Interdisciplinary Applied Mathematics

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The experimental results in (Cummings and Singh, 2000; Cummings, 2001), can also be used for verification of numerical models for electrokinetic and dielectrophoretic transport. The simulation domain is periodic; hence, it is free of external boundary conditions, with the exception of the imposed electric field, which is determined by Laplace’s equation.

In a combined experimental and numerical study, Ho and coworkers utilized AC filamentary dielectrophoresis to induce chaotic mixing in a microchannel (Deval et al., 2002). Their mixer consisted of a straight channel with two grooves on the top and bottom surfaces, see Figure 9.9 in Section 9.3. They have applied ± 10 V AC electric field on the groove surfaces to induce weak dielectrophoretic forces on the particles flowing through the channel. Although the flow was laminar and two-dimensional, particle trajectories exhibited chaotic motion that enhanced mixing in this continuous-flow mixer.

An interesting nanotechnology application of DEP has been demonstrated by Velev and coworkers in self-assembly of microscale wires using metallic nanoparticles (Hermanson et al., 2001; Bhatt and Velev, 2004). Figure 7.26 (a) shows an optical micrograph obtained during the wire growth process. Due to the DEP, the gold nanoparticles are highly concentrated at    the end    of    the    wire    tip,    which enable    extension    of    the    wire

in the electric-field gradient direction. The authors reported wire growth exceeding 50 micrometers per second with lengths on the oder of 5 millimeters. They have used planar electrodes and AC electric fields ranging from 50 to 200 V at frequencies 50 to 200 Hz. The wires are automatically assembled using 15 to 30 nm diameter gold particles, and the wires exhibited good ohmic conductance. Wire thickness can be controlled, resulting in high surface-to-volume ratio structures. The assembly process is simple and self-repairing, and the wires automatically form electrical connections to conductive islands or particles, as shown in Figure 7.26. These properties make the microwires promising for wet electronic and bioelectronic circuits (Hermanson et al., 2001; Bhatt and Velev, 2004).

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