Supplementary
S 1. Accuracy of the flow-tracking particles and PIV results
Stokes number Stk of the tracer particles can be expressed as follows (Burgmann et al. 2011;
Soo 1999)
Stk 
(  p   f )d p2U
18 D
where  p and  f indicate the particle and fluid density, respectively. U is the fluid velocity
at the center of the channel and  is the fluid viscosity. d p and D denote the diameter of
the particle and channel, respectively. Under the largest flow rate condition of 1.0 L/min tested
in the present stenosis flow, Stokes number of the particle is less than 0.1 (~10-3). Therefore,
the tracer particles are assumed to follow the flow faithfully.
To verify the accuracy of PIV measurements, the time-averaged axial velocity profile was
taken by averaging 1000 instantaneous velocity field and the result was compared with
theoretical parabolic velocity profile. The PIV result was found to be well agreed with the
theoretically estimated velocity profile with r-squared values of 0.9898. The comparison
supports that the effect of the tracer particles is negligible.
Fig. S 1 Axial velocity profile measured by PIV (■) was compared with a theoretical parabolic profile (dotted
line).
S 2. Variation of time-averaged centerline velocity and velocity fluctuations of radial
component according to flow rate
Fluctuations of radial velocity component (Figs.S2~4 indicates NN, NNN and ANN
respectively of each given flow rate) are also suppressed, when the flow rate of shear-thinning
fluids is lower than 0.5 L/min. Time-averaged radial velocity along the centerline is maintained
close to zero and velocity fluctuations exhibit turbulent characteristics. Fig.S5 shows the
difference of axial and radial turbulence intensity of ANN at a flow rate of 1.0 L/min. As shown
in the figure, the turbulent flow is non-isotropic.
Fig. S 2 Time-averaged centerline radial velocities and velocity fluctuations of NN
Fig. S 3 Time-averaged centerline radial velocities and velocity fluctuations of NNN
Fig. S 4 Time-averaged centerline radial velocities and velocity fluctuations of ANN
Fig. S 5 Difference of axial and radial turbulence intensities of ANN at a flow rate of 1.0 L/min
S 3. Criteria for transition from laminar-to-turbulent flow based on turbulence intensity
For a stenotic pipe flow, the transitional Reynolds number has been previously investigated.
Although there are some differences in the exact values, it lies in the range of 400~700. Sherwin
and Blackburn (2005) used linear stability analysis and direct numerical simulation to analyze
the steady and pulsatile flows passing through an axisymmetric stenosis. They reported that
turbulent transition occurs at Re of 722. On the other hand, Vétel et al. (2008) estimated the
transitional Reynolds number as 400 in their experiment. Ha et al. (2014) found that the
transition occurs at Re of 450 and their geometry is exactly the same as the present study.
Transitional flow has both of laminar and turbulent flows. Flow condition can be estimated
with turbulence intensity which represents relative level of velocity fluctuations. Criteria for
the laminar-to-turbulent transition may be slightly different depending on experimental
condition or its definition. However, it is generally considered as highly turbulent flow when
the turbulence intensity is higher than 10%. In this study, transitional flow was considered to
have a turbulence intensity in the range of 3~10%. When it is less than 3%, the flow was
regarded as laminar.
Reference
Burgmann S, Van der Schoot N, Asbach C, Wartmann J, Lindken R (2011) Analysis of tracer particle
characteristics for micro PIV in wall-bounded gas flows La houille blanche:55-61
Ha H, Choi W, Park H, Lee SJ (2014) Advantageous swirling flow in 45° end-to-side anastomosis Experiments
in Fluids 55:1-13
Sherwin S, Blackburn HM (2005) Three-dimensional instabilities and transition of steady and pulsatile
axisymmetric stenotic flows Journal of Fluid Mechanics 533:297-327
Soo SL (1999) Instrumentation for fluid particle flow. Elsevier,
Vétel J, Garon A, Pelletier D, Farinas M-I (2008) Asymmetry and transition to turbulence in a smooth
axisymmetric constriction Journal of Fluid Mechanics 607:351-386