Pulsatile Laminar Flow in a Viscoelastic System

Abstract

This work involves the study of Newtonian transitory and permanent flow regimes in a rigid tube that has been extended to include a viscoelastic enclosure. Variable pressures are applied at the free end of the tube. The problem is solved analytically by direct integration of the Navier-Stokes equations. In addition to the nondimensional parameter γ1 introduced previously by other authors, we found a new nondimensional parameter γ2 which also governs the fluid flow. This parameter may be interpreted as the ratio of the and the membrane viscosity force to the fluid friction force. The effects of small values of the membrane viscosity only attenuate the oscillating effect when inertia dominates on fluid friction force. When the membrane viscosity is important, however, it may cancel out the inertial effect resulting in a damped aperiodic flow. When the fluid friction force predominates, the membrane viscosity slows down an already damped aperiodic flow. All these types of flow are well characterized by well defined intervalls of variation of γ1 , and γ2 . In addition to the transitory flow regime, we also consider permanent pulsatile flow. An experimental device makes it possible to validate the theoretical assertions in the particular case of a pulsed pressure.