Journal of Colloid and Interface Science, Vol.213, No.1, 101-111, 1999
Exact and approximate expressions for bubble-particle collision
The flotation microprocess of collision is investigated and an exact expression for the probability of collision (P-c) is developed based on the intermediate flow of Yoon and Luttrell (1). This expression for P-c only assumes that the bubble and particle are spherical and that the particle radius is less than the bubble radius (i.e., R-p < R-B). In addition to removing the requirement that R-p much less than R-B, the influence of a particle settling velocity is also included in the model development, The expression for P-c is shown to be a function of three dimensionless groups: (i) the magnitude of the dimensionless particle settling velocity, \G\; (ii) the bubble Reynolds number, Re-B; and (iii) the ratio of particle to bubble radius, R-p/R-B. The probability of collision model is compared to available experimental data and good agreement is shown. A parametric study is also completed for 0 less than or equal to \G\ less than or equal to 1, 0 less than or equal to Re-B less than or equal to 500, and 0.001 less than or equal to R-p/R-B < 1. In general, P-c is independent of Re-B when R-p/R-B less than or similar to 0.03, the particle settling velocity is important for small values of R-p/R-B, and R-p/R-B dominates as R-p/R-B --> 1.