Effect of geometric constraint caused by nearby particles on the detachment from the particle-laden interface

Abstract

The bubble-particle detachment interaction is critical to the flotation of coarse (composite) particles which has attracted significant research interest in recent years. It is principally controlled by the capillary forces arising from the deformation of the air–water interface that has been quantified employing the single-particle models. However, these single-particle models can be far away from the detachment in the actual flotation process in which the bubble surface is covered by many attached particles. Here, we investigate the effect of the presence of nearby (attached) particles on the interfacial deformation, thereby influencing the particle detachment from the laden interface. Specifically, the detaching force and the deformed interface shape were simultaneously recorded for a floating sphere at the center of a hexagonal lattice unit that comprised six spheres fixed at an initially planar air–water interface. The 3-dimensional Young–Laplace equation was numerically solved to determine the interface deformation, quantify the detachment process, and validate the model prediction for the detaching force. The results show that the effect of nearby particles called the constraint effect on the interface deformation and the detaching force is significant. The nearby particles confine the interface deformation around the test particle, thereby restricting the movement of the three-phase contact line (TPCL) on the particle surface, leading to smaller changes in the TPCL radius and displacement into the liquid phase during the detachment interaction than those in the absence of nearby particles. However, the change in the contact angle and polar angle of TPCL on the test particle is insignificant. The constraint effect reduces the tenacity which is critical to the stability of bubble-particle aggregates and was not expected. The results of this work provide useful details about the detachment and floatability of particles at the particle-laden interface, which is relevant in many industrial applications, including flotation separation.