Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

TL;DR

This paper investigates the transient shear banding phenomena in nematic liquid crystalline polymers using an extended nematic dumbbell model, revealing flow instabilities and inhomogeneous velocity profiles during shear flow.

Contribution

It introduces a gradient term into the ND model and performs a linear stability analysis to predict flow inhomogeneities in LCPs under shear.

Findings

Transient flow instability to inhomogeneous velocity profiles.

Flow reversal behavior varies with shear rate.

Inhomogeneous flow predicted during flow reversal experiments.

Abstract

In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials, but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semi-flexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly non-uniform spatial velocity profiles have been observed in experiments. We analyse the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress, and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behaviour of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.