Modeling Approaches and Challenges of Evaporating Sessile Droplets - Drops and Bubbles in Contact with Solid Surfaces - page 150

Figure 7. Streamlines (left section) and isotherms (right section) in a droplet for T s = 60 ◦ Cand
several values of θ . θ = 80 ◦ (a), θ = 50 ◦ (b), θ = 20 ◦ (c). Black arrows show the circulation of the
velocity field. Some values of T ∗ are also indicated. L s = R = 1 mm.

as droplet height decreases. Regarding Marangoni velocity, its largest magnitude
is several tens of mm/s and indicates that water circulation in the convective cells
can be relatively fast and still accurately described by FEM' approach. This cir-
culation will enhance the heat transfer from the substrate to the droplet interface.
But, although important for thermocapillary phenomena, it has been shown that it
does not influence significantly the overall evaporative mass flow and hence, the
evaporation kinetics of the droplets [6].
One more point that can be discussed in the frame of this chapter is the precise
influence of the substrate geometry in the droplet hydrodynamics. In the example
proposed here, the substrate is ideal and presents the peculiar geometry illustrated in
Fig. 3. Such geometry is technically challenging due to the absence of heat transfer
between the substrate heater and the rest of it. From the numerical point of view,
it has however the important interest to provide the possibility to emphasize the
precise impact of such large temperature differences on the droplet hydrodynamics.
In the above discussion, the condition L s =

R was imposed and the substrate heater
was exactly of the same size as that of the droplet contact radius R . The ratio =

L s /R that was set to 1 with the relevant parameter here since it is the one that
allows the control of the substrate heat flow inside the droplet. When < 1the
substrate heater is smaller than the contact line radius and all the heat it provides
flows into the droplets and contributes to the evaporation kinetics. When > 1, the
substrate heater is larger and only part of the heat flow is used for water heating and
evaporation. thereafter controls the adiabatic character of the heat exchanges in
the substrate/droplet system.