Influence of Contact-Line Curvature on the Evaporation of Nanodroplets from Solid Substrates

The effect of the three-phase contact-line curvature on the evaporation mechanism of nanoscopic droplets from smooth and chemically homogenous substrates is studied by molecular dynamics simulations. Spherical droplets, whose three-phase contact line is curved, and cylindrical droplets, whose contact radius is infinite, are compared. It is found that the evaporation of cylindrical droplets takes place at constant contact angle, while spherical droplets evaporate by simultaneous reduction of their contact area and their contact angle. This is independent of the substrate-liquid interaction strength. The dependence of the evaporation mechanism on the contact-line curvature can be rationalized with the help of the concept of a contact-line tension, and the evaporation simulations of the spherical droplets are used to extract the line tension on each surface. The corresponding values for the Lennard-Jones systems studied here are of the order of ${10}^{-11}\mathrm{N}$, which is in a good agreement with previous theoretical and experimental estimates. With this order of magnitude, the line tension is expected to have an effect on the contact angle of spherical droplets only, when their diameter is less than about 100 nm. The observed difference in evaporation mechanism is interpreted as a manifestation of the line tension whose existence has been controversial.

Figure 1

(a) Cylindrical droplet on a substrate. The left picture is the front view; the right one is the top view. (b) Spherical droplet on a substrate.

Figure 2

Droplet evaporation at $T^{*}=0.83:\text{time}$ evolution of the spherical droplets’ (a) contact angles and (b) contact radii; time evolution of the cylindrical droplets’ (c) contact angles and (d) pseudocontact radii defined as half the distance between two contact lines. The dashed lines are the linear least-squares fits to the contact angle and show its decreasing behavior in (a) and indicate its average value in (c).

Figure 3

Variation of ${\gamma }_{lv}(\cos {\theta }_{\infty }-\cos \theta )$ vs $1/R$ in reduced units for spherical drops with surface interactions ${ϵ}^{*}=0.4$, 0.6, and 0.7 for systems S4, S6, and S7, respectively. Only every third data point is shown in this profile for clarity. The green lines represent the results of fitting the modified Young’s equation to the data, i.e., the lines are constrained to pass through the origin.