Mechanical stability of particle-stabilized droplets under micropipette aspiration

We investigate the mechanical behavior of particle-stabilized droplets using micropipette aspiration. We observe that droplets stabilized with amphiphilic dumbbell-shaped particles exhibit a two-stage response to increasing suction pressure. Droplets first drip, then wrinkle and buckle like an elastic shell. While particles have a dramatic impact on the mechanism of failure, the mechanical strength of the droplets is only modestly increased. On the other hand, droplets coated with the molecular surfactant sodium dodecyl sulfate are even weaker than bare droplets. In all cases, the magnitude of the critical pressure for the onset of instabilities is set by the fluid surface tension.

Figure 1

Micropipette aspiration of particle-laden droplets. (a) Schematic of the experiment. (b) Tongue length, $\mathrm{\Delta }h$, versus suction pressure, $\mathrm{\Delta }P=P^{\left(\text{pip}\right)}-P^{\left(\text{atm}\right)}$, which is increased quasistatically. The dashed line connects data points continuously leading up to pinch off. We identify the onset of capillary instability as the point where $\mathrm{\Delta }h$ grows despite holding the pressure constant, $\mathrm{\Delta }{P}_c^{\text{cap}}$ (blue line). The droplet eventually buckles at critical pressure $\mathrm{\Delta }{P}_c^{\text{buc}}$ (red line). (c–e) Images of the droplet (c) at the capillary instability, (d) at the buckling instability, and (e) far above the buckling threshold. The scale bar in all images is 15 $\mu \mathrm{m}$.

Figure 2

Gallery of elastic instabilities. At the onset of buckling, we observe surface deformations including (a) multiple dimples, (b) large surface folds, (c) localized wrinkles, and (d) catastrophic failure. The scale bar in all images is 20 $\mu \mathrm{m}$.

Figure 3

Critical pressure data for particle-laden droplets, varying pipette, and droplet radii. (a) Critical pressures, $\mathrm{\Delta }{P}_c^{\text{cap}}$ (open circles) and $\mathrm{\Delta }{P}_c^{\text{buc}}$ (filled circles) versus pipette radius $R_p$. Marker size scales with corresponding droplet radius $R_d$. (b) The same critical pressures versus $R_d$. Marker size now scales with corresponding $R_p$.

Figure 4

Critical pressure $\mathrm{\Delta }{P}_c^{\text{cap}}$ for bare droplets (green) and bare droplets in $1\%$ SDS (magenta). (a) Critical pressure $\mathrm{\Delta }{P}_c^{\text{cap}}$ versus pipette radius $R_p$. Marker size scales with corresponding droplet radius $R_d$. (b) The same $\mathrm{\Delta }{P}_c^{\text{cap}}$ versus $R_d$. Marker size now scales with corresponding $R_p$.

Figure 5

Apparent tension at the onset of the capillary instability, ${\tau }_c$, based on Laplace Eq. (2) for various droplets (a) ${\tau }_c$ versus droplet radius $R_d$ for particle-laden droplets (blue), bare droplets (green), and bare droplets in 1% SDS (magenta). Solid line is the expected surface tension for a bare droplet, $\gamma =53.1$ mN/m [27]. (b) Spread in ${\tau }_c$ normalized by number of droplets.

Figure 6

Pressure inside various droplets at the onset of instability (a) $\mathrm{\Delta }{P}_c^{\text{drop,}\text{cap}}$ at the onset of capillary instability versus droplet radius $R_d$ for particle-laden droplets (blue) and bare droplets (green). The purple line is a Laplace fit and gives ${\gamma }_{\text{fit}}=58\pm 1$ mN/m. (b) $\mathrm{\Delta }{P}_c^{\text{drop,}\text{buc}}$ at the onset of buckling instability. The red curve shows the prediction of Eq. (3) for $E^{\prime }{t}^2=560\mathrm{kPa}\mu {\mathrm{m}}^2$.