Dielectrophoresis (DEP) has been extensively used in lab-on-a-chip systems for trapping, separating, and manipulating of micro particles suspended in a liquid medium. The most widely used analytic model, the dipole model, provides an accurate prediction on the crossover frequency of submicron particles, but cannot explain the significant drop in crossover frequency of larger particles. Here, we present numerical simulations using the Maxwell stress tensor (MST) and finite element method to study the size effect of the DEP crossover frequency of spherical polystyrene particles suspended in de-ionized water. Our results show that the surface conductance due to the electrical double layer plays a key role, and the size dependency of crossover frequency obtained by the MST method agrees reasonably well with published experimental data. The exponents of the power law are approximately -1.0 and -4.3 for smaller (diameter < 4.6 μm) and larger particles (diameter > 4.6 μm), respectively. The free surface charge distribution reveals that the charge begins accumulating on the particle equator for particle diameters larger than a critical diameter of 4.6 μm, a result not captured by the dipolar approximation. This method may be extended to analyze bioparticles with complex shapes and composition, and provides new insights into the interpretation of dielectrophoresis applications using lab-on-a-chip systems.

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.

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