Capture of Small Particles on a Bubble Collector by Brownian Diffusion and Interception

Abstract

This paper considers capture of small particles on the surface of a much larger bubble by Brownian diffusion and interception induced by flow. The bubble is assumed to rise under the action of gravity, and the terminal rising velocity is determined for the bubble size typical of bubble flotation processes. The mechanism of particle transport to the surface of bubble is controlled by the ratio of particle ( a) to bubble radius ( A). The dominant transport mechanism changes from diffusion to interception as the size ratio δ(≡ a/ A) increases above a certain critical value. Although the Marangoni effect caused by the adsorbed particles reduces the collection efficiency, the general features of transport mechanism are preserved when the tangential velocity is nonzero on the bubble surface. Specifically, the analysis shows that for a bubble collector with slip boundary the critical value follows δ cr ∝ A -4/3, in contrast to the result δ cr ∝ A -1 for a no-slip collector. In the diffusion-control region, the collection efficiency of a collector with slip boundary decreases with increasing collector radius as A -3/2, which is much slower than A -2 for the case of a no-slip collector. On the other hand, in the interception-control region, the collection efficiency increases in proportion to the size ratio δ. In this limit, the efficiency of a collector with slip boundary is very large compared to the result for the case of a no-slip collector where the efficiency is only O (δ 2).