Cylindrical columns, instability

Similarly, the majority of the investigations reported conclude that for both rectangular and cylindrical columns the high frequency instabilities are 3D and have to be resolved by the use of 3D models. Nevertheless, in a few recent papers [5, 6, 21] it has been shown that 2D mixture model formulations can be used to reproduce the time-dependent flow behavior of 2D bubble... 

Tomotlka S. "The Instability of Cylindrical Column of a Perfect Liquid Surrounded by Another Perfect Fluid " Proc. Physlco. Math. Soc. Japan Vol, 18, pp. 550-562 1936. 

Cylindrical coordinate along symmetry axis in stability analysis of liquid jet Fraction of column cross-sectional area available to solute Thermal diffusivity Amplification factor in jet instability Particle diameter to minimum separation between particles, Eq. (9.3.9)... 

It is noteworthy, especially in relation to our later discussions on electrospinning, that cylindrical liquid columns are also subject to the Rayleigh-type instability, in which case the pressure balance is given by ... 

A review article gives a thorough review of creep instability of steel and other metal shells and pressure vessels at elevated temperatures. Some of the same analyses can be adopted here for polymers at lower temperatures, for example, room temperature. For example, consider the axisymmetric buckling mode of a cylindrical shell under compression. (The beam column mode can be included under column buckling. Section 4.2.) For the axisymmetric mode, where axisymmetric buckling waves occur for RJh < 33, the critical buckling stress in compression is given by... 

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