FAST METHODS FOR PARTICLE DYNAMICS IN DIELECTROPHORETIC BIOCHIPS Indranil Chowdhury * , Xiren Wang * and Vikram Jandhyala * ACELAB, Electrical Engineering, University of Washington, USA, burunc@u.washington.edu , xrwang@u.washington.edu , vj@u.washington.edu ABSTRACT This paper introduces a Schur-complement based boundary element method (BEM) for predicting the motion of arbitrarily shaped three-dimensional particles under combined external and fluidic force fields. 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. In addition, the Schur complement based scheme leads to a huge reduction in solution time during time- stepping in the microfluidic domain. Parallelized oct-tree based O(N) multilevel iterative solvers are used to accelerate the setup and solution costs. Keywords: BEM, cell-handling devices, microfluidics 1 INTRODUCTION Many lab-on-chip (LoC) devices use dielectrophoretic (DEP) manipulation of polarized species inside microfluidic channels [1-3]. Understanding the fluidic and electromagnetic forces in these devices require rigorous treatment of the underlying physics. BEM based system matrix is dense in nature due to the highly coupled interaction between the wall and the particles, especially when the particle size is comparable to that of the channels (Fig. 1). Conventionally, the numerical treatment of such systems is achieved via brute-force computation of the whole fluidic domain during each time-step of the iteration. Hence, during computation of the motion of rigid or deformable particles a large number of time steps are required, where each time step consists of a computationally expensive solution of a dense matrix system. Previous work on Lab-on-chip modeling has been mainly based on finite-element and volume based methods [3-6,9]. The problem with these methods lie in the fact that they need to remesh the whole channel for each time step, while in BEMs only the surface is meshed, which significantly reduces the number of unknowns [6, 17, 18]. Here a scheme based on Schur-complement is presented to accelerate the time-stepping algorithm by partially decoupling wall-particle interactions. Particle motion can be predicted for arbitrarily shaped three-dimensional particles under combined external and fluidic force fields. Parallelized oct-tree based O(N) multilevel iterative solvers are used to accelerate the setup and solution costs [12-16]. In the past BEM techniques have been used to study low Re flows [8, 17], however, fast algorithms for dynamic systems remain a topic of active research [10]. Besides the fluidic fields, DEP fields are produced by on-chip electrodes. A coupled circuit-EM formulation is used for accurate prediction of DEP field distribution that allows circuit control of resulting electromagnetic fields [11] (fig 5). Simulations of particle trajectory in pressure-driven dielectrophoretic LoCs are presented. Evidence of applications of the current methodology to a large class of flow devices [7] for particle transport is presented. 2 INTEGRAL EQUATIONS The integral representation for incompressible Stokes flow are given by the following expressions [17,18]: 0 0 0 1 ( ) ( , ) ( ) ( ) 4 1 ( ) ( , ) ( ) ( ) 4 i ij j D PV j ijk k D u G f dS u T n dS πμ π - = + ∫ ∫ x x x x x x x x x x No-slip and pressure boundary conditions are applied on the surface of the channel, while force and torque balance equations are setup for rigid particles, ext dS F σ = ∫ i  ( ) ext r dS T σ × = ∫ i  ; particle u U r = +Ω× U and Ω are the translation and angular velocities. The external forces and torques can be DEP fields for example. The surface of the domain is discretized using triangular patches and subsequently a collocation method is used for solving the unknown traction and velocity fields. The particle velocities can be solved at each time step and the resulting trajectory can be encountered for. However solving the whole dense matrix system for each time step becomes prohibitively expensive and an algorithm to reduce this cost is described below. The first step in this algorithm is the isolation of the particle under study and is achieved by identifying the patches belonging to the mathematical surface bounding the particle p S . This surface isolates the problem into two parts – a subset of the problem which is constant over time NSTI-Nanotech 2008, www.nsti.org, ISBN 978-1-4200-8505-1 Vol. 3 497