Influence of the hydrophobic force model on the capture of particles by bubbles: A computational study using Discrete Element Method

• Three different hydrophobic force models have been simulated.
• Similar capture behaviour for particles close to the bubble was found in all models.
• Drastic differences appeared in the capture of particles further from the bubble.
• The influence of the initial random particle velocity was also studied.

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 μm, 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/λ). 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 μm from the bubble surface in the cases simulated using Models B and C (λ = 1 μm), 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.

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