Biomedical Engineering Reference
In-Depth Information
Figure 8. Water circulation inside the droplet for T s = 50 Cwhen θ = 60 .(a) = 0 . 1and
(b) = 1 . 0. Insets illustrate the details of the velocity field in the vicinity of the water/air interface
and bold arrows show the direction of water circulation. The values of the velocity can be obtained
using the full visible arrows in the bottom right corner of the insets and are respectively 3.0 mm/s (a)
and 1.5 mm/s (b). The dark grey area of the substrate is the heater.
The influence of the value of on the hydrodynamical evolution of the droplet
is illustrated in Fig. 8 for =
1 . 0. This last case is again presented
here to ease comparison and was shown to exhibit a clockwise rotating convective
cell (cf. Fig. 7). A similar convective cell shows up when =
0 . 1and =
0 . 1 but with the
important difference that it now rotates counter clockwise due to reversed thermo-
capillary effects. The apex of the droplet is indeed now warmer than its contact line
that turns out to be too far from the substrate heater to rapidly reach temperature
T s . Surface tension is therfore larger in its vicinity leading to a thermocapillary cir-
culation that now flows from the droplet apex to the contact line. This temperature
and flow inversion clearly indicates that the substrate heater size plays key role in
heated droplet hydrodynamics. A detailed study of the evaporative mass flux and
droplet volume evolution for such substrates has been discussed in [26, 34, 48]. It
has been shown for example that the overall droplet evaporation time is almost in-
dependent of as long as
1. The velocity scales in Fig. 8 can be estimated
from the velocity vector in the lower right corner of the insets. They differ by a fac-
tor of two with faster velocities when
=
0 . 1 due to larger interfacial temperature
60 is reached, the absolute value of the
temperature difference between the droplet apex and contact line is close to 0.1 C
when
gradients. Indeed, when contact angle θ
=
1 . 0 and reaches 0.4 Cwhen
0 . 1. The driving force for thermocap-
illary convection is therefore stronger in this last case. This is actually not always
true since Marangoni flow can be strongly modified for small values of as will
be discussed next in this chapter.
Figure 9 displays the Marangoni velocity profile v mar along the water/air inter-
face for two different contact angles with the initial condition of table 1 and for
=
=
0 . 1. It indicates important modifications as contact angle decreases. Initially,
when θ
=
80 , it shows a single maximal value close to r =
0 . 5 that is a typical sit-
uation realized initially for almost all values of T s and L s . In the case of large values
=
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