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Exact and Approximate Expressions for Bubble-Particle Collision
1Engineering Division, Institute of Paper Science and Technology, 500 10th St., N.W., Atlanta, Georgia, 30318
Journal of Colloid and Interface Science
|April 7, 1999
Summary
This study develops a new model for particle-bubble collision probability (Pc) in flotation, considering particle settling velocity. The model accurately predicts collision probability across various conditions, improving flotation process understanding.
Area of Science:
- Mineral Processing
- Chemical Engineering
- Fluid Dynamics
Background:
- The probability of collision (Pc) is a critical factor in froth flotation.
- Existing models often assume particle radius is much smaller than bubble radius (Rp << RB).
Purpose of the Study:
- To develop an exact expression for Pc that removes the Rp << RB assumption.
- To incorporate the influence of particle settling velocity into the Pc model.
Main Methods:
- Developed an exact expression for Pc based on Yoon and Luttrell's intermediate flow model.
- The model considers spherical bubbles and particles.
- Included particle settling velocity in the model development.
Main Results:
- The derived Pc expression is a function of three dimensionless groups: particle settling velocity (||G||), bubble Reynolds number (ReB), and particle-to-bubble radius ratio (Rp/RB).
- The model shows good agreement with experimental data.
- Parametric study reveals Pc is generally independent of ReB for Rp/RB < 0.03.
- Particle settling velocity is significant for small Rp/RB, while Rp/RB dominates as it approaches 1.
Conclusions:
- The new Pc model provides a more accurate representation of flotation microprocess collisions.
- The model's dependence on ||G||, ReB, and Rp/RB offers insights into flotation parameter optimization.
- This work advances the fundamental understanding of collision phenomena in mineral processing.