(381d) Absolute-Convective Instability Regimes in Liquid Film Flow Down Vertical Cylinder in Counterflowing Gas Stream.

Stability analysis (temporal and spatiotemporal) of gravity driven liquid film flow outside a vertical cylinder in the presence of an opposing pressure gradient is studied. This system in its most fundamental configuration is inherently unstable known as the Rayleigh-Plateau instability. Non-dimensional terms appearing in the problem include Bond Number (Bo), aspect ratio (ε, ratio of average film thickness H₀ and radius of the cylinder R) and the opposing pressure gradient (φ). The momentum balance equation is simplified using the lubrication approximation. In order to account for the curvature more accurately, the other terms are expanded in ε and the series is truncated at O(ε²). The Rayleigh-Plateau stability result is recovered for ε=0. The effect of φ is not observed on the temporal stability as it appears only in the convective terms in the film evolution equation. Neutral stability curve is presented in k (wavenumber)-ε plane. In spatiotemporal analysis, Briggs criterion is utilised to mark the transition of the unstable system from absolute to convective one in ε-R/L_c parametric space. A good match is seen with previous work on isothermal flows over cylinder for ε~0.4. A positive value of φ results in this transition to occur at smaller aspect ratio, ε. Non-linear simulations for both temporal and spatiotemporal studies are carried and a good agreement is seen with the linear stability analysis.