Triboelectric charging is present in numerous technologies and everyday processes, providing both problems and opportunities. Despite this, there is no generalised model for the amount of charge that will build up on surfaces in contact. Here, we develop a new model for the saturation charge on triboelectrically charged spherical insulators, accounting for both equalisation of surface potentials and electrical breakdown of the surrounding medium. Experiments are conducted under controlled temperature and humidity using two independent methods, measuring the saturation charge on polymer spheres contacting grounded stainless steel. The results verify our equalisation of surface potentials model which describes how saturation charge density increases for smaller particle sizes. Key triboelectric properties are calculated: The estimated saturation charge on a flat surface and the equalisation potential between different materials, which can be used to predict charge saturation and quantify a triboelectric series. The transition radius below which electrical breakdown will cause saturation of charge is also calculated theoretically. Limitations to the model are demonstrated experimentally. As particle size reduces, a point is reached at which the electrostatic adhesion of particles to the grounded charging surface prevents further charge build-up. Furthermore, it is found that the saturation charge for smaller particles in humid conditions is greatly reduced. These calculations, and the demonstrated procedure, can serve as a tool for the design of technologies and processes influenced by triboelectric charge build-up, including triboelectric nanogenerators and electrostatic mineral separators.

It is widely accepted that particles stabilise flotation froths and that stable froths result in improved flotation performance. Predicting the effect of particle addition on froth stability is, however, challenging. Dynamic surface tension measurement using maximum bubble pressure presents an attractive technique to investigate the effect of surfactant and particles at the air-water interface. The range of bubble lifetimes that can be studied (typically 0.1 to 60 s) is analogous to variations in air rate in flotation cells, and the corresponding changes in surface tension give an indication to the diffusion and adsorption rates of particles at the interface. In this paper, we use dynamic surface tension measurements to investigate the effect of particles on bubble surfaces at the microscale and link this to bulk froth stability measurements carried out using a froth column. Using the maximum bubble pressure method, the results show that the addition of particles results in lower surface tension, both at the dynamic (i.e. short) bubble lifetimes and towards equilibrium (i.e. 60 s bubble lifetime). This corresponds with the bulk froth stability measurements, where the three-phase system yielded more stable froths than the surfactant only system. Furthermore, increased particle loading at the air-water interface, whether through higher surfactant concentrations or lower air rates (longer bubble lifetimes), gave lower surface tension and higher froth stability. This demonstrates the link between bubble loading and froth stability. It is proposed that the maximum bubble pressure technique can be used to predict froth stability for two- and three-phase systems, enabling the effect of particle loading to be accounted for and quantified. Moreover, the technique has the potential to allow rapid determination of particle and surfactant diffusion at the air-water interface and prediction of the corresponding effect on bulk froth behaviour.