Nanobubbles at Water-Solid Interfaces: Calculation of the Contact Angle Based on a Simple Model

Nanobubbles have been found to form at the interface of water and solid surfaces. We examine the conditions for such bubbles to form and estimate the pressure inside the bubble based on thermodynamic considerations. Using a simple model we calculate the contact angle for a wide range of temperatures and hypothetical substrates possessing a continuous range of strengths. We show that as the temperature increases the shape of a bubble changes continuously from a spherical cap with low curvature to a complete sphere. An equivalent effect results from either increasing the strength of the solid or decreasing the surface tension. A model of a substrate formed by layers of materials is proposed to obtain a nanobubble with a particular contact angle.