The ability to manipulate biological objects from micrometer to nanometer scale in microfluidic devices plays an important role in many biological and colloidal science applications. Selective seperation, trapping and focusing of micro/nanoscale particles are some of the key tasks for preparation and detection on a lab-on-a-chip device. Using electric forces, fluid motion can be induced with electroosmosis, while charged particles can be transported by electrophoresis, and polarisable particles may be manipulated with dielectrophoresis.

We study here the manipulation of micro to nanosize particles in an interdigitated electrode array channel. Inhomogeneities in the electric-field allow the utilization of dielectrophoresis DEP. In our setup a rotating fluid flow due to AC electroosmosis (ACEO) is also present.

We first present a method to increase the efficiency of particle separation using DEP by applying a more general electric field shape than single-frequency. We later focus on the complex problem when DEP, ACEO and Brownian motion are all significant. We introduce a model for particle motion using a closed form solution of the DEP force and an analytical expression for the fluid flow. Fixed points and stability analysis is performed which predicts the location of the trapping region depending on the particle’s size. For nanoparticles however Brownian motion must be taken into account, which was done with an advection diffusion equation. The Peclet number for the particle studied can be high. At high Peclet number, finite element methods don’t perform well. We present a novel method to solve the advection diffusion equation. Particle motion is described by a stochastic process. The solution is written as an expected value which is evaluated using averaging in space. This numerical method permits the study of diffusive particles density distribution moved by a rotating fluid flow perturbed by a non divergence-free velocity. This analysis gives an understanding of the dynamical equilibrium focusing of nanoparticles with ACEO perturbed by DEP force.

This work is aiming to enable precise control development by providing efficient analysis tools which reduces the time between system analysis and control design.