Biomedical Engineering Reference
In-Depth Information
tive cell when
=
0
.
1 due to the larger temperature at the droplet apex that was
not present when
1
.
0.
The two convective cells displayed in Fig. 10(a) result from a bifurcation in the
droplet hydrodynamics from a single cell configuration, common to all droplets
for large contact angles, to a two cell configuration for small contact angles. The
critical contact angle is
θ
=
35
◦
. Numerical simulations suggest that subsequent bi-
furcations show up as contact angles become smaller with an increasing number of
convective cells. The existence of this bifurcation scenario results from the conju-
gated effect of thermocapillary convection and an increasingly confined geometry
due to the vanishing droplet volume with time. But it raises important questions in
the interpretation of the simulation results in particular due to the difficulty here to
properly mesh such flat droplets and to ensure numerical convergence. For small
values of
θ
water circulation appears indeed to be unstable even with very refined
unstructured mesh grids. Efforts still have to be devoted to analyse this problem
and to determine whether hydrodynamics remains laminar or if turbulent regimes
are finally supported by the droplet at small contact angles.
This illustration of the evaporating history of water droplets on copper substrates
shows that FEM based approaches and simplified models can provide insights into
the phenomenology of such a system. The specificity of FEM being the condition
for the droplets to be pinned and exhibiting a spherical cap geometry, allowed im-
portant simplifications and fast simulations. Still, this example presents a number
of important limitations. Among them, quasi-steadiness of the hydrodynamics and
heat/mass transfer, axi-symetry, absence of evaporative cooling or pinned contact
lines, etc. All these approximations have been discussed and were shown to be jus-
tified for specific experimental conditions. Important efforts therefore still have to
be dedicated to improve both the modelling and the numerical techniques in order
to provide a more accurate and general description of evaporating droplets. First of
all the full 3D geometry has to be implemented since droplet evaporation is known
to involve non axi-symetric effects even in pinned regimes. This is for example the
case of thermal waves recently observed [77]. The description of thermal waves
will require important efforts in both modelling and numerics to significantly speed
up 3D computations. The second important limiting factor of the present illustra-
tion is the omission of evaporative cooling that has clearly to be accounted for. As
for front tracking, it leads to potential problems in the present FEM illustration n
particular for the local mass fluxes simulation with robust and stable algorithms.
Last but not least is the description of the contact line dynamics that was assumed
to be time independent while receding contact line regimes are known to show up
[78]. One efficient way to overcome these limitations is the use of Eulerian single
fluid techniques. But, as for FEM, these approaches have their own restrictions dis-
cussed in Paragraph B. Spurious currents induced by interfacial tension algorithms
in such approaches is the most important issue. They generate parasitic sources and
a numerical noise that can create, by their cumulative effect, a thickening of the
interfaces and, overall, to the destabilization of the simulations. Spurious currents
≈
Search WWH ::
Custom Search