Non-Newtonian Behavior of Blood in Oscillatory Flow

Abstract

Sinusoidal oscillatory flow of blood and of aqueous glycerol solutions was produced in rigid cylindrical tubes. For aqueous glycerol, the amplitude of the measured pressure gradient wave form conformed closely to that predicted by Womersley's theory of oscillatory flow, up to Reynolds numbers approaching 2000. Blood differed significantly from aqueous glycerol solutions of comparable viscosity, especially at low frequencies and high hematocrits. As frequency increased, the hydraulic impedance of blood decreased to a minimum at a frequency of about 1-2 CPS, increasing monotonically at higher frequencies. The dynamic apparent viscosity of blood, calculated from Womersley's theory, decreased with increasing flow amplitude. The reactive component of the hydraulic impedance increased with frequency as predicted by theory; the resistive component decreased with increasing frequency, differing from the resistance of a Newtonian fluid which increased with frequency.

On the high frequency oscillatory tube flow of healthy human blood

“…Under these circumstances, it was found that the dynamic apparent viscosity was an increasing function of frequency, and was a convincing demonstration of the non-Newtonian character of blood in this flow. This result was in contrast to the earlier findings of Kunz and Coulter [21] who reported that the dynamic apparent viscosity decreased with increasing oscillatory frequency. It should be borne in mind, however, that in the case of the experiments in [21] the stroke volume rather than the volume flow rate amplitude was fixed, thus resulting in a linear dependence of the latter on the oscillatory frequency.…”

“…The dependence of the rheological properties of human blood on the frequency of oscillations in oscillatory tube flow has been investigated by a number of authors and some classic treatises are to be found in articles by Coulter and Singh [11], Kunz and Coulter [21] and Thurston [37,38]. We may define, as did the authors of the first two articles just cited, a dynamic apparent viscosity for blood as being the viscosity of a Newtonian fluid which exhibits the same pressure gradient-volume flow rate under the same conditions of oscillatory flow.…”

A non-homogeneous constitutive model for human blood

“…For all the tube radii considered, non-Newtonian effects are showcased by comparing the calculated velocity proles with those of a Newtonian uid having a viscosity chosen equal to the apparent viscosity of the model blood under steady Poiseuille ow conditions (ω = 0) and dp/dz = −600Rλ H /η ∞ in the same tube. An apparent viscosity for oscillatory ow could have been dened as the viscosity of the Newtonian uid which yields the same volume ow rate amplitude as the blood model at a given pressure gradient amplitude [7,15], but we thought it more enlightening to see how dierences in the volume ow rate amplitudes of the model blood and Newtonian uid developed in tubes of various radii. In Figs.…”

“…But since higher frequencies meant higher volume ow rate amplitudes it was not clear from the Kunz and Coulter paper to what extent the dynamic apparent viscosity depended on frequency and to what extent on ow rate. The behaviour of the dynamic apparent viscosity with increasing oscillatory frequency in [15] was interpreted some four years later by Coulter and Singh [7] as being due to the higher shear rates at higher frequencies experienced by the uid. In the Coulter and Singh paper [7] the authors decoupled the ow rate and frequency by performing experiments in rigid-walled tubes at various frequencies but at xed ow amplitudes.…”

“…In [15] Kunz and Coulter considered the sinusoidal oscillatory ow of blood at various hematocrits and of an aqueous glycerol solution in a rigid tube of radius 1.7mm. The stroke volume V s was xed at 0.204cc, so that from (1) it may be seen that as the frequency ω of the oscillations varied, so did the volume ow rate U .…”