Flow curves are based on uniform steady simple shear flow, whether in
Couette or Poiseuille realizations. It is still often argued by many a
uthors that, for rheologically simple fluids, a maximum in a flow curv
e is inadmissible on physical grounds. A simple thixotropic (isotropic
viscous) constitutive model, based on a simple structure parameter, w
hich includes yield stress and which is known experimentally to be rea
listic for gelling suspensions, is shown to predict such maxima. Chang
es in either stress or flow rate, as in startup, lead to unsteady flow
s, whose ultimate steady-state nature are history dependent. This hist
ory dependence can be removed by introducing a term in the conservatio
n equations to represent diffusion of structure.