Influence of scale on electrostatic forces and torques in AC particulate electrokinetics

Dielectrophoretic forces and torques move and manipulate biological cells, typically of the order of 10 μm (∼10^-5 m) in diameter and ordinarily suspended in aqueous liquids, using electrodes with dimensions around 100 μm (∼10^-4 m). The ability to exploit these same electromechanical effects for particles below 1 μm, that is, <10^-6 m, creates opportunities for remote manipulation and handling of subcellular components, biological macromolecules, and DNA. In this paper, Trimmer´s bracket notation (1989) is adapted for systematic examination of the scaling laws governing electrokinetic behaviour. The purpose is to shed light on how critical performance measures relevant to the laboratory on a chip are affected by reducing particle sizes and electrode dimensions into the nanometre range. The scaling methodology facilitates consideration of the effect of electrode structure and particle size reduction on voltage, electric field, heating, and response time. Particles with induced moments, dipolar and quadrupolar, as well as permanent dipoles are examined. Separate consideration is given to electrical torque and its application in electrorotation and particle alignment. An eventual goal of these scaling studies is to identify the lower limit on the size of particles that can be manipulated effectively using electrokinetic phenomena.