Influence of the capillary pressure in bubbles on their adherence to particles during froth flotation

Abstract

A new procedure of calculating the energy possibility of the transition of free bubble A with shape β = 0 into bubble M with shape β < 0 adhered to the substrate particle, namely, the A → M transition (AMT), is described. A criterion which makes it possible to avoid the error admitted previously when determining the volume of bubble A (VA) from the selected volume of bubble M (VM) is introduced into the calculation. It is established due to this criterion that the previously accepted equality VA = VM in the AMT instant is admissible only for relatively large bubbles and, for diameters smaller than 20–30 μm, bubble A in the adherence instant is expanded to VM by approximately a 10 millionth part of its initial value. Calculations showed that, as the size of bubble A decreases, the increment of its volume during AMT increases symbately and the energy barrier on the AMT way to hydrophilic surfaces decreases antibately. The decay reaches zero or becomes negative for bubbles <1 μm in size. These results make it possible to consider that the capillary gas pressure in the bubble is the intensity factor of the AMT process. It is mentioned that precision AMT calculations can be performed only based on the results of a numerical solution of the Laplace equation, which was presented until 1883 in the form of Bashforth and Adams tables. A new variant of a table of such a type with the numerical example of its application to the solution of the flotation problem is presented.