Closed-form solutions in the electrical field analysis for dielectrophoretic and travelling wave inter-digitated electrode arrays

We derive closed-form solutions of electric fields, dielectrophoretic (DEP) forces, and time-averaged DEP forces in a parallel electrode array for three cases: first, the case of a two-phase DEP electrode array with a first-order approximate boundary condition; second, the case of a two-phase DEP electrode array with the exact boundary condition; and last, the case of a four-phase travelling wave DEP electrode array with a first-order approximate boundary condition. We also compare these analytic solutions with numerical solutions