  We provide an explicit analytical solution of the planar Poiseuille flow of a
viscoplastic fluid governed by the constitutive equation proposed by De Kee and
Turcotte (Chem. Eng. Commun. 6 (1980) 273-282). Formulae for the velocity and
the flow rate are derived, making use of the Lambert W function. It is shown
that a solution does not always exist because the flow curve is bounded from
above and hence the rheological model can accommodate stresses only up to a
certain limit. In fact, the flow curve reaches a peak at a critical shear rate,
beyond which it exhibits a negative slope, giving rise to unstable solutions.
