G. Q. Gu

Electrorotation in graded colloidal suspensions

Biological cells can be treated as composites of graded material inclusions. In addition to biomaterials, graded composites are important in more traditional materials science. In this paper, we investigate the electrorotation spectrum of a graded colloidal suspension in an attempt to discuss its dielectric properties. For that, we use the recently obtained differential effective dipole approximation and generalize it for nonspherical particles. We find that variations in the conductivity profile may make the characteristic frequency redshifted and have also an effect on the rotation peak. On the other hand, variations in the dielectric profile may enhance the rotation peak, but do not have any significant effect on the characteristic frequency. In the end, we apply our theory to fit experimental data obtained for yeast cells and find good agreement.

Dielectric response of graded spherical particles of anisotropic materials

Anisotropic dielectric response occurs naturally due to the presence of gradation, like in functionally graded materials or graded biological cells. However, these materials with locally anisotropic dielectric responses can have macroscopically isotropic responses. In treating graded particles of anisotropic materials, traditional isotropic gradation methods need to be modified. In this work, we developed a first-principles approach, as well as an anisotropic differential effective dipole approximation, for calculating the dipole moment of these particles. To this end, the two methods are shown in excellent agreement. As a result, these approaches offer convenient and effective ways to investigate the dielectric properties and optical responses of graded spherical particles of anisotropic materials, as well as the electrokinetic phenomena of biological cells.

Electrorotation of a pair of spherical particles

We present a theoretical study of electrorotation (ER) of two spherical particles under the action of a rotating electric field. When the two particles approach and finally touch, the mutual polarization interaction between the particles leads to a change in the dipole moment of the individual particle and hence the ER spectrum, as compared to that of the well-separated particles. The mutual polarization effects are captured by the method of multiple images. From the theoretical analysis, we find that the mutual polarization effects can change the characteristic frequency at which the maximum angular velocity of electrorotation occurs. The numerical results can be understood in the spectral representation theory.

Variational calculation of strongly nonlinear composites

Abstract A variational approach is used to study the effective response of a class of strongly nonlinear conducting composite media which obey a current-field relation of the form J =χ| E | 2 E , i.e. cubic nonlinearity. We use the various trial functions for the effective response of strongly nonlinear composite media with a low concentration of spherical as well as coated spherical inclusions.

Effective conductivity of composites of graded spherical particles

We have employed the first-principles approach to compute the effective response of composites of graded spherical particles of arbitrary conductivity profiles. We solve the boundary-value problem for the polarizability of the graded particles and obtain the dipole moment as well as the multipole moments. We provide a rigorous proof of an ad hoc approximate method based on the differential effective multipole moment approximation (DEMMA) in which the differential effective dipole approximation (DEDA) is a special case. The method will be applied to an exactly solvable graded profile. We show that DEDA and DEMMA are indeed exact for graded spherical particles.

ELECTROROTATION OF COLLOIDAL SUSPENSIONS

Abstract When a strong electric field is applied to a colloidal suspension, it may cause an aggregation of the suspended particles in response to the field. In the case of a rotating field, the electrorotation (ER) spectrum can be modified further due to the local field effects arising from the many-particle system. To capture the local field effect, we invoke the Maxwell–Garnett approximation for the dielectric response. The hydrodynamic interactions between the suspended particles can also modify the spin friction, which is a key to determine the angular velocity of ER. By invoking the spectral representation approach, we derive the analytic expressions for the characteristic frequency at which the maximum angular velocity of ER occurs. From the numerical calculation, we find that there exist two sub-dispersions in the ER spectrum. However, the two characteristic frequencies are so close that the two peaks actually overlap and become a single broad peak. We report a detailed investigation of the dependence of the characteristic frequency and the dispersion strength of ER on various material parameters.

Electrokinetic behavior of two touching inhomogeneous biological cells and colloidal particles: Effects of multipolar interactions

We present a theory to investigate electrokinetic behavior, namely, electrorotation and dielectrophoresis under alternating current (ac) applied fields for a pair of touching inhomogeneous colloidal particles and biological cells. These inhomogeneous particles are treated as graded ones with physically motivated model dielectric and conductivity profiles. The mutual polarization interaction between the particles yields a change in their respective dipole moments, and hence in the ac electrokinetic spectra. The multipolar interactions between polarized particles are accurately captured by the multiple images method. In the point-dipole limit, our theory reproduces the known results. We find that the multipolar interactions as well as the spatial fluctuations inside the particles can affect the ac electrokinetic spectra significantly.

Effective conductivity of strongly nonlinear composites: variational approach

Abstract A variational approach is used to study the effective response of a class of strongly nonlinear conducting composite media which obey a current-field relation of the form J = χ| E | 2 E . Various trial functions for the field distribution are used to establish explicit formulas for the effective response of strongly nonlinear composite media with a low concentration of cylindrical inclusions. The results are compared with the recently established bounds and estimates. We discuss the proper choice of trial functions and improve the approach by including more variational parameters. Moreover, we verify the approach by examining the local field distribution in composite media.

Relaxation of surface charge on rotating dielectric spheres: Implications on dynamic electrorheological effects.

We have examined the effect of an oscillatory rotation of a polarized dielectric particle. The rotational motion leads to a redistribution of the polarization charge on the surface of the particle. We show that the time-averaged steady-state dipole moment is along the field direction, but its magnitude is reduced by a factor that depends on the angular velocity of rotation. As a result, the rotational motion of the particle reduces the electrorheological effect. We further assume that the relaxation of the polarized charge is arised from a finite conductivity of the particle or host medium. We calculate the relaxation time based on the Maxwell-Wagner theory, suitably generalized to include the rotational motion. Analytic expressions for the reduction factor and the relaxation time are given and their dependence on the angular velocity of rotation will be discussed.

Electrostatic boundary-value problems of nonlinear media: a perturbation approach

Abstract We develop perturbation expansions to solve nonlinear partial differential equations pertaining to the electrostatic boundary-value problems of nonlinear media. As an example in two dimensions, we apply the method to deal with a cylindrical inclusion in a host, both of either linear or nonlinear current-voltage characteristics, and derive the zeroth, first and second order series in the nonlinear conductivity coefficient.