  An analytical analysis is presented of the transport and capture of magnetic
micro/nano-particles in a magnetophoretic microsystem that consists of an array
of integrated soft-magnetic elements embedded beneath a microfluidic channel.
The elements, which are polarized by a bias field, produce a nonuniform field
distribution that gives rise to a force on magnetic particles within the
microchannel. The equations governing particle motion are derived using
analytical expressions for the dominant magnetic and fluidic forces. The
magnetic force is obtained using an analytical expression for the field
distribution in the microchannel combined with a linear magnetization model for
the magnetic response of particles. The theory takes into account particle size
and material properties, the bias field, the dimensions of the microchannel,
the fluid properties, and the flow velocity. The equations of motion are solved
to study particle transport and capture. The analysis indicates that the
particles exhibit an oscillatory motion as they traverse the microsystem, and
that a high capture efficiency can be obtained in practice.
