Evaporation-driven vapour micro flows: analytical solutions from moment methods

Our recent research article has recently been accepted in Journal of Fluid Mechanics. The general interest of this study was to explore boundary value problems for moderately rarefied gas flows, with an emphasis on evaporation from nanostructures. In this article we developed macroscopic models based on R26-moment equations to describe the transport process near the phase boundary between a liquid and its rarefied vapour due to evaporation and condensation. For evaporation from a spherical droplet, analytic solutions were obtained to the linearized equations from the Navier Stokes & Fourier (NSF), regularised 13-moment (R13) and regularised 26-moment (R26) frameworks. Results are shown to approach computational solutions to the Boltzmann equation as the number of moments are increased, with good agreement for Knudsen number smaller than 1.

Knudsen layer functions in temperature-driven flow (far field temperature is twice of the temperature in liquid) are shown in Figure above. Curves of the normalised pressure (left) and the temperature defect (right) are plotted against scaled distance from the interface, for the NSF, R13 and R26 theories with complete evaporation and compared with the solutions of the linearized Boltzmann equation (denoted by symbols).   

Our results indicate that the R26 equations with evaporation boundary conditions yield an excellent quantitative description in all cases, which are not matched by the NSF or R13 theories. The R26 system provides three exponential functions to form the Knudsen layer, thus capturing the more complex behaviour in Knudsen layer.