Modeling Approaches and Challenges of Evaporating Sessile Droplets - Drops and Bubbles in Contact with Solid Surfaces - page 149

Figure 6. Snapshot of the dimensionless temperature T ∗ as a function of dimensionless radius r ∗ for
different values of the substrate temperature T s , with L s = R = 1 mm. (a) (respectively (b)) shows T ∗
along the interface when θ ≈ 70 ◦ (respectively θ ≈ 30 ◦ ). The value of T s is given in legend. r ∗ = 0is
the droplet apex and r ∗ = 1 is the contact line.
are considered here. The droplets are indeed initially exactly at the same tempera-
ture as that of the substrate and the only way to create temperature gradients is heat
transfer from the droplet to cooler surrounding air. As the droplet apex is farthest
from the substrate (and thereafter from the heat source) it is clear that the cooling
effect of air, although very limited, will be most efficient in this region. Conversely,
in the contact line region, such a cooling is no more possible due to the dominating
influence of the substrate.
Although relatively small, temperature differences along the droplet interface il-
lustrated in Fig. 6 will locally modify the interfacial tension according to Eq. (10).
The resulting Marangoni stress will generate a shear in the adjacent water and fi-
nally induce thermocapillary motion [26, 34, 48, 70, 75]. The water streamlines are
shown in Fig. 7 together with the corresponding isotherms. As water is initially at
temperature T s , temperature gradients inside and at the droplet interface are small
(Fig. 7 right section) but sufficient to trigger thermocapillary convection (Fig. 7
left section). This figure also shows the existence of a convective cell that flattens