A theoretical method of electrical field analysis for dielectrophoretic electrode arrays using Green's theorem

A new method, based on Green's theorem, for calculating the electric fields produced by two-dimensional electrode arrays for the dielectrophoretic (DEP) characterization and manipulation of particles is presented. This method transforms the problem of solving the second-order differential Laplace equation for the electrical potential into an integral problem at the electrode plane. It relies on the knowledge of the electrical potential distribution on the electrode plane (the Dirichlet type boundary condition). The effectiveness of the method is demonstrated in the examples of an array of parallel electrodes under various voltage signal excitation modes. The field distributions so obtained are compared with those calculated by the numerical charge density method. Furthermore, an approach is described for utilizing boundary conditions for mixed Dirichlet and Neumann types as appropriate for realistic electrode configurations. Finally the method's applicability to two-dimensional electrode arrays and its significance for dielectrophoresis studies are considered. Because of its analytical nature, the Green's theorem-based method has many advantages over numerical simulations: (1) depending on the complexity of the electrode geometry, analytical expressions may be obtained not only for the potential distribution but also for the electric field and the time-averaged DEP force, circumventing the need for numerical differentiation; (2) accurate field and DEP force determinations can be made right up to the electrode plane and the electrode edges; (3) the approach is computationally much more efficient than numerical techniques.