Multipole polarizability of a graded spherical particle

TL;DR

This paper introduces a new differential effective multipole moment approximation (DEMMA) method to accurately compute the multipole polarizability of graded spherical particles in nonuniform electric fields, relevant for non-dilute suspensions.

Contribution

The paper presents the DEMMA method for calculating multipole moments of graded particles, validated against exact solutions for power-law profiles, advancing modeling of complex suspensions.

Findings

DEMMA accurately predicts multipole moments for graded particles.

Excellent agreement with exact solutions for power-law profiles.

Potential extension to anisotropic particles discussed.

Abstract

We have studied the multipole polarizability of a graded spherical particle in a nonuniform electric field, in which the conductivity can vary radially inside the particle. The main objective of this work is to access the effects of multipole interactions at small interparticle separations, which can be important in non-dilute suspensions of functionally graded materials. The nonuniform electric field arises either from that applied on the particle or from the local field of all other particles. We developed a differential effective multipole moment approximation (DEMMA) to compute the multipole moment of a graded spherical particle in a nonuniform external field. Moreover, we compare the DEMMA results with the exact results of the power-law graded profile and the agreement is excellent. The extension to anisotropic DEMMA will be studied in an Appendix.