Thermocapillary effect on the dynamics of liquid films coating the interior surface of a tube

This paper considers a thick liquid film of mean thickness h₀ coating the interior surface of a uniformly heated vertical tube of radius a under the influence of gravity (h₀ is not far thinner than the radius a). An asymptotic model based on the long-wave assumption is derived. Linear stability analysis shows that the Rayleigh-Plateau instability can be inhibited when the core air phase is warmer than the liquid phase; while the Rayleigh-Plateau instability is enhanced when the air phase is colder than the liquid phase. Linear stability analysis also shows that the absolute instability can be enhanced by the Marangoni effect. Traveling wave study reveals that two different phenomena could exist in this system: choke phenomenon and saturated traveling waves. For small tube radius α≲3.38 (α=a/h₀ is the dimensionless pipe radius), that the air phase always chokes. A cold air flow (the Marangoni number Ma>0) promotes the height of traveling wave, which therefore enhances the choke phenomenon. The choke phenomenon can be suppressed by a warm air phase (Ma<0). Numerical simulation shows that the traveling wave study predicts an upper bound of the critical tube radius, below which the air flow chokes. A self-similar analysis is carried out to investigate the dynamics of choke and the scaling (t_c-t)^1/5 is obtained. The power exponent 1/5 is independent of Marangoni effect, but the choke time t_c decreases as Ma increases.