Modeling of dielectrophoretic force for moving dielectrophoresis electrodes

Abstract

Moving dielectrophoresis has been recently introduced by the authors to fractionate and transport cells. This technique allows cells to be fractionated as in the conventional dielectrophoresis technique, but transported like in the traveling wave dielectrophoresis technique. This technique utilizes a series of finite width top electrode, and a common infinite width bottom electrode. This study presents analytical solutions for the electrical potential, the electric field and the multipolar dielectrophoretic (DEP) force for this electrode structure, whereby the top electrode is treated as semi-infinite. An analytical solution for the electrical potential is obtained by solving the Laplace equation subject to boundary conditions using the Wiener–Hopf method. Expressions for the electric field and higher order (multipolar) DEP forces are obtained by recursively taking the corresponding derivatives. These analytical expressions allow the evaluation on the importance of higher order forces, which are not possible using conventional numerical techniques, such as those based on finite element or meshless methods. An application of the model is for the prediction of the trajectory of a cell driven by dielectrophoretic force generated in the parallel-plate electrode structure. Our analyses indicate that to exploit moving dielectrophoresis effectively, the electrode dimension and spacing are to be minimized. The channel height should also be small, but should be sufficiently larger than the size of the cells for the cells to travel freely in the channel.