We impose the ambient temperature at the bottom of substrate and on the dry area on the top of subst

1
INFLUENCE OF THE SUBSTRATE THERMAL CONDUCTIVITY
ON EVAPORATING SESSILE DROPS UNDER REDUCED
PRESSURE S. David a, K. Sefiane a,, G. Dunn b ,
S. Wilson b , B. Duffy b a School of Engineering
and Electronics, University of Edinburgh, UK b
Department of Mathematics, University of
Strathclyde, Glasgow, UK
Introduction The evaporation of sessile drops is
a very important phenomenon occurring in a vast
number of applications including desalination,
painting, ink-jet printing or DNA mapping. The
present study investigates, both experimentally
and theoretically, the role of the thermal
conductivity of the substrates and reduced
ambient pressure on the wetting of evaporating
sessile drops. First, the experimental set up is
introduced with details on the choice of the four
substrates and liquid and the main results are
presented. Finally the mathematical model
developed for the diffusion-limited evaporation
of an axisymmetric droplet of liquid whose
contact line is pinned by surface roughness
effects is developed and compared with the
experimental results. It is shown that the
evaporation of water drops is higher on high
conductivity substrates. This effect is amplified
at reduced pressure.

Experiment
All the experiments have been realized with
droplets of deionised water (milliQ) deposited on
four different substrates (10101mm) chosen
regarding their thermal conductivity properties
Aluminium (237 W/m.K), Titanium (21.9 W/m.K),
Macor (1.46 W/m.K) and PTFE (0.25 W/m.K). To
control the ambient pressure, the drops have been
placed in chamber (see Figure) which is connected
to a vacuum pump and a gas supply. All the
experiments were realized with an identical
initial volume, 2.5 µL, which corresponds to a
drop base radius of 1.35 mm. Thus the radius is
smaller than the capillary length (2.7 mm for
water), it means that the gravity forces are
dominated by surface tension, the drop shape is
then spherical (see Figure). The drops evaporates
in Helium (no humidity) at 22C with the pressure
varying from 40 mbar to 1000 mbar.
Due to the surface roughness, the triple line is
pinned throughout the evaporation process, see
Figure above. The volume decreases linearly with
time, the evaporation rate is constant. On the
Figure on the left, we can see that by reducing
the pressure, there is an important increase of
the evaporation rate. But the most significant
effect is the difference between the four
substrates. The evaporation of water drops
increases with the thermal conductivity of the
substrate and the difference becomes more
important at highest evaporation rate. It is
thought that due to evaporation the drop
temperature tends to decrease. On high
conductivity substrates the heat coming from the
solid is much greater and diminishes the cooling
effect, thus the evaporation is maintained as a
highest rate.
Model
Following the experimental results, we developed
a 2D model with a constant base radius. In the
absence of heating, the evaporation of the drop
is limited by the diffusion of the saturated
vapour layer at the interface into the
surrounding atmosphere.
Both the temperature of the drop and the
substrate are governed by the Laplace equation
We impose the ambient temperature at the bottom
of substrate and on the dry area on the top of
substrate
Temperature and heat flux are continuous
At the interface liquid-gas we have heat loss due
to the evaporation
The vapour concentration is also governed by the
Laplace equation,
,with
Even if the evaporation rates obtained by the
model slightly over estimate the experimental
results, the general trend is very similar. It
confirms that when the drop is placed on high
conductivity substrate, the evaporation is much
higher. It is then essential to consider the
nature of the substrate to estimate the evolution
of freely evaporative sessile drops.
k.sefiane_at_ed.ac.uk