  The blood protein Von Willebrand Factor (VWF) is critical in facilitating
arterial thrombosis. At pathologically high shear rates the protein unfolds and
binds to the arterial wall, enabling the rapid deposition of platelets from the
blood. We present a novel continuum model for VWF dynamics in flow based on a
modified viscoelastic fluid model that incorporates a single constitutive
relation to describe the propensity of VWF to unfold as a function of the
scalar shear rate. Using experimental data of VWF unfolding in pure shear flow,
we fix the parameters for VWF's unfolding propensity and the maximum VWF
length, so that the protein is half unfolded at a shear rate of approximately
5,000 s$^{-1}$. We then use the theoretical model to predict VWF's behaviour in
two complex flows where experimental data is challenging to obtain: pure
elongational flow and stenotic arterial flow.
  In pure elongational flow, our model predicts that VWF is 50% unfolded at
approximately 2,000 s$^{-1}$, matching the established hypothesis that VWF
unfolds at lower shear rates in elongational flow than in shear flow. We
demonstrate the sensitivity of this elongational flow prediction to the value
of maximum VWF length used in the model, which varies significantly across
experimental studies, predicting that VWF can unfold between 600 - 3,200
s$^{-1}$ depending on the selected value. Finally, we examine VWF dynamics in a
range of idealised arterial stenoses, predicting the relative extension of VWF
in elongational flow structures in the centre of the artery compared to
high-shear regions near the arterial walls.
