ Institute for Nanotechnology, and JM Burgers Center for Fluid Dynamics, University of Twente , P.O. Box 217, 7500 AE Enschede, The Netherlands.|Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.
authors.forename: Detlef
authors.initials: D
authors.lastname: Lohse