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. (C) 1999 Academic Press.