Particle Deposition from Rising Bubbles

The total number of particles in the bubble at lime t is obtained by integrating over r  

When we substitute (3.84) in (3.85) and integrate term by term with (3.86), the ratio of the aerosol mass remaining in the bubble at any lime to the original mass is 

The time for the concentration to fall to l/e of its original value is tj = 0.05a /D. The center and average concentrations for bubbles are shown in Fig. 3.9. 

If special precautions are taken to avoid contamination of the bubble surface, particle deposition by diffusion to the water surface is enhtinced by internal circulation. The internal flow can be calculated for very low bubble Reynolds numbers in the creeping flow approximation (Lamb, 1953). A solution ha.s been obtained to the equation of convective 

Eitamplet A l-mm bubble carrying submicron aerosol panicles rises through a column of water at 25 C. How high must the column be to remove 90% of the 0.1-fxm particles The velocity of rise of a 1 -mm bubble that behaves like a rigid sphere is about 10 cm/sec. Assume the aerosol in the bubble Is initially uniformly mixed. 

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