Nanobubble capillary force between parallel plates

Abstract

The aggregation of fine or ultrafine particles in liquid due to the nanobubble (NB) bridging capillary force is a key process for many industrial applications. The magnitude and direction of the NB capillary force (NBCF) are directly affected by the geometry of the NB gas bridge between two adjoining particles. Although the NBCF can be accurately measured using experimental techniques, it is very challenging to monitor the images of a NB capillary bridge in nanoscale spatial resolution in NBCF measuring experiments. As a result, the capillary force model that predicts the dependence of the NBCF on the geometry of the NB bridge has never been explicitly verified using experimental means. In this work, molecular dynamics (MD) simulations are carried out to study the NBCF between two parallel plates. MD simulations can readily measure both the NB bridge geometry and the resulting NBCF, which allows us to explicitly verify the predictions from the capillary force model. Our modeling results show that the capillary force model gives a good prediction of the NBCF for both concave and convex NB capillary bridges. Furthermore, with the assumption of constant contact angle and number of gas atoms inside the capillary bridge, we develop an improved capillary force model, which predicts the variation of the bridge geometry and the NBCF with the separation between two parallel surfaces. The continuum predictions from the improved capillary force model are corroborated by the MD simulation results and are consistent with the existing experimental data on NBCFs between two solid surfaces.

Nanobubble-Induced Aggregation of Ultrafine Particles: A Molecular Dynamics Study

“…In our previous work, 14 we have successfully used MD simulations to measure both the geometry of the NB gas bridge between two stationary solid surfaces and the resulting NBCF and explicitly verified the relationship between the NBCF and the NB bridge geometry that is predicted by the capillary force theoretical model. 14−16 In this work, we will dive deeper into the dynamic NBIA process by releasing the constraint on the positions of two solid surfaces that are connected by a single NB bridge in MD simulations.…”

“…In our previous work, we have successfully used MD simulations to measure both the geometry of the NB gas bridge between two stationary solid surfaces and the resulting NBCF and explicitly verified the relationship between the NBCF and the NB bridge geometry that is predicted by the capillary force theoretical model. − In this work, we will dive deeper into the dynamic NBIA process by releasing the constraint on the positions of two solid surfaces that are connected by a single NB bridge in MD simulations. Specifically, we will carry out MD simulations to investigate the effects of NB size, surface wettability, surface roughness, and contact line pinning on the aggregation speed, final state of the particle agglomeration, and whether the particle aggregation will occur.…”

“…Therefore, to determine the gas pressure in eq , we calculate the bridge volume over time as a function of bridge geometry. Using the toroidal approximation of the NB gas bridge, the volume V and the liquid–gas interface area A of the gas bridge are given by and where r 1 and r 2 are the principal radii of the NB gas bridge as shown in Figure c. In eqs and , r 1 is always positive, and r 2 is positive for concave gas bridges and negative for convex gas bridges.…”

“…If the solid surfaces are hydrophilic, the NB bridge between them becomes convex. For a convex NB bridge, the NBCF exhibits a transition from attractive to repulsive as the two surfaces approach each other. ,− This indicates that there is an equilibrium separation between two hydrophilic surfaces at which the NBCF equals to zero. At the equilibrium separation, the NB bridge and the distance between two solid surfaces will be stable.…”

“…From the F cap vs h curve, we can readily obtain the equilibrium separation (h f ) that makes F cap = 0. The theoretical model described in this section is the improved capillary force model developed in our previous work 14 for the study of NBCF between two stationary plates. The improved capillary force model shows that for an NB bridge between two parallel solid surfaces in a given liquid, the F cap vs h relation only depends on three parameters, i.e., θ, T, and N g .…”