The influence of the capillary pressure in nanobubbles on their attachment to particles during froth flotation: Part IV. Spreading nanobubbles as natural fractals

Abstract

The specific property of nanobubbles with spontaneous spreading over the solid hydrophobic particle substrate adhered to them, which is caused by a high capillary gas pressure in nanobubbles (P_c > 10⁶ N/m²), is considered. The computational principle of bubble spreading curves is considered and parameter X characterizing the intensity is introduced. Dependence X(a) (a is the bubble base diameter) is presented by a bimodal curve, which confirms that the nanobubble spreading is energetically provided by two sequentially acting independent sources. The first source is conditioned by the reduction (approximately by 11%) of the nanobubble curvilinear surface area at the initial spreading stage, and the second source is conditioned by the work of gas expansion caused by the drop of P_c when the bubble is spreading. Parameter X is characterized by a considerably larger slope of dependence X(a) at the first spreading stage compared to the second one. It now turned out that the revealed property, which determines the efficiency of industrial flotation processes in past, finds prospects for application again after its recognition. Since it manifests itself in a limited range of bubble sizes, it is proposed to attribute it to the proper or natural fractal by analogy with the Brownian motion, which manifests itself in a definite range of particle sizes. The influence of the surface activity of flotation reagents on the shape of bubble spreading curves is shown.