Modelling nanoparticle transport in dielectrophoretic microdevices using a FourierBessel series and applications for data analysis

D J Bakewell (1)

1 Department of Electrical Engineering and Electronics

A Fourier-Bessel series solution is derived that describes the dielectrophoretic-driven transport of nanoparticles in a microdevice. The solution assumes that the nanoparticles do not interact and is based on a linear Fokker Planck equation that includes the effects of thermal diffusion. The solution is applicable for a dielectrophoretic force that varies exponentially in the microdevice, such as, in the far field of planar interdigitated arrays. Important applications of the Fourier-Bessel solution are demonstrated that include simulation and system classification of nanoparticle movement under the action of weak and strong dielectrophoretic forces. Methods are demonstrated for the inverse process of estimating model parameters, such as the dielectrophoretic force, based on nanoparticle concentration data obtained experimentally. Data decomposition into separate spatial and temporal modes is demonstrated and Fourier transformation of the series solution yields a representation in the frequency domain. The frequency response predicted by transforming the time dependent Fourier-Bessel solution indicates the presence of a DEP modulation bandwidth that concurs with observations of preliminary experiments. 1. Introduction Dielectrophoresis (DEP) is a versatile noncontact electrokinetic method for controlling the movement of nanosize biomolecules and colloids in micro-environments. DEP nanoparticle transport processes have been intensely researched for lab-on-chip (LOC) type fabricated microdevices [ 1, 2 ], and for other diverse scientific and technological applications, including textile fabrics, scanning probe microscopes, biological manipulation tools, quantum dots, nano-circuit assembly and optical fluidics [ 3-13 ]. DEP is the movement of polarisable nanoparticles arising from the action of nonuniform electric fields [ 14 ]. It is often achieved by applying radio frequency electrical potentials to microfabricated electrodes immersed in low conductivity electrolyte. The application of DEP electrokinetics in micro-technologies means nanoscale nanoparticle movement needs to be modeled and measured quantitatively. Quantitative measurements of the DEP driven nanoscale transport by us [ 15-17 ] identified a number of time constants that raised questions about the theoretical basis of their origin and subsequently motivated this work on modelling.

Mots clés: AC electrokinetics; dielectrophoresis; Fourier-Bessel series; modified diffusion equation; Fokker- Planck equation. PACS: 87.85.Tu; 87.10.Ed; 87.85.Ox; 02.60.Cb

D J Bakewell. Modelling nanoparticle transport in dielectrophoretic microdevices using a FourierBessel series and applications for data analysis. Journal of Physics D: Applied Physics, 2011, 44 (8), pp.85501. ⟨10.1088/0022-3727/44/8/085501⟩. ⟨hal-00597848⟩