# Fluctuating stresslets and the viscosity of colloidal suspensions

## TL;DR

This paper reveals a previously unobserved discrepancy in colloidal suspension viscosity measurements, which is resolved by incorporating fluctuating Brownian stresses and non-fluctuating stresslets into the hydrodynamic model, ensuring consistency between different calculation methods.

## Contribution

It introduces an extended fluctuation-dissipation theorem that accounts for fluctuating Brownian stresses and non-fluctuating stresslets, improving viscosity measurement consistency in colloidal suspensions.

## Key findings

- Discrepancy between shear stress and Green-Kubo viscosity methods identified.
- Inclusion of fluctuating Brownian stresses resolves the discrepancy.
- Non-fluctuating stresslets are essential for consistent viscosity calculations.

## Abstract

Theory and simulation of Brownian colloids suspended in an implicit solvent, with the hydrodynamics of the fluid accounted for by effective interactions between the colloids, are shown to yield a marked and hitherto unobserved discrepancy between the viscosity calculated from the average shear stress under an imposed shear rate in the Stokesian regime and the viscosity extracted by the Green-Kubo formalism from the auto-correlations of thermal stress fluctuations in quiescent equilibrium. We show that agreement between both methods is recovered by accounting for the fluctuating Brownian stresses on the colloids, complementing and related to the traditional fluctuating Brownian forces and torques through an extended fluctuation-dissipation theorem based on the hydrodynamic grand resistance matrix. Time-averaging of the fluctuating terms gives rise to novel non-fluctuating stresslets. Brownian Dynamics simulations of spheroidal particles illustrate the necessity of these fluctuating and non-fluctuating contributions to obtaining consistent viscosities.