Modeling adhesive forces caused by nanobubble capillary bridging

Abstract

Adhesive forces between particles immersed in a poorly wetting liquid can be much higher than the predicted forces by the DLVO-theory. This could be caused by so called nanobubbles at the solid surfaces. If these bubbles are between two approaching solid surfaces the formation of gaseous bridges between them becomes possible. These capillary bridges lead to capillary forces as known from liquid bridges. In contrast to the calculation of adhesive forces cause by liquid bridges the compressibility of the gaseous bridge as a function of the pressure difference must be taken into account. The proposed model uses the minimization of the free surface energies to calculate the adhesive forces cause by gaseous bridges. By adding the ideal gas law to the set of equations the compressibility of the bridge is respected. Beside adhesive forces also the pressure inside the bridges as well as contact angles and dipping angles are calculated. The results show a direct correlation between the particles radius, the surface energy of the liquid gas interface as well as the macroscopic contact angle and the adhesive force. However the amount of molecules has no influence on the adhesive forces. Furthermore the well-known stepping behavior of the measured force distance curves shown in literature can be explained by the model.