  In this paper, we propose a novel approach to obtaining a reliable and simple
mathematical model of a dielectrophoretic force for model-based feedback
micromanipulation. Any such model is expected to sufficiently accurately relate
the voltages (electric potentials) applied to the electrodes to the resulting
forces exerted on microparticles at given locations in the workspace. This
model also has to be computationally simple enough to be used in real time as
required by model-based feedback control. Most existing models involve solving
two- or three-dimensional mixed boundary value problems. As such, they are
usually analytically intractable and have to be solved numerically instead. A
numerical solution is, however, infeasible in real time, hence such models are
not suitable for feedback control. We present a novel approximation of the
boundary value data for which a closed-form analytical solution is feasible; we
solve a mixed boundary value problem numerically off-line only once, and based
on this solution we approximate the mixed boundary conditions by Dirichlet
boundary conditions. This way we get an approximated boundary value problem
allowing the application of the analytical framework of Green's functions. Thus
obtained closed-form analytical solution is amenable to real-time use and
closely matches the numerical solution of the original exact problem.
