Pulsatile flow in a thin-walled viscoelastic tube.

Low inertia, pulsatile flows in highly distensible, viscoelastic vessels exist in many biological and engineering systems. However, many existing works focus on inertial, pulsatile flows in vessels with small deformations. As such, here we study the dynamics of a viscoelastic tube at large deformation conveying low Reynolds number, oscillatory flow using a fully-coupled fluid/structure interaction computational model. We focus on a detailed study on the effect of wall (solid) viscosity and oscillation frequency on the tube deformation, flow rate, phase shift and hysteresis, and the underlying flow physics. We find that the general behavior is dominated by an elastic flow surge during inflation and a squeezing effect during deflation. When increasing the oscillation frequency, the maximum inlet flow rate increases and tube distention decreases, whereas increasing solid viscosity causes both to decrease. As the oscillation frequency approaches either 0 (quasi-steady inflation cycle) or ∞ (steady flow), the behaviors of tubes with different solid viscosities converge. Our results suggest that deformation and flow rate are most affected in the intermediate range of solid viscosity and oscillation frequency. Phase shifts of deformation and flow rate with respect to the imposed pressure are analyzed. We predict that the phase shifts vary throughout the oscillation; while the deformation always lags the imposed pressure, the flow rate may either lead or lag depending on the parameter values. As such, the flow rate shows hysteresis behavior that traces either a clockwise or counterclockwise curve, or a mix of both, in the pressure-flow rate space. This directional change in hysteresis is fully characterized here in the appropriate parameter space. Furthermore, the hysteresis direction is shown to be predicted by the signs of the flow rate phase shifts at the crest and trough of the oscillation. A distinct change in the tube dynamics is also observed at high solid viscosity which leads to global or "whole-tube" motion that is absent in purely elastic tubes.