Pressure dependence of the instability of multiwalled carbon nanotubes conveying fluids

Based on an elastic beam model, the instability of multiwalled carbon nanotubes (MWCNTs) induced by the moving fluid inside is investigated. At critical flow velocities, the MWCNTs become unstable and undergo pitchfork bifurcation and subsequently Hopf bifurcation. These critical velocities are found to increase very quickly with respect to decreasing inner radius and are inversely proportional to the length-to-outer-radius ratio. The effect of the van der Waals (vdW) interaction between tubes is investigated and it is found that the vdW interaction can enhance the stability of MWCNTs in general, but the vdW interaction reduces the stability capacity of MWCNTs with very small inner radius.