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Colloidal dispersions are common in nature with wide industrial applications. One of the central theoretical problems in the field is to determine the rheological properties of the colloidal dispersion from the microstructures of the systems. Because of the difficulties associated with the boundary-value problems of the many-particle system, existing theories for colloidal suspensions are limited to low particle concentrations. In this work, a method of transformation field is developed by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops). The predictions of the theory are in good agreement with the Einstein's formula for suspensions and the Taylor's formula for emulsions at low particle concentrations. At higher particle concentrations, the results of Nunan and Keller are produced. The method is also applicable to the viscosity of colloidal systems with non-spherical particles.

The homotopy continuation method is employed to solve electrostatic boundary-value problems of nonlinear media. The difficulty associated with matching the inherently nonlinear boundary conditions on the interface is overcome by the mode expansion method, by which the nonlinear partial differential equations of the original problem are transformed into an infinite set of nonlinear ordinary differential equations. In this regard, the homotopy method has to be modified to handle the nonlinear boundary conditions. As an illustration, we study two cases:(a) nonlinear inclusion in linear host and (b) linear inclusion-in nonlinear host, both in two dimensions. The homotopy method is validated by comparing the results with the exact solution of case (a) and the results derived by perturbation method in case (b).

We have investigated the effect of particle shape on the eletrorotation (ER) spectrum of living cells suspensions. In particular, we consider coated oblate spheroidal particles and present a theoretical study of ER based on the spectral representation theory. Analytic expressions for the characteristic frequency as well as the dispersion strength can be obtained, thus simplifying the fitting of experimental data on oblate spheroidal cells that abound in the literature. From the theoretical analysis, we find that the cell shape, coating as well as material parameters can change the ER spectrum. We demonstrate good agreement between our theoretical predictions and experimental data on human erthrocytes suspensions., RevTex; 5 eps figures

Recent experiments revealed that the dielectric dispersion spectrum of fission yeast cells in a suspension was mainly composed of two sub-dispersions. The low-frequency sub-dispersion depended on the cell length, while the high-frequency one was independent of it. The cell shape effect was simulated by an ellipsoidal cell model but the comparison between theory and experiment was far from being satisfactory. Prompted by the discrepancy, we proposed the use of spectral representation to analyze more realistic cell models. We adopted a shell-spheroidal model to analyze the effects of the cell membrane. It is found that the dielectric property of the cell membrane has only a minor effect on the dispersion magnitude ratio and the characteristic frequency ratio. We further included the effect of rotation of dipole induced by an external electric field, and solved the dipole-rotation spheroidal model in the spectral representation. Good agreement between theory and experiment has been obtained., 19 pages, 5 eps figures

This paper investigates analytically the electric field distribution of graded spherical core-shell metamaterials, whose permittivity is given by the graded Drude model. Under the illumination of a uniform incident optical field, the obtained results show that the electrical field distribution in the shell region is controllable and the electric field peak's position inside the spherical shell can be confined in a desired position by varying the frequency of the optical field as well as the parameters of the graded dielectric profiles. It has also offered an intuitive explanation for controlling the local electric field by graded metamaterials.

The optical properties are investigated numerically in infrared (IR) regions for GaAs/AlAs corrugated lateral surface superlattices (CLSSLs) with short lateral periods. The calculations are carried out for refractive indexes and optical absorption coefficients with and without inclusion of electron interactions in an attempt to study the effects of intersubband plasmons on the IR optical properties of CLSSLs. As lateral periods of CLSSLs increase from 10 nm to 30 nm, their IR optical properties change from the behavior dominated by single electron transitions between conduction subbands to those dominated by intersubband plasmon excitations. Strong and sharp peaks in the optical absorption coefficients, large variations of the refractive indexes and strong anisotropic optical properties of CLSSLs are predicted in IR regions.