Jump-to-contact instability: The nanoscale mechanism of droplet coalescence in air

We study experimentally by means of atomic force microscopy (AFM) the jump-to-contact instability between two droplets in air, with radii ranging between 0.7 and $74\mu \mathrm{m}$. This instability which occurs at the nanoscale is responsible for droplet coalescence. The AFM experiments were conducted in contact and frequency-modulation modes where the interaction force and the frequency shift are monitored while the two droplet interfaces approach each other. The critical distance $d_{\min }$ at which the jump to contact takes place is determined by fitting the experimental curves by the theoretical expressions for the force and the frequency shift. The results point out the existence of two regimes. For submicrometer droplets, $d_{\min }$ scales as ${(H{R}_{\text{eq}}/\gamma )}^{1/3}$ where $R_{\text{eq}}$ is the equivalent droplet radius, $H$ the Hamaker constant, and $\gamma$ the surface tension of the liquid. For larger droplets, $d_{\min }$ no longer depends on the droplet size and scales as ${(H/\gamma )}^{1/2}$. This second scaling is the one that controls droplet coalescence in most situations.

Figure 1

Sketch of the experimental setup: AFM coupled with a high-speed camera and an inverted optical microscope.

Figure 2

Side view of a cantilever droplet before coalescence with a sessile droplet.

Figure 3

Contact AFM experiments: force versus displacement. Fits are obtained by means of Eq. (1).

Figure 4

FM-AFM experiments: frequency shift versus displacement. Fits are obtained by means of Eqs. (1) and (2).

Figure 5

$d_{\min }$ versus $R_{\text{eq}}$. The blue dots correspond to $R_1/R_2<0.3$ and the red dots to $R_1/R_2>0.3$.

Figure 6

$d_{\min }^{*}$ versus $Ha$. The blue dots represent the data of the jump to contact between droplets. The blue dots correspond to $R_1/R_2<0.3$ and the red dots to $R_1/R_2>0.3$. The black dots represent the data from [12] of the jump to contact between a liquid puddle and a droplet, which corresponds to $R_1/R_2\approx 0$.