This paper considers the electrophoretic motion of a circular particle in a T-shaped slit microchannel, where the size of the channel is close to that of the particle. During the process, the electric field (i.e., the gradient of the electric potential) changes with the particle motion, which in return influences the flow field and the particle motion. Therefore, the electric field, the flow field and the particle motion are coupled together, and this is an unsteady process. The objective is to obtain a fundamental understanding of the characteristics of the particle motion in the complicated T-shaped junction region. Such influences on the electric field and the particle motion are investigated as the applied electric potentials, the geometry of the channel and the size of the particle. In the theoretical analysis, the liquid phase is divided into the inner region and the outer region. The inner region consists of the electrical double layers and the outer region consists of the remainder of the liquid. Under the assumption of thin electrical double layer, a mathematical model governing the inner region, the outer region and the particle motion is developed. A direct numerical simulation method using the finite element method is employed. In this method, a continuous hydrodynamic model is adopted. By this model, both the liquid phase in the outer region and the particle phase are governed by the same momentum equations. ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field is influenced by the applied electric potentials, the geometry of the channel and the particle suspension, and that the particle motion is mainly dominated by the local electric field. It is also found that the magnitude of the particle motion is dependent on its own size in the same channel.
