Ramin Haghgooie and Patrick S. Doyle. Chemical Engineering, MIT, 77 Massachusetts Ave., 66-053, Cambridge, MA 02139
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 cross-over in the behavior of the system from 2D to 3D as the slit-thickness is increased. A simple model is presented to describe this cross-over 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, for the first time, 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. Energy barriers appear in many systems in nature and are often important in determining whether a system can reach its lowest energy state. We present a general analysis of the energy barriers to colloidal self-assembly in this system and demonstrate their importance over a range of slit-thicknesses. Our analysis explains the discrepancies between previous experimental and theoretical work on the self-assembly of MR fluids confined in thin-slits.