Nanobubble capillary force between parallel plates

Molecular dynamics (MD) simulations are carried out to study the capillary force induced by a nanobubble (NB) capillary bridge between two parallel plates. While detection of the geometry of the capillary bridge in NB capillary force (NBCF) measuring experiments is currently very challenging, MD simulations can readily measure both the geometry of the NB capillary bridge and the resulting NBCF so that the correlation between the bridge geometry and the NBCF predicted by the capillary force model can be explicitly examined. Our modeling results show the simple capillary force model gives good prediction of the NBCF for both concave and convex NB capillary bridges. Furthermore, using the combination of the capillary force model and the ideal gas equation, we develop a theoretical model to predict the variation of the bridge geometry and the NBCF with the separation between two parallel solid surfaces. The continuum prediction of the NBCF shows the NBCF induced by a concave bridge remains attractive in the plate retraction process until the pinch-off of the bridge occurs, while the NBCF induced by a convex bridge exhibits a transition from repulsive to attractive in the plate retraction process. For convex bridges, there is an equilibrium separation between two solid surfaces where the NBCF is zero. The equilibrium separation depends on the contact angle and size of the capillary bridge. The continuum theoretical predictions are corroborated by the discrete MD simulation results and are consistent with the existing experimental data on NBCFs between two solid surfaces.