A THEORETICAL METHOD OF ELECTRICAL-FIELD ANALYSIS FOR DIELECTROPHORETIC ELECTRODE ARRAYS USING GREENS THEOREM

A new method, based on Green's theorem, for calculating the electric f ields produced by two-dimensional electrode arrays for the dielectroph oretic (DEP) characterization and manipulation of particles is present ed. This method transforms the problem of solving the second-order dif ferential Laplace equation for the electrical potential into an integr al problem at the electrode plane. It relies on the knowledge of the e lectrical potential distribution on the electrode plane (the Dirichlet type boundary condition). The effectiveness of the method is demonstr ated in the examples of an array of parallel electrodes under various voltage signal excitation modes. The field distributions so obtained a re compared with those calculated by the numerical charge density meth od. Furthermore, an approach is described for utilizing boundary condi tions for mixed Dirichlet and Neumann types as appropriate for realist ic electrode configurations. Finally the method's applicability to two -dimensional electrode arrays and its significance for dielectrophores is 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, analytica l expressions may be obtained not only for the potential distribution but also for the electric field and the time-averaged DEP force, circu mventing the need for numerical differentiation; (2) accurate field an d DEP force determinations can be made right up to the electrode plane and the electrode edges; (3) the approach is computationally much mor e efficient than numerical techniques.