Armoring a droplet: Soft jamming of a dense granular interface

Droplets and bubbles protected by armors of particles have found vast applications in encapsulation, stabilization of emulsions and foams, or flotation processes. The liquid phase stores capillary energy, while concurrently the solid contacts of the granular network induce friction and energy dissipation, leading to hybrid interfaces of combined properties. By means of nonintrusive tensiometric methods and structural measurements, we distinguish three surface phases of increasing rigidity during the evaporation of armored droplets. The emergence of surface rigidity is reminiscent of jamming of granular matter, but it occurs differently since it is marked by a step by step hardening under surface compression. These results show that the concept of the effective surface tension remains useful only below the first jamming transition. Beyond this point, the surface stresses become anisotropic.

Figure 1

(a) Evolution of an evaporating liquid marble from liquidlike (left) to wrinkled. (b) Mean surface pressure $\tilde{\pi }$ in the granular shell as a function of $\varphi$ (logarithmic scale), the surface fraction of grains (dark line). $L$ (liquid shell), $S_1$ (solid shell 1), and $S_2$ (solid shell 2) regions are distinguished by linear trend lines (light gray) and illustrated with top views of the grain network. Inset: The $\tilde{\pi }$ curve rectified by the linear regression in the $S_1$ region.

Figure 2

(a) Normalized mean contact number $\tilde{Z}=4^{*}Z/Z_w$ as a function of $\varphi$. Gray: $L$ region. Dark blue (black): $S_1$ and $S_2$ regions. Distinct symbols represent distinct experiments. Inset in (a): Variance ${\sigma }_z^2$ of the contact numbers as a function of $\varphi$. (b) Distribution of coordination numbers ($p_i$, $i=1...6$) as a function of $\varphi$. The lines are best linear fits used to interpolate the variance ${\sigma }_z^2$ of the contact numbers [inset in (a)]. (c) Deviatoric stress $\tau$ as a function of $\varphi$. (d) Typical $Q$ [Eq. (4)] vs time curve. The $W$ line shows the onset of wrinkling.

Figure 3

Surface modulus $K$ as a function of the initial surface fraction ${\varphi }_0$. Inset: Maximal variance (${\sigma }_m^2$) of the number of contacts as a function of ${\varphi }_0$.

Figure 4

Granular shell state as a function of ${\varphi }_0$. (a) In the surface fraction ($\varphi$) plane. Points indicate ${\varphi }_l$ and ${\varphi }_s$. The vertical dotted line provides the boundary of stable nonwetting droplets. Inclined dotted line: $\varphi ={\varphi }_0$. (b) Average pressure $\tilde{\pi }$ at transitions. The dashed lines indicate linear regressions for ${\tilde{\pi }}_0$, ${\tilde{\pi }}_l$, ${\tilde{\pi }}_s$, and ${\tilde{\pi }}_w$.