Entry length and wall shear stress in uniformly collapsed veins

The laminar steady flow of incompressible Newtonian fluid is computed in rigid pipes with wall configurations corresponding to various degrees of collapse of a flexible tube to determine both the entry length and the wall shear stress. The investigated configurations range from the unstressed state to a contact collapse with a finite and infinite curvature radius at the contact point. The cross-section configurations are not aimed at mimicing actual collapsed veins but at creating at the cell scale a shear stress which generates a shear force and a shear torque applied at the cell inertia center. The Navier-Stokes equations were solved by a finite element method. The numerical tests are performed with the same value of the volume flow rate whatever the tube configuration and the test Reynolds number (35, 500 and 1000). Entry length, axial and cross variations in wall shear stress axe computed to design flow chambers and to explore the mechanotransduction function of the venous endothelial cells.