Active, Reactive, and Apparent Power in Dielectrophoresis: Force Corrections from the Capacitive Charging Work on Suspensions Described by Maxwell-Wagner's Mixing Equation.

Jan Gimsa

doi:10.3390/mi12070738

Abstract

A new expression for the dielectrophoresis (DEP) force is derived from the electrical work in a charge-cycle model that allows the field-free transition of a single object between the centers of two adjacent cubic volumes in an inhomogeneous field. The charging work for the capacities of the volumes is calculated in the absence and in the presence of the object using the external permittivity and Maxwell-Wagner’s mixing equation, respectively. The model provides additional terms for the Clausius-Mossotti factor, which vanish for the mathematical boundary transition toward zero volume fraction, but which can be interesting for narrow microfluidic systems. The comparison with the classical solution provides a new perspective on the notorious problem of electrostatic modeling of AC electrokinetic effects in lossy media and gives insight into the relationships between active, reactive, and apparent power in DEP force generation. DEP moves more highly polarizable media to locations with a higher field, making a DEP-related increase in the overall polarizability of suspensions intuitive. Calculations of the passage of single objects through a chain of cubic volumes show increased overall effective polarizability in the system for both positive and negative DEP. Therefore, it is proposed that DEP be considered a conditioned polarization mechanism, even if it is slow with respect to the field oscillation. The DEP-induced changes in permittivity and conductivity describe the increase in the overall energy dissipation in the DEP systems consistent with the law of maximum entropy production. Thermodynamics can help explain DEP accumulation of small objects below the limits of Brownian motion.

Highlights

Up to the high radio frequency range, polarization processes in complex media, such as particle suspensions, are classified either by their electric mechanisms such as polarizations of electric double layers, of structural interfaces (Maxwell-Wagner) and of molecular dipoles through orientation (Debye) or by the frequency range in which they disperse [1,2,3]
The DEP force was derived from the electrical charge work of a single-object suspension
Its permittivity has been described by the Maxwell-Wagner mixing equation, which contains the volume fraction but not the number of objects that show the ponderomotive character, i.e., the volume character of the DEP force

Summary

Introduction

Up to the high radio frequency range, polarization processes in complex media, such as particle suspensions, are classified either by their electric mechanisms such as polarizations of electric double layers, of structural interfaces (Maxwell-Wagner) and of molecular dipoles through orientation (Debye) or by the frequency range in which they disperse (alpha, beta, and gamma dispersions) [1,2,3]. Slower processes disperse and their contributions to medium polarization fade, which is reflected in a frequency-dependent permittivity decrease and the corresponding increase of the complex (specific) conductivity σ in S/m by up to several orders of magnitude over several frequency decades (complex parameters are underscored). This behavior is described mathematically by the dispersion relation, which considers the field-induced motion of bound charges, which at high frequencies cannot be distinguished from the motion of charges, such as ions, which can already move freely under DC. While neighboring objects of even polarizability are attracted toward one another, they are attracted or repelled toward electrode surfaces depending on the electrode and object shapes and the object’s polarizability relative to that of the suspension medium

Results

Discussion

Conclusion