The stability of the laminar flow in flexible tubes and channels could be influenced by the flexibility of the walls, and these instabilities are qualitatively different from those in rigid tubes and channels. In this paper, the instabilities of the laminar flow in flexible tubes and channels are classified according to the asymptotic regime in which they are observed, the flow structure, the scaling of the critical Reynolds number (rVR/m) with the dimensionless parameter å = (rGR2/m2), and the mechanism that destabilizes the flow. Here, r and m are the fluid density and viscosity,G is the shear modulus of the wall material, R is the cross stream length scale and V is the maximum velocity. Three types of instabilities have been analysed. The viscous instability is observed in the limit of low Reynolds number when the fluid inertia is insignificant, and the critical Reynolds number scales as Re µ å. The destabilizing mechanism is the transfer of energy from the mean flow to the fluctuations due to the shear work done by the mean flow at the surface. In the high Reynolds number inviscid modes, the critical Reynolds number scales are Re µ å1/2, and there is a critical layer of thickness Re–1/3 where viscous stresses are important. The destabilizing mechanism is the transfer of energy from the mean flow to the fluctuations due to the Reynolds stresses in the critical layer. The high Reynolds number wall mode instability has a wall layer of thickness Re–1/3 at the wall, where viscous stresses are important and the critical Reynolds number scales as Re µ å3/4. The destabilizing mechanism is the transfer of energy from the mean flow to the fluctuations due to the shear work done by the mean flow at the interface.
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