The effects of frequency of oscillatory flow on the impedance of rigid,blood-filled tubes

Abstract

The theory for oscillatory flow of a linear viscoelastic fluid in rigid circular tubes is reviewed. It differs from that for a viscous fluid in that the Newtonian viscosity is replaced by the complex coefficient of viscosity ${\mathit{\eta }}^{\ast }={\mathit{\eta }}^{\prime }-\mathit{i}{\mathit{\eta }}^{″}$ . The theory reduces to Newtonian case for η″ = 0. The theory for the tube impedance is compared with measurements over the frequency range from 0.2 to 200 Hz in tubes having radii, a, from 0.02 to 0.35 cm. This is done for a glycerol solution and for human blood (H = 46%). The shear rate in the blood is kept in the lower range where the viscoelasticity is linear. When the dispersion of η ^* with frequency is taken into account, the agreement with theory is excellent. At low frequencies the tube reactance is negative (spring-like) and changes to positive (mass-like) when the radian frequency ${\mathit{\omega }}_0=6{\mathit{\eta }}^{″}\mathrm{/}\mathit{\pi }{\mathit{a}}^2$ , a condition for resonance. The glycerol, being Newtonian and purely viscous, does not exhibit the viscoelastic resonance.