Linear Stability Analysis of a Collapsible-Tube Model
Abstract A linear stability analysis is performed for a collapsible tube model consisting of a reservoir with inlet and outlet flow conditions. The downstream pressure in the collapsible regime is modeled as a cubic nonlinearity. From the nonlinear model, we assume small perturbations around the steady states and utilize Liapunov stability criteria to describe the linear model. Steady-state pressure drops, stable and unstable boundaries are determined analytically for ranges of mass flow rate and compressible volume in the reservoir. Mechanisms that give rise to unstable behavior of pressure and flow rates in collapsible tube systems are examined based on numerical results. The model also provide us with stable and unstable boundaries that may give us the insight on the operation, control, and safety of collapsible tube systems in biological systems such as veins, arteries etc.