# Interdisciplinary Applied Mathematics

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MR fluids can dynamically change their optical properties, anisotropy, mechanical rigidity, and electronic properties, often in a reversible way. The applications are many, but perhaps the most exciting ones are based on self-assembly of magnetic colloidal particles into chains or columnar structures (Doyle    et    al.,    2002;    Furst    et    al.,    1998;    Liu    et    al.,    1995).    In    (Doyle

et al., 2002), self-assembled magnetic matrices were developed for DNA separation chips. Compared to previous separation media, suspensions of paramagnetic particles have several advantages: they have a low viscosity in the absence of magnetic field, their pore size can be tuned (from 1 to 100 microns), and they do not require sophisticated microlithography.

There has been a lot of work in understanding ER fluids, and at least their field-induced structures are reasonably well understood (Gast and Zukoski, 1989; Halsey and Toor, 1990; Tao and Sun, 1991; Chen et al., 1992; Martin et al., 1992). There are, however, several complicating factors (e.g., surface charge, electrode polarization; see (Promislow et al., 1995)), which have limited the range of their application in microfluidics research today. These can be avoided with MR fluids, which exhibit an analogous field-induced aggregation and can also be controlled by a single external magnetic field. However, the behavior of particles interacting through induced magnetic fields is more complex than that of ER fluids, and their dynamics are not well understood. For example, the long-range nature of the particle interaction can persist even when they form chains or columns; the range of the interaction depends sensitively on the chain length.

There are several experimental studies focused on understanding the dynamics of magnetic chains and columns (Liu et al., 1995; Furst et al., 1998; Promislow et al., 1995), as well as a few simulation studies (Cli-ment et al., 2004). Here we consider two main classes of problems. The first category involves flow geometries and devices with tens of suspended

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