Supplementary information
The simulations were performed using classical NVE molecular dynamics method
(Ref[24] in the main body of the paper) on systems of the particles interacted via the truncated
and shifted Lennard-Jones potential in the following form:
4 [( / r)12  ( / r) 6 ]  4 [( / rC )12  ( / rC ) 6 ]
u(r)  
0

for r  rC  2.5
for
r/  rC
(1)
where  and  are the size and energy parameters, respectively.
The scheme of the intersection of simulation system at t = 0 is given in Figure S1. In the
middle of the simulation box we have a droplet. The boundaries are heated to Tb. Initially the
temperature of the gas and liquid droplet is Teq. Table SI presents the values of initial
equilibrium thermodynamic parameters of the system for the simulation runs given in Table 1.
The data from Table S1 are in agreement with the vapor-liquid coexistence simulation results
from the literature Ref[a1,a2]. Figure S2 gives the phase diagram of the system and compares
the densities from Table S1 with those from the cited papers. In Fig.S3 we show the pressure
and temperature inside the box for two different times during evaporation (without rescaling
the data as in Fig.1)
During the evaporation process the droplet was “kept” very close to the center of the
sphere by scaling the velocities of the droplet particles as to change adequately the velocity of
the center of droplet mass. Five simulation runs were repeated without application of the
procedure. Additional simulation runs showed that the influence of the procedure on the
obtained results was insignificant.
The energy per particle and the pressure of a liquid droplet, necessary to evaluate the
enthalpy of evaporation, were measured (in central part of the droplet) during simulation
using standard formulas (Ref[24] in the main body of the paper). The energy and pressure for
the gas phase were taken from additional simulations (while preparing initial state for
evaporation and/or for the  vap measurement, discussed further).
Determination of the heat conductivity
The heat conductivity,  vap , was measured using a direct method proposed by MullerPlathe (MP) (Ref[26] main body of the paper). In our simulations the amount of kinetic
energy, Ek, was transferred (by scaling velocities) between all the particles from the cooling
region to the heating one. This enabled us to consider very large systems. The system
diameters were many times larger (here, never less than 5) than the mean free path of
molecules in the gas. The simulations were performed for total number of particles N = 32768
to 307200. The number increased with decreasing gas. The length of the simulation box along
the z axis (Lz) was 4.8 – 8.0 times larger than that for x and y (Lx and Ly). The energy transfer
was realized for the time interval t = 0.8. Both the total energy and the momentum of the
system were conserved. Mean values of temperature gradient T/z were obtained by fitting
the temperature profile T(z) with a straight line(rectangular geometry) . For the considered
state points any systematic dependence of <T/z>/Ek on Ek was not observed, however
the temperature difference between the heating and the cooling region never exceeded 0.15T.
The number of simulation runs performed for a given state point decreased with increasing N
from 10 for N=32768 to 2-3 for N=307200. The final value of  vap was evaluated from the
formula of MP (Ref[26] in the main body of the paper):
 vap 
E k
2  T/z  Lx Ly t
(2)
averaging over all the simulation runs for a given state point. The results are presented in
Table SII. The values in parenthesis estimate the standard deviation (in units of the last digit
of the corresponding value).Final values of the heat conductivity used in Table 1were
obtained by linear interpolation of those from Table SII.
Two last lines of Table SII (marked by E1 and E2) present the results obtained by applying
the Evans method (Ref[24,27] in a main body of the paper). The difference in  vap for E1 and
MP5 can be easily explained by simulation errors but the deviation between E2 and MP15-17
is much too high. The results of MP method seem to be more credible since the method is a
direct one and does not require any additional assumptions. The MP results do not depend on
the size of the simulation box.  vap for MP16 (N=175616) is fully consistent with that for
MP15 and 17 (N=32768). Even if the Evans method gives better estimation of  vap , this does
not influence conclusions from the simulations. The correction between the value of heat
conductivity obtained by different methods was about 10% and decreased to 0 with
decreasing gas density (the value of  vap E1 agrees with that of MP5). Such corrections have
no significant influence on the interpretation of the simulation results.
Determination of the surface tension
The surface tension was measured directly simulating a flat layer of liquid (about 20 thick)
being in equilibrium with the gas. The system consisted of N=223904 particles was enclosed
in the box of Lx = Ly = 111.6 and Lz = 245.0. The surface tension, , was evaluated from [a3]:
 
phase( 2 )
 [ Pn ( z )  Pt ( z )]dz
(3)
phase(1)
where Pn and Pt, the pressure components normal and tangential to the phase boundary, were
measured directly during simulation [a3]. The obtained equilibrium parameters were Teq =
0.813, liq = 0.7233, gas = 0.0222 and the surface tension  = 0.3735(11) where the value in
bracket gives the standard deviation in units of the last digit of the corresponding value. The
equilibrium parameters of liquid are very close to that of the evolution 3 from Table I (main
body of the paper) and we can assume that the value of  is very close to that of the droplet
during evaporation.
REFERENCES
a1. J. Vrabec, G. K. Kedia, G. Fuchs, and H. Hasse, Mol. Phys. 104, 1509 (2006)
a2. P. J. Camp and M.P. Allen, Mol. Phys. 88, 1459 (1996)
a3. B. Shi, S. Sinha, and V. K. Dhir, J. Chem. Phys. 124, 204715 (2006).
Table SI
Teq
1
2
3
4
5,6,7
8,9
0.679
0.713
0.758
0.800
0.851
0.903
0
 vap
0.0065
0.0096
0.0148
0.0219
0.0327
0.0484
0
 liq
0.800
0.783
0.760
0.732
0.704
0.665
0
pvap
0.0042
0.0063
0.010
0.015
0.023
0.033
0
pliq
0.37
0.38
0.40
0.42
0.45
0.47
R ( 0)
Rb
37.1
34.0
31.5
26.8
26.8
35.9
402
354
306
197
266
233
Table S1. The system (droplet plus gas) was equilibrated. The thermodynamic parameters at
equilibrium are given in this Table. Rb is also given. This parameters were used in the
simulations listed in Table 1 of the paper. Simulation runs (as in Table 1) are given in the first
column. After equilibration we raised the boundary temperature. Teq - equilibrium
0
0
0
0
temperature,  vap
and  liq
- gas and liquid densities, pvap
and pliq
- gas and liquid pressures,
Table SII
MP1
MP2
MP3
MP4
MP5
MP6
MP7
MP8
MP9
MP10
MP11
MP12
MP13
MP14
MP15
MP16
MP17
E1
E2

T
N
0.0065
0.0065
0.0065
0.0096
0.0096
0.0096
0.0096
0.0148
0.0148
0.0148
0.0220
0.0220
0.0327
0.0327
0.0485
0.0485
0.0485
0.0096
0.0485
0.729
0.873
1.023
0.750
0.850
0.978
1.116
0.833
0.970
1.150
0.857
0.949
0.901
1.102
0.970
1.029
1.050
0.850
1.012
307200
307200
307200
307200
307200
307200
307200
307200
307200
307200
73728
73728
175616
175616
32768
175616
32768
1331000
1331000
 vap
0.314(6)
0.370(4)
0.423(4)
0.327(8)
0.364(2)
0.423(2)
0.480(5)
0.383(3)
0.424(4)
0.516(6)
0.405(2)
0.438(5)
0.446(4)
0.509(3)
0.522(3)
0.556(7)
0.552(10)
0.356(3)
0.494(4)
Table SII. Thermal conductivity coefficient  vap for a gas at different densities  and
temperatures T. N is the total number of particles used for the simulation. MP – the method of
Muller-Plathe,E – the Evans method. The values in parenthesis give the standard deviation in
units of the last digit of corresponding value. All expressed in standard L-J units
boundary (T=Tb)
200
100
liquid (T=Teq)
0
-100
gas (T=Teq)
-200
-200
-100
0
100
200
Figure S1 A schematic picture of the intersection of our simulation system at time t = 0.
Liquid droplet is in equilibrium with the surrounding vapor at temperature Teq and at time t=0
temperature is raised at the boundary from Teq to Tb. Table SI contains the equilibrium
parameters of the liquid and vapor phases (density, pressure).
liquid
0.8
density
0.6
0.4
0.2
0.0
gas
0.65 0.70 0.75 0.80 0.85 0.90 0.95
kBT/
Figure S2 The vapor liquid coexistence densities versus temperature for “infinite systems”
(filled triangles up – Ref. a1, filled triangles down – Ref. a2) and for the droplet simulations
(empty circles our results– Table S1).
temperature
1.20
1.00
0.80
pressure
0.06
0.04
0.02
0.00
0
40
80
360
400
r/
Figure S3 The temperature (triangles) and pressure (circles) as a function of the distance from
the droplet center, r, for two different times during evaporation (the simulation run n0. 1 from
Table 1). Filled symbols – t = 8400 R(t) = 33.3, empty symbols – t = 20900 R(t) = 23.9. The
gas pressure for larger t (empty circles) is of a few percent higher than that for the lower t.
This is probably a consequence of the finite size of the simulation sphere. The total number of
gas particles increases by nearly 10% during the whole evaporation process