A nonlinear analysis of flow in an elastic artery model-steady streaming effects

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=(D_max-D_min)/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, R_s=(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