Magnetization of concentrated polydisperse ferrofluids: Cluster expansion

TL;DR

This paper develops a cluster expansion method to calculate the equilibrium magnetization of concentrated polydisperse ferrofluids, extending previous monodisperse models to account for particle size distribution and interactions.

Contribution

It introduces a power series expansion approach for polydisperse ferrofluids, generalizing earlier monodisperse results to more realistic systems with particle size variation.

Findings

Magnetization expressed as a power series in volume fraction and interaction strength.

Extension of previous monodisperse models to polydisperse ferrofluids.

Provides analytical tools for predicting magnetization in concentrated ferrofluids.

Abstract

The equilibrium magnetization of concentrated ferrofluids described by a system of polydisperse dipolar hard spheres is calculated as a function of the internal magnetic field using the Born--Mayer or cluster expansion technique. This paper extends the results of Phys. Rev. E 62, 6875 (2000) obtained for monodisperse ferrofluids. The magnetization is given as a power series expansion in two parameters related to the volume fraction and the coupling strength of the dipolar interaction, respectively.