A direct numerical simulation method for complex modulus of particle dispersions

TL;DR

This paper extends a numerical simulation method to calculate the complex shear modulus of particle dispersions by introducing oscillatory forces, validated across various particle concentrations and frequencies.

Contribution

The paper introduces a novel extension of the smoothed profile method to compute complex moduli under oscillatory shear, enabling detailed rheological analysis of particle dispersions.

Findings

Validated the method for different particle volume fractions.

Accurately evaluated storage and loss moduli across frequencies.

Demonstrated consistency with expected rheological behavior.

Abstract

We report an extension of the smoothed profile method (SPM)[Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E {\bf 26}, 361(2008)], a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage $G'(\omega)$ and loss $G"(\omega)$ moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of $\Phi=0$, 0.41, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions.