Part I:
The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle.It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid.By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases.Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete.The effects of solidification are noticeable.
Part II:
When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs.This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees.The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values.The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit.In the continuum limit, the mass flux rate is proportional to the pressure difference alone.
