# Interdisciplinary Applied Mathematics

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Most of the dielectrophoretic applications utilize AC electric fields. However, as we have stated earlier in the chapter, it is possible to utilize a DC electric field. In this case the Clausius-Mossotti factor given by equation (7.50) is real, and there is no frequency dependence in the electrophoretic force. Cummings and Singh built arrays of insulated circular and square posts without embedded electrodes (as shown earlier in Figures 7.19 and 7.20). The flow is driven by electrodes outside the post arrays with a DC electric field at a desired angle to the post row orientation (Cummings and Singh, 2000). Under a weak electric field, dielectrophoretic effects are overwhelmed by the electrokinetic effects and diffusion, since dielectrophoresis is a second-order effect in the applied electric field. When the electric

field is increased, two additional distinct flow phenomena are observed. The first occurrs when dielectrophoresis starts to dominate diffusion over a certain magnitude of electric field, where “filaments” of low and high particle concentration appear in the flow. Depending on the angle between the electrodes and the    post    arrays    as    well    as    the    shape of the    posts    (cir

cular or square), flow with various concentration gradients is observed, which is identified as filamentary dielectrophoresis (Cummings and Singh, 2000; Cummings, 2001). The second phenomenon occurs at higher electric fields, where dilectrophoresis is comparable and greater than the advection and electrokinetic effects. These experiments have shown “trapping” of reversibly immobilized particles near the insulator surfaces, and this flow regime is identified as trapping dielectrophoresis (Cummings and Singh, 2000; Cummings, 2001). Figure 7.25 shows particle fluorescence image of filamentary (upper plot) and trapping (lower plot) dielectrophoresis in arrays of circular posts. Other experiments of Cummings, obtained under DC electric fields, were used to systematically analyze the electrokinetic, filamentary dielectrophoretic, and trapping dielectrophoretic transport in complex microgeometries (Cummings, 2001).

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