Universal buckling kinetics in drying nanoparticle-laden droplets on a hydrophobic substrate

We provide a comprehensive physical description of the vaporization, self-assembly, agglomeration, and buckling kinetics of sessile nanofluid droplets pinned on a hydrophobic substrate. We have deciphered five distinct regimes of the droplet life cycle. Regimes I–III consists of evaporation-induced preferential agglomeration that leads to the formation of a unique dome-shaped inhomogeneous shell with a stratified varying-density liquid core. Regime IV involves capillary-pressure-initiated shell buckling and stress-induced shell rupture. Regime V marks rupture-induced cavity inception and growth. We demonstrate through scaling arguments that the growth of the cavity (which controls the final morphology or structure) can be described by a universal function.

Figure 1

Droplet life cycle. (a) Recirculation flow pattern inside the droplet (see Video 1 [25]) using laser sheet of 175 microns in thickness. (b) Shell inhomogeneity at the onset of buckling; TZ is the top zone, MZ is the middle zone, and BZ is the bottom zone. (c) Buckling onset (formation of parent cavity PC) and shell rupture due to stretching (formation of daughter cavity DC). (d) Evaporation through the porous shell, air invasion though the punctured PC, and DC growth in the $r\text{−}{y}_c$ direction.

Figure 2

Dynamic morphological transformation of a drying $n\text{-Si}{\mathrm{O}}_2$ dispersion droplet $(40\mathrm{wt}\%)$ from buckling onset until the formation of the final precipitate. Top row depicts the front view while the bottom row shows the corresponding top view. (a) Buckling onset, (b) stretching of the parent cavity, (c) shell puncturing and formation of daughter cavity, (d)–(g) radial-longitudinal cavity expansion, and (h) final microstructure. Images are at time instants 0, 20, 64, 76, 96, 128, 184, and 236 s. Scale bar equals 1.2 mm.

Figure 3

Dynamic deformation of the droplet from buckling onset until the formation of the final precipitate structure for initial particle loading of $20\mathrm{wt}\%$. (a) Droplet at the onset of buckling, (b) buckling onset marked by the stretch marks on the top surface, (c) stretching of the shell, (d) shell punctures forming a cavity, (e)–(h) radial-longitudinal cavity spreading, and (i) final precipitate structure. The images are at time instants 0, 25, 33, 53, 61, 67, 92, 117, and 135 s. Scale bar equals 1.1 mm.

Figure 4

Dynamic three-stage growth process of the daughter cavity.

Figure 5

SEM micrographs of the final precipitate: (a) Overall view for ${\phi }_{\mathrm{o}}=20\mathrm{wt}\%$, (c) ${\phi }_{\mathrm{o}}=40\mathrm{wt}\%$ and cut sections showing the inhomogeneous shell structure (b) ${\phi }_{\mathrm{o}}=20\mathrm{wt}\%$, (d) ${\phi }_{\mathrm{o}}=40\mathrm{wt}\%$. Scale bar equals $200\mu \mathrm{m}$. Magnified view showing closely packed NPs at (e) the equatorial plane and (f) the base. Scale bar equals 100 nm.

Figure 6

Temporal variation of nondimensional daughter cavity volume. Inset shows the droplet height and radius at buckling onset as a function of NP concentration (wt%).