Dimensional analysis and prediction of dielectrophoretic crossover frequency of spherical particles

The manipulation of biological cells and micrometer-scale particles using dielectrophoresis (DEP) is an indispensable technique for lab-on-a-chip systems for many biological and colloidal science applications. However, existing models, including the dipole model and numerical simulations based on Maxwell stress tensor (MST), cannot achieve high accuracy and high computation efficiency at the same time. The dipole model is widely used and provides adequate predictions on the crossover frequency of submicron particles, but cannot predict the crossover frequency for larger particles accurately; on the other hand, the MST method offers high accuracy for a wide variety of particle sizes and shapes, but is time-consuming and may lack predictive understanding of the interplay between key parameters. Here we present a mathematical model, using dimensional analysis and the Buckingham pi theorem, that permits high accuracy and efficiency in predicting the crossover frequency of spherical particles. The curve fitting and calculation are performed using commercial packages OriginLab and MATLAB, respectively. In addition, through this model we also can predict the conditions in which no crossover frequency exists. Also, we propose a pair of dimensionless parameters, forming a functional relation, that provide physical insights into the dependency of the crossover frequency on five key parameters. The model is verified under several scenarios using comprehensive MST simulations by COMSOL Multiphysics software (COMSOL, Inc.) and some published experimental data. (C) 2017 Author(s).