There is great interest in trapping and manipulating small sized particles such as biological, glass, polymer and carbonaceous particles suspended in a liquid. One way to trap such micro/nano sized particles is by means of a microfluidic chamber equipped with electrodes at the bottom and thus generating conventional dielectrophoresis based on an electric field of spatially varying magnitude. In this work, we explore the use of traveling wave dielectrophoresis induced by an electric field of spatially varying phase, which offers both particle capturing/separation and transport capabilities (without having to pump the fluid itself). Particles are subjected to electrostatic and hydrodynamic forces and torques that are computed solving trie full equations of motion for both the fluid and the particles without any modeling (from first principles) and using a finite element scheme based on the Distributed Lagrange Multiplier (DLM) method. We consider two typical microfluidic channels (MEMS devices) with electrodes embedded in the bottom wall. It is found that the motion and destination of the particles strongly depend on the frequency dependent complex Clausius-Mossotti factor (the mismatch between the particles and fluid electric properties), and that the hydrodynamic and electrostatic particle-particle interactions play a crucial role on the particles dynamics. These conclusions are demonstrated on model particles having the properties of yeast cells.