Transient flow of viscoelastic, thixotropic fluid in a vane rheometer or infinite slot

Abstract

Transient flow of a thixotropic viscoelastic fluid in a wide-gap Searle (or vane) viscometer is modelled using the MBM constitutive relation (E. Boek, J. Padding, V. Anderson, P. Tardy, J. Crawshaw, J.R.A. Pearson, Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model, J. Non-Newton. Fluid Mech., 126 (2005) 39–46), which predicts that in steady shear flow the shear stress is proportional to shear rate at very low shear rates. Thus the fluid does not possess a yield stress. After the inner rotor starts to rotate, from rest, at constant speed, the wall shear stress increases to a maximum before decaying to a final steady value. The non-monotonic variation in stress is caused by changes in the fluid structure, which occur on a different timescale to that for relaxation of elastic stress. Such a stress maximum is commonly observed in vane studies of thixotropic fluids with a yield stress, but the numerical simulations for the MBM fluid show that the stress maximum depends upon the velocity of the rotor and therefore should not be interpreted as a yield stress. The final steady stress is independent of rotation rate over a wide range of rates, and reflects the intermediate range of shear rates for which the MBM fluid exhibits a steady shear stress plateau. This might (erroneously) be interpreted as a yield stress in the absence of measurements at sufficiently low shear rates. The numerical scheme is based on a set of ordinary differential equations, and with minor modification can be applied to transient flow in an infinitely long, two-dimensional channel. Shear bands do not occur in steady flow, since the steady shear stress increases monotonically with shear rate. However, if thin regions of high shear rate are introduced artificially, they are long-lived.