As a new technique, dielectrophoresis has been proven to be successful in the separation, transportation, entrapment and manipulation of cells, DNA molecules, and viruses. One typical design uses an array with interdigitated parallel electrodes to manipulate and separate particles using traveling wave and conventional dielectrophoresis. In order to obtain an analytical solution for the dielectrophoretic force or traveling wave dielectrophoretic force, the electric potential equation needs to be solved. Unfortunately, the mixed type of boundary condition (Dirichet and Neumann) for the electric potential equation poses a large challenge for obtaining an analytical solution. Although some analytical solutions have been achieved using an approximate single type of boundary condition instead of the exact boundary condition, this leads to inaccurate results especially in the zone near the electrodes which cannot be neglected. In this paper, we present an analytical method for solving the electric potential equation with the mixed type of boundary condition. We compare our analytical solution with the numerical results obtained using the Computational Fluid Dynamics Research Corporation, CFDRC, code which verifies our analytical method is correct for solving this problem. In addition, comparisons are made between the analytical solutions with approximate boundary conditions and those with exact boundary conditions. The comparison shows our analytical solution gives a more accurate analysis for the conventional and traveling wave dielectrophoretic forces.
Analytical solution of electric potential produced by a direct current point sou rce located in a multilayered spherical volume conductor
