Blood’s critical Taylor number and its flow behavior at supercritical Taylor numbers

Abstract

When the inner cylinder of a fluid-filled Couette viscometer is rotated rapidly, a vortical flow pattern develops when a dimensionless value referred to as the critical Taylor number (Tc) is reached. We have determined its magnitude in our viscometer for three Newtonian fluids and for blood at 37°C, using the inflection point of torque/RPM vs. RPM (sudden rise in apparent viscosity). Its position was identified by least squares line fitting. Because blood was studied, the viscosity used in Tc calculation was the apparent bob shear stress/shear rate ratio at the inflection marking vortical flow onset. For glycerol-water mixtures Tc was 41.8 ±0.3 (N=11), for propylene glycol 42.0 ±0.2 (N=14), for silicone oil 41.8 +0.2 (N=11). For healthy blood Tc was 40.7 ±0.9 (N=140). This evidence against blood’s increased resistance to flow instability was accompanied by a slower rate of rise in torque both above and below Tc compared to the three Newtonian fluids. Newtonian fluids and blood both developed wavy vortical flow at a rotation rate moderately higher than Tc. Blood resisted this unstable flow behavior more than the Newtonian fluids but it also experienced a slower rate of rise in torque with increasing rotation rate above the critical Taylor number. Shear-thinning is the simplest explanation for blood’s mildly altered Taylor vortex behavior; blood’s resistance to flow instability is otherwise not found to be sufficient to affect its flow stability in man.