Flow-history-dependent orientational relaxation in dilute polydisperse colloidal rod suspensions

TL;DR

This study investigates how flow history influences the orientation relaxation of polydisperse rod-like colloids, revealing that pre-shear rate and polydispersity jointly determine relaxation times.

Contribution

We developed a polydisperse Fokker-Planck model and experimentally validated how flow history affects orientation relaxation in dilute CNC suspensions.

Findings

Average relaxation time decreases with higher pre-shear rate.

Data aligns with theory when using Péclet number based on weighted average rod length.

Flow history shifts dominant contribution from longer to shorter rods.

Abstract

Orientation and relaxation dynamics of rod-like colloids under flow govern the optical and mechanical properties of many emerging soft materials. In polydisperse suspensions, particles of different lengths exhibit distinct rotational diffusion timescales, yet how this polydispersity influences relaxation following flow cessation remains unclear. In particular, it is not well understood how the pre-shear rate determines the subsequent orientation relaxation dynamics. To address this question, we performed simple shear on dilute cellulose nanocrystal (CNC) suspensions in a narrow-gap Taylor-Couette cell and measured birefringence relaxation after flow cessation using high-speed polarization imaging. To interpret the experiments, we formulated a polydisperse Fokker-Planck model parameterized by the measured length distribution. As a result, the average orientation relaxation time systematically decreases with increasing pre-shear rate. Moreover, when organized by the P\'{e}clet number based on the rotational diffusion coefficient of the weighted average rod length, the data agree well with the theory over a wide range of shear rates. This trend arises because the rod sub-population contributing most strongly to the orientation shifts from longer rods to shorter rods as the pre-shear rate increases, showing that the flow history governs the orientation relaxation dynamics. In polydisperse systems, the orientation relaxation time is no longer a material-specific constant but is determined by both the flow conditions and the polydispersity. This study provides a quantitative framework for understanding orientation dynamics in polydisperse rod suspensions and for interpreting rheo-optical measurements.