Control-oriented model of dielectrophoresis and electrorotation for arbitrarily shaped objects

International audience"The most popular modeling approach for dielectrophoresis (DEP) is the effective multipole (EM) method. Yet nowadays, in an unrestricted source electric field, a general multipolar description of the potential caused by their charge distribution is only available for spherical objects. We present a method for computing such multipolar representation of arbitrarily shaped objects polarized by arbitrary electric fields. The method is based on numerical solutions of Laplace equation for the potential and the orthonormality of spherical harmonics. We show how the superposition principle holding for the potential can be utilized to construct a basis of solutions, from which the total potentical can be composed in real time. It is then possible to calculate the DEP forces and torques for arbitrarily shaped objects under the influence of arbitary electric fields in fractions of a second, which is needed in model-based control applications. This contrasts with the Maxwell stress tensor-based numerical method. We validate the proposed method against reference numerical solutions and analyse the importance of the higher-order multipolar moments using a sample case of a Tetrisshaped micro-object placed inside a quadrupolar micro-electrode array and exposed to electrorotation. The implementation of the model in Matlab and Comsol are offered for free download.