Modified Mason number for charged paramagnetic colloidal suspensions

The dynamics of magnetorheological fluids have typically been described by the Mason number, a governing parameter defined as the ratio between viscous andmagnetic forces in the fluid. For most experimental suspensions of magnetic particles, surface forces, such as steric and electrostatic interactions, can significantly influence the dynamics. Here we propose a theory of a modified Mason number that accounts for surface forces and show that this modified Mason number is a function of interparticle distance. We demonstrate that this modified Mason number is accurate in describing the dynamics of a rotating pair of paramagnetic colloids of identical or mismatched sizes in either high or low salt solutions. The modified Mason number is confirmed to be pseudoconstant for particle pairs and particle chains undergoing a stable-metastable transition during rotation. The interparticle distance term can be calculated using theory or can be measured experimentally. This modified Mason number is more applicable to magnetorheological systems where surface forces are not negligible.