An accelerated boundary element method (BEM) is proposed for predicting the motion of bio-particles under combined electromagnetic and fluidic force fields. Many Lab-on-chip (LoC) designs are based on dielectrophoretic (DEP) manipulation of polarized species inside microfluidic channels. The BEM approach presented here relies entirely on modeling the surface of the computational domain, significantly reducing the number of unknowns when compared to volume-based methods. Additionally, the need for re-meshing the whole domain at each time-step of particle movement is prevented. A coupled circuit-EM formulation is presented for accurate prediction of dielectophoretic field distribution due to on-chip electrodes. This allows the circuit control of the resulting electromagnetic fields. Next, BEM formulations for predicting DEP and fluidic traction forces on arbitrarily shaped bio-particles are presented. EM fields produced by the electrodes induce the DEP forces, while the fluid flow is driven by a pressure gradient across the channel. The resultant motion of the subjected particles is studied using a simple time-stepping algorithm. The algorithm has a time complexity of O(N3), where N is the number of unknowns), which leads to a large bottleneck during simulation of each time step. This problem is addressed by implementing oct-tree based O(N) multilevel iterative solvers. The methodology is used to study the field distribution due to distributed electrode systems and particle motion in fluidic channels. Evidence of O(N) behavior of the fast solver is presented. The resulting simulator can be used to study complicated distributed structures and explore new LoC design ideas.

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