Transition to turbulence in non-Newtonian fluids: An in-vitro study using pulsed Doppler ultrasound for biological flows

Blood is a complex fluid and has been established to behave as a shear thinning non-Newtonian fluid when exposed to low shear rates (<200s -1). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high shear rates. Shear thinning fluids have been shown to exhibit differences in transition to turbulence compared to that of Newtonian fluids. Incorrect assumption of the transition point in a simulation could result in erroneous prediction of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and standard blood analogs in a straight rigid pipe and an S-shaped pipe under a range of steady flow conditions. Reynolds number for blood was defined based on the viscosity at a shear rate of 400s -1. The rheometer was calibrated at shear rates of interest using Newtonian viscosity standards. Doppler ultrasound was used to measure velocity profiles of whole porcine blood and a Newtonian fluid in an in vitro experiment at 18 different Reynolds numbers ranging from 750 to 3500 (straight pipe) and 21 different Reynolds numbers ranging from 500 to 2800 (S- iv shaped pipe). Three samples of each fluid were examined and fluid rheology was measured before and after each experiment. Straight pipe results show parabolic velocity profiles for both whole blood and the Newtonian fluid at Reynolds numbers less than 2100 (based on high shear rate viscosity). The Newtonian fluid had blunt velocity profiles with large velocity fluctuations (root mean square as high as 18%) starting at Reynolds numbers ~2100-2300 which indicated transition to turbulence. In contrast, whole blood did not transition to turbulence until a Reynolds number of ~2500-2700. This delay was consistent for all three samples. For Reynolds numbers larger than 2100, the delay in transition resulted in differences in velocity profiles between the two fluids as high as 20%. A Newtonian assumption for blood at flow conditions near transition can lead to large errors in velocity prediction for steady flow in a straight pipe. For the S-shaped pipe geometry, the RMS velocity results show that the minimum Re where transition initiated for whole blood (~1000-1200) is slightly larger (>10%) than that observed for a Newtonian fluid (~900-1000) under steady flow conditions. Repeated measurements show these results to be consistent for three different samples. These results show large differences in the magnitude of mean and fluctuation velocity between whole blood and a Newtonian fluid for Re>1000. Further research is necessary to understand this relation in more complex geometries and under pulsatile flow conditions.