Nanosize particle movement in time-modulated nonuniform electric fields: a Fourier-Bessel series model

Abstract

Dielectrophoresis (DEP) is a popular, noncontact electrokinetic method for separating and transporting nanosize biomolecules and colloids in microdevices. DEP is the movement of polarizable particles arising from the action of nonuniform electric fields. The spatial-temporal distribution of nanosize particles moving under the action of a deterministic DEP force and stochastic Brownian thermal motion can be described by the Fokker Planck equation (FPE). The application of DEP electrokinetics in micro-technologies means nanoscale particle movement needs to be modeled and measured quantitatively. Quantitative FPE prediction (using numerical values for relevant dielectric and fluid parameters) of DEP-driven particle transport is usually achieved numerically by using Finite Element methods (FEMs). The drawbacks of FEMs are inaccuracy where the electric field is extremely inhomogeneous and they offer little insight into the mathematical structure of the FPE solution. The latter is important, not only for prediction of particle movement, but also the 'reverse' process where parameter values are estimated from measurements of DEP experiments. In this paper, a Fourier-Bessel series solution to the FPE is derived that describes particle movement under the action of DEP in a simple chamber. The solution assumes the DEP force exhibits a hyperbolic spatial profile and can be extended to the case that assumes an exponential decay. This applies to planar arrays, such as, interdigitated electrodes. Time-dependent DEP particle collection and release (after the DEP is switched off) from a surface is evaluated for strong and weak DEP forces. Temporal DEP responses can be classified as state-transitions and perturbations, respectively.