This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.In this study we present a universal theoretical formulation of the particle motions in electrophoretic and dielectrophoretic traps. It is extended from the well-known Mathieu equation based theories for Paul trap. The white noise random force model is utilized to form the Brownian motion of particle in the traps and the instantaneous dielectrophoretic force is employed rather than the time-averaged ponderomotive expression. The new approach enables many interesting properties of dielectrophoretic traps about stability and random motion. This study will be expected to provide a concrete protocol for the design of nanoscale traps which is essential in single molecule analysis
