An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence

Recent experiments suggest that short fibers in concentrated suspensions align more slowly as a function of strain than models based on Jeffery’s equation predict. We develop an objective model that captures the slow orientation kinetics exhibited by short-fiber suspensions. The standard moment-tensor equation of fiber orientation is used to find equations for the change rates of the eigenvalues and eigenvectors of the orientation tensor. As a phenomenological assumption, the growth rates of the eigenvalues are reduced by a constant scalar factor, while the rotation rate expressions for the eigenvectors are unchanged. The eigenvalue/eigenvector equations are then reassembled as a tensor equation. An equivalent kinetic theory is also developed. The new model is tested in a variety of flows, and found to exhibit slower kinetics than the standard model but similar steady-state orientations. The model provides an excellent fit to the shear stress transient in a shear reversal experiment with a 30% glass fiber filled polybutylene terephthalate resin melt, and we show how this experiment can be used to determine the parameters of the model.