Universalities in the dynamics of suspensions of magnetic colloidal chains confined in thin films

A quasi two-dimensional model of magnetic colloidal chains is examined by extensive Browniandynamics simulations on dilute suspensions of monodisperse magnetic colloidal chains confined in thin films at different thicknesses under an external magnetic field applied perpendicular to the films. Universalities in the dynamics of chains are explored based on the mean-field theory recently proposed by Tokuyama. The long-time self-diffusion coefficient of a chain is shown to obey a singular function of a control parameter proportional to the square of the applied field strength. The value of the control parameter at the singular point, where the long-time self-diffusion coefficient of a chain becomes zero, is then shown to be inversely proportional to the square of the number of magnetic colloids forming one chain.