Title :
A nonlinear analysis of flow in an elastic artery model-steady streaming effects
Author :
Wang, D.M. ; Tarbell, J.M.
Author_Institution :
Dept. of Chem. Eng., Pennsylvania State Univ., University Park, PA, USA
Abstract :
An analysis of the nonlinear flow of a Newtonian fluid in a linearly elastic tube when subjected to an oscillatory pressure gradient is presented. Two parameters, α=a(w/μ)1/2 and ε=(Dmax-Dmin)/D mean, where μ is the kinematic viscosity, w is the angular frequency, a is the mean radius, and D is the artery diameter, are important to characterize this flow problem. The diameter variation is taken to be small so that the perturbation method is valid, and asymptotic solutions for two limiting cases of the steady-streaming Reynolds number, Rs=(αε)2 (either small or large), are discussed. The nonlinear convective acceleration induces finite mean pressure gradient and mean wall shear rate even when no mean flow occurs. The magnitude of this effect depends on the oscillatory flow rate, the diameter variation, and the impedance phase angle. The impedance phase angle, which represents the degree of wave reflection, can even change the direction of induced flow. It is shown that the induced mean wall shear rate is approximately proportional to α when α is large
Keywords :
haemodynamics; physiological models; Newtonian fluid; artery diameter; diameter variation; elastic artery model; impedance phase angle; induced flow; kinematic viscosity; nonlinear convective acceleration; nonlinear flow analysis; perturbation method; steady streaming effects; wall shear rate; Acceleration; Arteries; Chemical analysis; Chemical engineering; Impedance; Kinematics; Navier-Stokes equations; Nonlinear equations; Perturbation methods; Reflection;
Conference_Titel :
Bioengineering Conference, 1990., Proceedings of the 1990 Sixteenth Annual Northeast
Conference_Location :
State College, PA
DOI :
10.1109/NEBC.1990.66285