Transition from two-dimensional to three-dimensional behavior in the self-assembly of magnetorheological fluids confined in thin slits

We study the effects of extreme confinement on the self assembly of the colloids found in magnetorheological (MR) fluids using Brownian dynamics simulations. The MR fluid is confined in a thin slit with a uniform external magnetic field directed normal to the slit. We find a crossover in the behavior of the system from two dimensions to three dimensions as the slit thickness is increased. A simple model is presented to describe this crossover as a function of the slit thickness and volume fraction of the MR fluid. The model is able to predict the salient features of the structure formation that has been observed in these systems. Furthermore, the model predicts the approximate time scales for structure formation under a variety of conditions. We present a quantitative analysis of the effect of volume fraction on the behavior of the system. Additionally, we show quantitatively how energy barriers to structure formation play a crucial role in determining the steady state structure of these systems. Our analysis explains the discrepancies between previous experimental and theoretical work on the self-assembly of MR fluids confined in thin slits.