The analysis of the movement of particles in a nonuniform field requires accurate knowledge of the electric field distribution. In this letter, the Schwarz-Christoffel mapping method is used to analytically solve the electric field distribution in a dielectrophoretic focusing electrode structure. The analytical result for the electric field distribution is validated by comparison with numerical simulations using the finite element method. The electric field solution is used to calculate the dielectrophoretic force on a particle in the system. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2916827͔ Dielectrophoresis ͑DEP͒ 1-3 is one of the ac electrokinetic techniques where the interaction between a fieldinduced dipole moment on the particle and a nonuniform electric field produces a force on the particle. Since the dielectrophoretic forces are generated from the interaction between the electric field and the induced dipole, it is important to characterize the strength and direction of the electric field distribution in the system.In this work, we use the Schwarz-Christoffel mapping ͑SCM͒ method 4-7 to calculate the electric field generated by the dielectrophoretic focusing electrode structure shown in Fig. 1͑a͒. By using negative DEP ͑nDEP͒, the particles are repelled from the electrode edges and focused into a tight stream in the channel center. [8][9][10][11] Since the electrodes are long compared to their width, the electric field analysis can be performed through a cross section of the device, 9 as shown in Fig. 1͑b͒. Since the electrodes are much thinner than their width, they can be represented as a section of the bottom boundary at a fixed potential. The Neumann boundary condition ͑insulating͒ is used for the potential at the electrolyte/ glass interfaces. 6,12,13 Applying symmetry, only a quarter of the system ͑ABCDEF͒ needs to be solved in the analysis. Figure 1͑c͒ shows the three complex planes used for the SCM procedure. The selected cell ABCDEF is rotated 90°a nd set in the Z plane with the boundary conditions for as shown: ץ / ץn = 0, along the insulating walls BC, CD, and EF. Dirichlet boundary conditions define the fixed potential = V along the electrode ͑DE͒ and the boundary for the axis of the odd symmetry, =0 ͑AF and AB͒. The interior of the polygon ABCDEF in the Z plane is mapped into the upper half of the T plane by using the SCM method. The polygon ABCDEF is opened at point G and the boundaries of the polygon mapped to the real axis of the T plane. The coordinates of the corresponding points Z A -Z F in the T plane are T A -T F , respectively. The point G is mapped to positive and negative infinities. The SCM integral 14 from the T plane to the Z plane is given by