Direct Numerical Simulation of Particles in Spatially Varying Electric Fields*

A numerical scheme is developed to simulate and study the motion of dielectric particles in the uniform and nonuniform electric fields of microfluidic devices. The motion of particles is simulated using a distributed Lagrange multiplier method (DLM) and the electric force acting on the particles is calculated by integrating the Maxwell stress tensor (MST) over the particle surfaces. The MST is obtained from the electric potential, which, in turn, is obtained by solving the electrostatic problem. In our numerical scheme, the domain is discretized using a finite element scheme and the Marchuk-Yanenko operator-splitting technique is used to decouple the difficulties associated with the incompressibility constraint, the nonlinear convection term, the rigid-body motion constraint and the electric force term. The MST results show that the ratio of the particle-particle interaction and dielectrophoretic forces decreases with increasing particle size. Consequently, when the spacing between the electrodes is comparable to the particle size, instead of collecting on the same electrode by forming chains, they collect at different electrodes.