Influence of the liquid layer thickness on the stability of a plane-parallel flow in a two-phase system with evaporation

The widespread use of evaporating liquids and gas-vapor mixtures in different technologies and industrial processes causes keen interest in study of convection accompanied by phase transitions. Methods of mathematical modelling present an alternative to the pilot development of technological techniques and experimental investigations of convective heat and mass transfer. In this paper, the problem of evaporative convection in a two-phase liquid-gas system is considered within frame of the Oberbeck-Boussinesq approximation. A partially invariant exact solution of the governing equations is used for description of stationary advective flows occurring under diffusive-type evaporation. The solution allows one to correctly take into account the impact of external thermal load and thermodiffusion effects in the gas-vapor layer. The influence of the liquid layer height on the kinematic and temperature characteristics of arising regimes, as well as on the parameters of phase transitions and vapor content in the carrier gas, is investigated on the basis of the exact solution. The increase of the fluid layer thickness leads to an alteration in the flow regime from the pure thermocapillary flow to the mixed or Poiseuille type flows and to qualitative changes in mass transfer processes at the thermocapillary interface. The linear stability of the exact solution with respect to both plane and spatial normal wave perturbations is investigated by means of the normal mode method. The threshold stability characteristics are obtained, and the evolution of neutral curve topology and instability forms in response to changes in the system geometry is demonstrated. The growth of the liquid layer thickness has destabilizing influence; the oscillatory instability is always realized in this case in the system. The dependencies of the phase velocities of disturbances are presented for the systems of different geometry. The instability forms in the evaporating liquid layer driven by a co-current gas flux, predicted on the basis of the exact solution, coincide with those observed in thermophysical experiments.