by Professor Aldo Frezzotti from Politecnico di Milano

12/01/2016 - 3:45 PM - Conference room

Evaporation and condensation processes play  a fundamental role in many vapor-liquid flows. When the main flow spatial scale has a macroscopic  size, the bulks of the vapor and liquid regions are well described by hydrodynamic equations. However, the boundary separating the liquid and vapor phase has a complex  structure  which still requires experimental and theoretical investigations for a better formulation of the boundary conditions to be used to match hydrodynamic regions. In non-equilibrium conditions,  the boundary  region  can  be separated  into the vapor-liquid interface  itself  [1] and  a Knudsen layer whose size and importance depends on flow conditions[2]. The latter is a kinetic layer in the vapor where macroscopic variables undergo variations on the scale of the mean free path, which manifest as “jumps” at the macroscopic scale.

The study of the Knudsen layer structure in evaporation/condensation problems  has been made clear by a considerable number of studies based on the Boltzmann  equation or kinetic model equations [2]. Studies cover monatomic, polyatomic gases and mixtures [3]. A common drawback of most kinetic theory investigations of the vapor phase is the coupling with the liquid phase which has been mostly based   on  simple   phenomenological   models,   whose   validity  had to  be  demonstrated.   Later investigations  [4],  mostly based  on molecular  dynamics  simulations,  led  to the  formulation  of alternative models for coupling the liquid-vapor interface to the kinetic region [3,4]. Although the interest and importance of improving boundary conditions models at the vapor-liquid interface cannot be denied, two aspects of the problem  need also consideration. First, available models have not yet been satisfactorily  tested in more or less  simple  flow configurations  in which the vapor phase  is dynamically coupled to an evolving liquid phase. The lack of such studies prevents the assessment of the accuracy of proposed models.  Second, even if the boundary conditions  model would be very accurate, the whole  two-phase flow would be described  by two distinct  models  and the boundary conditions applied on an interface to be tracked. In this respect, a single model capable of describing both phases including the interface region would be, in principle, to be preferred[5].

In view of the considerations described above, the talk will review existing results on Knudsen layer structure  in  evaporation/condensation  problems   and  discuss  the problem  of  boundary condition
models. The evaporation of a liquid film, simulated by molecular dynamics will be used as benchmark
to compare the predictions of a hybrid model, coupling fluid equations to describe the liquid phase with the Boltzmann  equation to describe the vapor phase, with the predictions of a diffuse interface model providing  a unified description of the two phases [6].

References

[1] Rowlinson J.S., & Widom B. , Molecular theory of capillarity, Dover.
[2] Sone,  Y. (2000). Kinetic  Theoretical  Studies  of the  Half-Space  Problem  of Evaporation  and Condensation. TTSP 29, 227-260.
[3] Frezzotti, A. (2011). Boundary conditions  at the vapor-liquid interface.  Physics  of Fluids 23, 030609.
[4] Fujikawa  S., Yano T., & Watanabe M. (2011). Vapor-Liquid  Interfaces,  Bubbles and Droplets, Berlin: Springer.
[5] Anderson D.M., McFadden G.B., & Wheeler A.A. (1998). Diffuse-Interface Methods in Fluid Mechanics. Annu. Rev. Fluid Mech. 30, 139–165 .
[6] Frezzotti A., Barbante P., & Gibelli L., (2014). A Comparison of Molecular Dynamics and Diffuse Interface Model Predictions of Lennard-Jones Fluid Evaporation. AIP Conference Proceedings, 1628, 893-900. 

Location : von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, B-1640 Sint-Genesius-Rode, Conference Room