The dielectrophoretic and travelling wave forces generated by interdigitated electrode arrays: analytical solution using Fourier series

In alternating current electrokinetics, electric fields are used to generate forces on particles. Techniques have been applied for the manipulation of particles and the measurement of their dielectric properties. The fields are typically generated by microelectrode structures fabricated on planar surfaces. One particular design, using interdigitated bar electrodes, is used both in dielectrophoretic field flow fractionation and travelling wave dielectrophoresis. This paper presents a Fourier series analysis of the dielectrophoretic force on a particle generated by this type of electrode array, for both dielectrophoresis and travelling wave dielectrophoresis. Simple expressions are derived for the force at a distance of the order of the electrode spacing from the electrodes. A full analytical expression is given for the dielectrophoretic force in two dimensions. Comparisons are made with previously published experimental observations.