An Approximate Analytical Expression for the Probability of Attachment by Sliding

Area of Science:

• * Chemical Engineering and Materials Science
• * Separation Processes and Surface Chemistry

Background:

• * Attachment by sliding is a critical microprocess in flotation separation.
• * Understanding the forces governing this microprocess is essential for optimizing flotation efficiency, particularly in applications like flotation deinking.

Purpose of the Study:

• * To develop a closed-form approximation for the probability of attachment by sliding (P(asl)).
• * To identify key forces and parameters influencing attachment by sliding during flotation.

Main Methods:

• * Inclusion of resistive force from film drainage, gravitational force, and bubble-particle flow force.
• * Consideration of both Stokes and non-Stokes flow regimes.
• * Development of an expression for P(asl) as a function of fluid properties, bubble/particle characteristics, and initial-to-critical film thickness ratio (h(0)/h(crit)).

Main Results:

• * P(asl) generally decreases with increasing h(0)/h(crit) and increases with bubble/particle radii and particle density.
• * Observed local minima in P(asl) predictions.
• * Abrupt transition in P(asl) predictions at the Stokes to non-Stokes flow condition boundary.

Conclusions:

• * The developed model provides a quantitative understanding of attachment by sliding in flotation.
• * Film thickness, bubble/particle properties, and flow conditions significantly impact flotation separation efficiency.
• * The findings are crucial for the design and optimization of flotation processes.