(366c) Evaporation of Pure and Mixed Nano-Droplets: Molecular Dynamics Simulations

After an earlier paper on steady state evaporation from a planar surface [1], we study here transient evaporation processes of pure and mixed nano-droplets consisting of Lennard-Jones (LJ)- fluids (cut and shifted interactions at 2.5 σ) by molecular dynamics simulations under different initial and boundary conditions. The LJ mixture model uses the parameters σ_AA = σ_BB and ε_BB/ ε_AA = 1.25 together with Lorentz-Berthelot combining rules.

We have to start with several definitions. One concerns the question whether a particle belongs to the droplet or to the vapor [2,3]. Therewith, the droplet center can be calculated and the time-dependent number of droplet particles. A crucial question is the definition of the drift velocity- which is done on an time scale intermediate between the MD-time steps and the total evaporation time. Therewith, several space and time dependent hydrodynamic quantities as a ) the density, b) the drift velocity c) the radial, tangential, and total temperature, and d) the mean kinetic energy per particle can be calculated [4].

Next, the preparation of the droplet initial conditions is described. The general procedure is to start with two separate simulations for the bulk liquid and the bulk vapor and then to merge both phases Simulations will be either started from a droplet in equilibrium with its vapor ? we call this a wrapped droplet- or from a non-equilibrium situation. In case that a droplet has been simply cut out from a homogeneous liquid we call it a bare droplet.

Several initial and boundary value problems can be considered for pure and mixed LJ droplets. Case 1: A wrapped droplet is put together with its vapour into a larger volume which initially is empty. Case 2: A bare droplet is cut out and put into vacuum. Cases 1 and 2 have some physical similarity and are summarized as ?Adiabatic pressure jump evaporation?. Case 3: Start from a cold wrapped droplet and heat the vapour in some distance from the droplet. Case 4: Put a cold bare droplet into hot vapour and add energy to the system. Cases 3 and 4 have some physical similarity and are summarized as ?Continuous heat transfer evaporation?.

We will show and disccus selected results for the number of droplet particles and for the hydrodynamic quantity profiles as functions of time for adiabatic pressure jump as well as for continuous heat transfer evaporation processes. We will put some emphasis on the drift velocity which according to our knowledge has not yet been calulated by other authors.

As an example, the figure shows the number of droplet particles N_dA and N_dB as function of time t in picoseconds for evaporation of a wrapped mixture droplet of reduced temperature T_r = kT/ε_AA = 0.8 by adiabatic expansion of the volume from a box with length L₁ to a box with length L₂. The upper curves are the numbers of the less volatile B-particles (filled circles for L₂/L₁ = 1.5, empty circles for L₂/L₁ = 2.0) whilst the lower curves are the numbers of the more volatile A-particles (filled triangles for L₂/L₁ = 1.5, empty triangles for L₂/L₁ = 2.0). In particular we learn that the less volatile particles all stay in the droplet whilst the number of the more volatile particles in the droplet is reduced by about 20% in case of L₂/L₁ = 1.5 and by 36% in case of L₂/L₁ = 2.0. Moreover, not shown in the figure, we learn that the reduced temperature of the droplet decreases from T_r = 0.80 to 0.75 for L₂/L₁ = 1.5. This is caused by the fact that the "energy for evaporation" has to be supplied in the adiabatic case by the system itself.

A general conclusion is that the details of the evaporation process are strongly influenced by the initial and the boundary conditions.

[1] A. Lotfi (1993), Molekulardynamische Simulationen an Fluiden: Phasengleichgewicht und Verdampfung, Fortschritt-Berichte VDI, VDI-Verlag Düsseldorf, ISBN 3-18-143503-1. (see: www.map.boku.ac.at/2906.html)

[2] S. M. Thompson, K.E. Gubbins, J.P.R.B. Walton, R.A.R. Chantry, and J. S. Rowlinson (1984): A molecular dynamics study of liquid drops. J. Chem. Phys. 81, 530 ? 542.

[3] P. Rein ten Wolde and D. Frenkel (1998): Computer simulation study of gas-liquid nucleation in a Lennard-Jones system. J. Chem. Phys. 109, 9901- 9918.

[4] S. Sumardiono and J. Fischer (2006): Molecular simulations of droplet evaporation processes: Adiabatic pressure jump evaporation. Int. J. Heat and Mass Transfer 49, 1148-1161.