An experimental determination of the stress–microstructure relationship in semi-concentrated fiber suspensions

Abstract

The relationship between the stress and the fiber orientation distribution in semi-dilute ( nL 3⪢1, nL 2 d<1) and semi-concentrated ( nL 2 d>1) fiber suspensions was investigated. Here, n is the fiber number density, L the length, and d is the diameter. A highly viscous, index-matched suspension was developed to permit measurements of both the microstructure and rheology using the same suspension. By removing the ambiguity of comparing data taken using different suspending fluids and fibers, a more accurate evaluation of available stress–structure models was made possible. The measured period of rotation and the distribution among Jeffery orbits were compared to the results of a theory for hydrodynamic fiber interactions and a simulation incorporating mechanical contacts. At low concentrations, the period increased above the dilute, Jeffery value. As the fiber loading was increased, the period peaked and decreased to approach the dilute result. The distribution of orbits shifted slightly towards the vorticity axis with increasing concentration. The inclusion of a nematic potential in the hydrodynamic theory provided a possible explanation for the decrease in the period of rotation. Measurements of the viscosity and first normal stress differences of the same suspensions were compared to theoretical predictions based on the orientation results. The measured viscosity was in good agreement with the mechanical contact simulation results but was much larger than predicted by hydrodynamic theories. The high viscosity and the measurement of significant first normal stress differences are suggestive of an enhanced stress resulting from the presence of fiber–fiber contacts.