G

The upper limit of K = 0.1 corresponds for example to a situation of 20 |im particles in an aerated suspension of 0.2 mm bubbles. Bubbles of this size will rise through still water at U = 5cms"1.K for silica, chalcopyrite and galena under these conditions is respectively 0.06, 0.095 and 0.17; the corresponding G values are 0.028, 0.055 and 0.11.

Using eqn [45], the respective collision efficiencies are 0.027, 0.052 and 0.10. If the bubbles in the aerated suspension were larger, the collision efficiencies would drop. For example for 0.4 mm bubbles whose rise velocity U=10cms"1, the K values would fall further below 0.1 and the G values would also fall to 0.014, 0.027 and 0.055 with corresponding E values of 0.014, 0.026 and 0.052.

Thus, while 0.4 mm bubbles are probably satisfactory for floating chalcopyrite and galena, it might be necessary to generate smaller bubbles to float silica selectively. However, 60 | m silica particles will be efficiently floated with 1 mm bubbles. The bubble size required for the effective flotation of 60 |im chal-copyrite and galena need be no smaller that 5 mm.

These observations are obviously of both technical and economic importance, as while it is unnecessary to generate small bubbles for medium-size sulfide mineral particles, for light silicate mineral particles it may be necessary for selective separation to aerate the pulp suspension down to 100 |im microbubbles.

Bubble-particle contact time - general Following initial interception of the particle by the bubble, two possible modes of contact have been proposed.

First, the bubble shell is considered to deform elas-tically and for the particle either to attach to the bubble, or ultimately to be expelled from the shell under the elastic forces. The contact time is that lapsing between the moment of initial contact when the surface begins to deform, to the time when it first regains its original undistorted shape, subsequent oscillations being ignored.

In the second technique the particle after collision with the bubble is assumed to remain in contact with an undeformed surface, while being swept around from the point where it initially made contact, until it approaches the bubble's wake, where it is detached from the shell. The contact time according to this method is the time lapsed between the original contact to that when it first enters the bubble's wake.

Contact time assuming bubble - shell deformation

Ye and Miller developed a model based on estimating the penetration distance h(t) of a particle into the bubble shell. Figure 7 shows their concept of defining h(t) for the special case when contact is made on the line of centres. The deformed area increase is approximated in terms of h(t) as:

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Solar Panel Basics

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