A MATHEMATICAL MODEL OF FLOW IN A LIQUID-FILLED VISCOELASTIC TUBE

The propagation of waves in a distensible tube filled with a viscous fluid is studied numerically. The main application is in biofluid mechanics, where the fluid-solid interaction is of primary importance. Based on the assumption of long wavelength and small amplitude of pressure waves, a quasi-1D differential model was adopted. The model accounted for vessel wall viscoelasticity and included the wall deformations along both radial and axial directions. The nonlinear problem was solved in nondimensional form by a finite difference method on a staggered grid. The boundary conditions were for two relevant cases: natural oscillations in a deformable tube fixed at the ends and persistent oscillations due to a periodical forcing pressure. The natural frequency S t was found to be nearly equal to the square root of the elasticity coefficient K, with 0 K 6000 and is not affected by the viscosity. These results were strongly influenced by both wall viscoelasticity and blood viscosity: the damping time was found to be inversely proportional to the wall viscosity coefficient, while the fluid viscosity provides an even larger damping factor