Multipolar electrical forces for microscale particle manipulation

Dielectrophoresis is the motion of the particles due to the interaction between a non-uniform electric field and its induced multipole moments in the particle. Here a numerical solution for the gradient terms in the electric field strength, ∇→E²_RMS and ∇→V(∇ →E→_RMS:→∇→E_RMS), generated by interdigitated bar micro-electrodes is derived using the finite element method and numerical analysis. These gradients of the electric field produced by such electrodes are mainly effective on the magnitude of the DEP force exerted on micro/nano-particles. Interdigitated bar micro-electrodes can be better designed to control the induced dielectrophoretic force applied on the biological samples by understanding the effects of the dimensions of the electrodes on these quantities. In this paper we introduce the relationship between the geometry, the applied voltage and frequency and the height above the interdigitated micro-electrodes with the magnitude of the DEP force for non-uniform electrode widths and gaps by considering the basic dielectrophoresis. In order to explore the effects of higher-order multipoles, a correction factor was added to the basic dipolar DEP force. Based on the simulations, it was found, that the multipole contributions to the induced DEP force acting on particles can be very important specially for the particles of larger radii at lower heights, and also for micro-electrodes having smaller gap/width sizes; therefore, neglecting these effects could result in an unacceptable amount of error in predictions of DEP forces. The numerical solutions developed in this paper are in an excellent agreement with previous experimental and theoretical reports of particle levitations above the interdigitated micro-electrodes.