Dielectrophoretic manipulation of finite sized species and the importance of the quadrupolar contribution

Dielectrophoresis (DEP) is the movement of polarizable species in a nonuniform electric field. DEP is used to attract (positive DEP) to or repel from (negative DEP) regions of high field intensity and is useful for manipulating species, including biological species. Current theoretical and numerical approaches used to predict the response to DEP forces assume that the target species is a point particle; however, in practice, the target species is of finite size, e.g., macromolecules, spores and assay beads. To elucidate the importance of target species size effects, higher order terms in the DEP force multipole expansion must be considered [P.R.C. Gascoyne and J. Vykoukal, Electrophoresis 23, 1973 (2002)]. In this paper, we used the method of Green’s function to derive and explore the importance of the quadrupolar contribution to the DEP forces acting on finite-sized species produced by a planar, interdigitated array of electrodes. Based on the analysis, it was found, for example, that at a fixed height of 20 μm in an interdigitated DEP array with an electrode width and spacing of 20 μm energized by a 10 Vp p, 1.0 MHz ac signal, the quadrupolar contribution to the total DEP force was 5% for a latex bead with 4.2 μm in radius and 10% for the one with 6 μm in radius. For a fixed, fractional quadrupolar contribution, $\beta$, both the exact calculation and the scaling estimate elucidate that the critical size of particle increase linearly with the electrode width (and spacing) at a fixed height, while the critical particle radius increases with a square-root dependence on the width height above the electrode in the electrode array.