A mathematical model and numerical techniques are proposed to study AC electric field induced cellular assembly in a microfluidic device. In the mathematical model, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, the proposed model eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. The numerical method is based on hybrid immersed boundary-immersed interface methods. An immersed boundary method is used for the fluid equations and particle transport, while an immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles. For the immersed interface method, an iterative algorithm is developed to solve the complex Poisson equation using a real variable formulation. The decoupled algorithm for solving complex differential equations converges rapidly. The hybrid method is used to investigate the physics of AC dielectrophoresis in a cross-channel junction. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis.

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