  We experimentally and numerically investigate the flow of a Newtonian fluid
through a constricted geometry for Reynolds numbers in the range $0.1 - 100$.
The major aim is to study non-linear inertia effects at larger Reynolds numbers
(>10) on the shear stress evolution in the fluid. This is of particular
importance for blood flow as some biophysical processes in blood are sensitive
to shear stresses, e.g., the initialization of blood clotting. We employ the
lattice Boltzmann method for the simulations. The conclusion of the predictions
is that the peak value of shear stress in the constriction grows
disproportionally fast with the Reynolds number which leads to a non-linear
shear stress accumulation. As a consequence, the combination of constricted
blood vessel geometries and large Reynolds numbers may increase the risk of
undesired blood clotting.
