چکیده : 

Discrete Element Method computer simulations have been carried out to analyse the influence of the

hydrophobic force model on the capture of particles by a central bubble. Two hundred particles, with

diameters ranging between 24 and 66 lm, were randomly positioned within a maximum distance from

the surface of a bubble of 2 mm in diameter. Initial particle velocities were random in direction and value

and they followed Gaussian distributions with standard deviations between 0.0 and 1.0 m/s. Three possible

models, named A, B and C have been used in the simulations. The models correspond to different

published relationships of the hydrophobic force with the distance between particle and bubble surfaces,

d. Model A corresponds to a hydrophobic force that decays in the form 1/d; the hydrophobic force given

by Model B uses a relationship in the form 1/d2; Model C predicts a force that decays in an exponential

way in the form exp(d/k). These models have also been compared with a base case in which the hydrophobic

force only acted when the particles were in contact with the bubble. Therefore, we could better

discern between the influence of the initial particle velocities and the long range component of the

hydrophobic force. The differences in the capture efficiency of the particles predicted by the three models

were drastic. All particles were captured by the bubble in the cases simulated using Model A for any particle–

bubble surface distance smaller than 1 mm. However, only 40% and 60% of the particles were captured

even for particles located at distances of less than 50 lm from the bubble surface in the cases

simulated using Models B and C ( lm), respectively. In fact, the capture of particles seems to be more

strongly influenced by how the hydrophobic force decays with interparticle distance in the range of tens

of micrometres rather than by the differences between the models in the range of micrometres. Therefore,

this work should aid in the future determination of a general hydrophobic force model through

an experimental comparison of the kinetics of collision of particles against bubbles in flotation cells with

the simulation results