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

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 semiflexible 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 nonuniform spatial velocity profiles have been observed in experiments. We analyze 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 behavior 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.

Microstructural evolution and reverse flow in shear-banding of entangled polymer melts

“…Shear banding is a nonlinear response of viscoelastic materials that manifests as the spatial variation in viscosity and the localization of strain rate along the flow gradient direction. [1][2][3][4] It has been extensively investigated both theoretically and experimentally, as a variety of materials exhibit this behavior, including entangled polymer solutions and melts, [5][6][7][8] wormlike micelles, [9][10][11] liquid crystals, [12][13][14] glassy materials, [15][16][17] and biphasic liquids. 18 Reptation theory predicts a steady-state shear-banding instability and associates it with the nonmonotonic constitutive shear stress versus strain rate flow curve.…”

“…Adams and Corbert also illustrated a similar prediction of a recoiled velocity profile, i.e., reverse flow, in liquid crystalline polymers using a nematic dumbbell model. 12 Although a negative velocity gradient has been observed experimentally and predicted by continuum-level stability analysis, the molecular-level mechanism associated with this phenomenon has not been thoroughly investigated. To that end, it is reasonable to conjecture that this phenomenon is molecular-weight dependent and is associated with a dramatic change in polymer conformation at the onset of the inhomogeneity.…”