Vapor bridges between solid substrates in the presence of the contact line pinning effect: Stability and capillary force.

In this work, we focus on investigating how nanobubbles mediate long-range interaction between neighboring solid substrates in the presence of the contact line pinning effect caused by surface heterogeneities. Using the constrained lattice density functional theory (LDFT), we prove that the nanobubbles, which take the form of vapor bridges here, are stabilized by the pinning effect if the separation between two substrates is less than a critical distance. The critical distance strongly depends on the chemical potential (i.e., the degree of saturation) and could become extremely long at a special chemical potential. Moreover, under the pinning effect, the substrate chemistry only determines the stability of the vapor bridges and the range of the capillary force, but has less influences on the magnitude of the capillary force, indicating that the substrate chemistry or the apparent contact angle for droplets or bubbles on the substrates is no longer a direct parameter to determine the magnitude of capillary force. A qualitative analysis for the two dimensional vapor bridges by considering the feedback mechanism can explain the results from the LDFT calculations.