On stronger particle adhesion to a bubble in a pulsating liquid flow

A paradoxical experimental fact is considered, when dynamic conditions in a flotation process with slurry pulsation may significantly strengthen the contact between a bubble and a particle attached to it. The oscillatory effects on the flotation complex are due to turbulent pulsations in the flow, as well as to the deliberate effects created in vibratory flotation machines and other similar devices. There are various hypotheses as to the mechanism behind this phenomenon. This paper proposes a potential explanation for the effect. It is based on the assumption that particle behavior on an oscillating bubble is similar to the behavior of a pendulum with a vibrating axis of suspension (the Stephenson–Kapitza pendulum), which assumes a stable upper vertical position under a certain condition. It may be suggested that a flotation complex under turbulent pulsations or deliberately excited oscillations may convert into a miniature analogue of a vibrating pendulum. As a result, a particle may assume a stable upper position on a bubble. In this case, as follows from a simple force analysis, a greater force is required to separate the particle from the bubble as compared to the bottom position configuration, typically observed in the absence of pulsations. It may be expected that, at least in some aggregates (on average), particles will be adhering to bubbles more firmly than in the absence of vibration. It is noted that Stephenson–Kapitza pendulum type systems serve as a model for various situations when vibration stabilizes a naturally unstable equilibrium position of a nonlinear system.This work was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (subject No. 121112500313-6).