A fluid-beam model for flow in a collapsible channel

This paper proposes a fluid-beam model to overcome the shortcomings of the previous fluid-membrane models on flow in collapsible channels of Luo and Pedley. The new model employs a plane strained elastic beam with large deflection and incrementally linear extension. This model gives a more realistic and general description of the problem and reduces to several simpler models including the fluid-membrane model under special parameter ranges. Both numerical and asymptotic approaches are used to study the problem. A finite element code is developed to solve the coupled nonlinear fluid-structure interactive equations simultaneously, and a moving mesh with rotating spines is used to enable a movable boundary. It is found that as the wall stiffness approaches to zero, the fluid and the beam equations at the corners where the beam joins the rigid wall are decoupled, and that asymptotic solutions exist both for the beam, and the flow which is dominated by the Stokes flow even for Reynolds number of O(10(3)). The numerical code is validated in several different ways, and compared with the asymptotic solution at the corners. It is found that the numerical grid size has to satisfy certain conditions to resolve the boundary layers properly near the corners, especially for the smaller values of the wall stiffness. The results of the new model compare favourably with those of the fluidmembrane model for very small wall stiffness. However, different results are obtained if the wall stiffness is chosen to be applicable either to rubbers with wall thickness ratio greater than 0.01, or those of veins in the physiological range of wall thickness ratios. This model therefore provides a more realistic description to flow in collapsible channels. (C) 2002 Elsevier Science Ltd. All rights reserved.