Trajectories and Forces in Four-Electrode Chambers Operated in Object-Shift, Dielectrophoresis and Field-Cage Modes—Considerations from the System’s Point of View

In two previous papers, we calculated the dielectrophoresis (DEP) force and corresponding trajectories of high- and low-conductance 200-µm 2D spheres in a square 1 × 1-mm chamber with plane-versus-pointed, plane-versus-plane and pointed-versus-pointed electrode configurations by applying the law of maximum entropy production (LMEP) to the system. Here, we complete these considerations for configurations with four-pointed electrodes centered on the chamber edges. The four electrodes were operated in either object-shift mode (two adjacent electrodes opposite the other two adjacent electrodes), DEP mode (one electrode versus the other three electrodes), or field-cage mode (two electrodes on opposite edges versus the two electrodes on the other two opposite edges). As in previous work, we have assumed DC properties for the object and the external media for simplicity. Nevertheless, every possible polarization ratio of the two media can be modeled this way. The trajectories of the spherical centers and the corresponding DEP forces were calculated from the gradients of the system’s total energy dissipation, described by numerically-derived conductance fields. In each of the three drive modes, very high attractive and repulsive forces were found in front of pointed electrodes for the high and low-conductance spheres, respectively. The conductance fields predict bifurcation points, watersheds, and trajectories with multiple endpoints. The high and low-conductance spheres usually follow similar trajectories, albeit with reversed orientations. In DEP drive mode, the four-point electrode chamber provides a similar area for DEP measurements as the classical plane-versus-pointed electrode chamber.