The effect of capillary pressure in bubbles on their adhesion onto particles during foam flotation. Part 1

A new calculation procedure for the power possibility of transferring a free bubble A of shape β = 0 into a bubble M of shape
β < 0, which is adhered to a substrate-particle, namely transfer А → М (TAM) is described. A criterion is entered into the calculation
thus allowing us to avoid the error that has been supposed earlier in determining A bubble volume (VА) with the use of selected
volume (VМ) of M bubble. Thanks to the criterion it has been found that accepted earlier equation VA = VM at the moment
of TAM is admissible only for relatively large bubbles, and for diameters < 20÷30 μm the bubble A at the moment of adhesion
expands to VМ approximately by a 10-million part of its initial value. The calculations show when bubble A decreases, an increment
of its volume grows symbately in TAM, and the threshold energy decreases antibately on the way of TAM to hydrophilic
surfaces. The decrease reaches value zero or become negative for bubbles <1 μm. The obtained results allow us to regard that
gas capillary pressure in a bubble is a factor of TAM process intensity. It is noted that precision calculations of TAM can be carried
out only based on the results of numerical solution of Laplace equation, which have been presented in the form of Bashfort and
Adams tables beginning in 1883. A new alternative of the table of such type with a numerical instance of its application to the
solution of the floatation problem is given

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