# Experimental Realization of the Green-Kubo Relation in Colloidal Suspensions Enabled by Image-based Stress Measurements

## TL;DR

This study experimentally verifies the Green-Kubo relation in colloidal suspensions by using a novel image-based stress measurement technique, enabling precise stress fluctuation analysis and viscosity determination in 3D colloidal liquids.

## Contribution

We developed a non-invasive method combining confocal microscopy and SALSA to measure stresses in 3D colloids, validating the Green-Kubo relation for nearly hard-sphere suspensions.

## Key findings

- Green-Kubo relation accurately predicts viscosity in colloidal suspensions.
- Our method measures forces as low as 50 fN with high spatial resolution.
- Results agree with simulations and traditional rheometry.

## Abstract

By combining confocal microscopy and Stress Assessment from Local Structural Anisotropy (SALSA), we directly measure stresses in 3D quiescent colloidal liquids. Our non-invasive and non-perturbative method allows us to measure forces $\lesssim$ 50 fN with a small and tunable probing volume, enabling us to resolve the stress fluctuations arising from particle thermal motions. We use the Green-Kubo relation to relate these measured stress fluctuations to the bulk Brownian viscosity at different volume fractions and comparing against simulations and conventional rheometry measurements. We demonstrate that the Green-Kubo analysis gives excellent agreement with these prior results. This agreement provides a strong demonstration of the applicability of the Green-Kubo relation in nearly hard-sphere suspensions and opens the door to investigations of local flow properties in many poorly understood far-from-equilibrium systems, including suspensions that are glassy, strongly-sheared, or highly-confined.