Analytical instability theory of a liquid jet under a thermal field

Linear temporal instability analysis of a liquid jet emerging into a stationary gas environment under a radial thermal field is carried out in this work. The basic temperature profiles are obtained by solving the heat conduction problem between the liquid jet and the surrounding gas. The normal mode method is utilized to solve the temporal evolution of small disturbance, and an analytical dispersion relation on the growth of disturbance is derived. The inviscid asymptotic solution for the liquid jet is further obtained, which shows the explicit form of disturbance growth rate and also decouples the contribution of surface tension and Marangoni stress on the jet instability. The effects of various controlling parameters on the growth of disturbance for an inviscid liquid jet are investigated through a parametric study. Theoretical results show that the jet instability can be suppressed by increasing the temperature ratio between the liquid jet and the surrounding gas, enhancing the Marangoni stress on the surface, weakening the thermal conduction and decreasing the surface tension. The physical mechanisms of Rayleigh-Plateau instability and Marangoni instability which are responsible for the growth of disturbance are distinguished. Through comparing the inviscid asymptotic solution to the disturbance growth of the viscous jet, the applicable situation for the inviscid asymptotic solution is identified, which gives the Reynolds number ranges of Re = O(10(2)).

Automated summary

This work presents a linear temporal instability analysis of a liquid jet entering a stationary gas environment under a radial thermal field. The basic temperature distribution is obtained by solving the heat conduction problem between the liquid jet and the surrounding gas. The normal mode method is used to solve the temporal evolution of small disturbances, and an analytical dispersion relation for disturbance growth is derived. The effects of different control parameters on the disturbance growth of an inviscid liquid jet are investigated through a parametric study. Theoretical results show that increasing the temperature ratio, enhancing the Marangoni stress, weakening thermal conduction, and decreasing surface tension can suppress the jet instability. The physical mechanisms of Rayleigh-Plateau instability and Marangoni instability are distinguished as contributors to disturbance growth. The applicable range of the inviscid asymptotic solution is identified through comparison with the disturbance growth of a viscous jet, with Reynolds number ranges of Re = O(10^2).