Dielectrophoretic Trapping of Particles

The dielectrophoretic force F gp can be used to trap dielectric particles suspended in microfiu-idic channel. An inhomogeneous electric field is created in a microchannel by charging carefully shaped metal electrodes at the walls of the channel. Dielectric particles suspended in the liquid flowing through the microchannel are attracted to the electrodes. The particles get trapped by the electrodes if the DEP force Fpgp is stronger than the viscous drag force F rag  

The microfluidic channel is rectangular with length L, width w, and height h. The channel in the flat and wide channel limit w can be approximated by the inflnite parallel plate channel. The origin of the coordinate system is placed at the center of the floor wall such that -L/2 x L/2,-w/2 y w/2, and 0 z h. A pressure drop of Ap along the channel results in the flow profile given as 

The dielectric particles suspended in the liquid have radius R. One can approximate the drag force acting on a sphere trapped at the position r using the Stokes flow assumption as 

The planar top electrode with potential (pQie ) = 0 has been realized by placing a mirror electrode with the potential (f)(2he2) = -AV at r = 2he2. The above equation shows the potential to be equal to zero at r = 2he. The trapping of particles takes place close to the spherical electrode, that is, r h. The electrical field is given approximately in this region as 

Using the electrical field equation (6.210), one can derive an expression for the DEP force using equation (6.205) as 

---