Analytical expressions of the collision frequency function for aggregation of magnetic particles

Expressions are derived for the collision frequency function for particles whose dipoles are randomly oriented and aligned in magnetic fields. Closed form expressions obtained in this work by making mathematical approximations are in good agreement with numerical solutions of the exact forms of the potential expressions and those reported in the literature. Non-dimensional parameter (A) constraints for the validity of these expressions are derived. These expressions are then used in a simple population balance expression to illustrate their importance under a range of values of physical parameters encountered in practical systems.