Explosive Leidenfrost droplets

We show that Leidenfrost droplets made of an aqueous solution of surfactant undergo a violent explosion for a wide range of initial volumes and concentrations. This unexpected behavior turns out to be triggered by the formation of a gel-like shell during the evaporation when the surface concentration of surfactant reaches some critical value. Shortly thereafter, the temperature sharply increases above the normal boiling point, leading to fast bubble growth, shell stretching, and explosion. However, most of the droplet life is characterized by a self-similar evolution of the radial surfactant distribution during which surface and mean concentrations grow in proportion, independently of the initial conditions. The temperature rise (attributed to boiling point elevation with surface concentration) and nucleation followed by growth of vapor bubbles inside the shell are key features leading to the explosion, differing from the implosion (buckling) scenario reported by other authors.

Figure 1

(a) Example of an explosion of a droplet. The initial size of the drop is $100\mu \mathrm{L}$, the initial concentration is ten times the CMC, and the temperature of the plate is $400{}^{\circ }\mathrm{C}$. (b) Schematic representation of a droplet life. To begin with, free molecules and micelles are uniformly distributed. During the evaporation, the droplet shrinks and micelles accumulate at its surface, leading from $\tilde{t}={\tilde{t}}^{*}$ to the formation of a gel-like shell. From $\tilde{t}={\tilde{t}}_T$ the temperature of the droplet $T_d$ rises above the boiling temperature $T_0$, leading to vapor bubble nucleation, growth, shell stretching, and finally explosion of the droplet. Here $N$ denotes the SDS mass fraction and $\rho$ the density (with subscripts $i,l$, and $\mathrm{\Sigma }$ for initial, liquid, and surface, respectively).

Figure 2

(a) Volume vs time for water or SDS droplets of several initial sizes $V_i$ and initial SDS mass concentrations ${\rho }_i$: blue open squares, $V_i=1000\mu \mathrm{L}$ and ${\rho }_i=0.1$ of the CMC; green open squares, $V_i=1000\mu \mathrm{L}$ and ${\rho }_i$ equals the CMC; red open squares, $V_i=1000\mu \mathrm{L}$ and ${\rho }_i=10$ times the CMC; green open circles, $V_i=100\mu \mathrm{L}$ and ${\rho }_i$ equals the CMC; red open circles, $V_i=100\mu \mathrm{L}$ and ${\rho }_i=10$ times the CMC; and red open triangles, $V_i=10\mu \mathrm{L}$ and ${\rho }_i=10$ times the CMC. Closed symbols are used for the final volume just before the explosion. The plate temperature was $T_p=300{}^{\circ }\mathrm{C}$. In the inset, a time translation is applied to the data so as to shift the volume just before explosion onto a reference curve (selected as the one corresponding to $V_i=1000\mu \mathrm{L}$ and ${\rho }_i=0.1$ of the CMC). (b) Mean concentration ${\rho }_m={\rho }_i{V}_i/V\left(t\right)$ versus time. The symbols are the same as in (a). (c) Initial mass $m_i={\rho }_i{V}_i$ of SDS vs final volume just before explosion $V_f$ for all experiments at $T_p=300{}^{\circ }\mathrm{C}$. The open circles show the measurement and the solid line is the interpolation.

Figure 3

(a) Volume vs time for water or SDS droplets at several temperatures of the plate: $250{}^{\circ }\mathrm{C}(◯)$, $300{}^{\circ }\mathrm{C}\left(\square \right)$, $350{}^{\circ }\mathrm{C}\left(▵\right)$, $400{}^{\circ }\mathrm{C}\left(▿\right)$, and $450{}^{\circ }\mathrm{C}\left(\diamond \right)$. Closed symbols are used for the final volume before the explosion. The initial concentration of the droplet is ten times the CMC and the initial size of the droplet is $100\mu \mathrm{L}$. (b) The final volume before explosion $V_f$ is plotted vs the temperature of the plate $T_p$. The line is a linear fit.

Figure 4

(a) Encapsulation of a Leidenfrost drop. Shown on top is a Leidenfrost droplet of SDS, methylene blue, and water over a plate at $300{}^{\circ }\mathrm{C}$. On the bottom the Leidenfrost droplet is removed from the hot plate after the shell is formed and put on a cold plate. The whole droplet is covered by the shell, retaining water. (b) Evolution of the temperature of the top part of the droplet surface. The temperature $T$ is measured using an IR camera placed above the droplet (after a calibration procedure) and $\mathrm{\Delta }T\left(\mathrm{t}\right)=T_d\left(t\right)-{\langle T\rangle }_{\text{before}\text{shell}\text{formation}}$. The dashed line corresponds to the beginning of the formation of the shell.

Figure 5

Stretching ratio $\delta =R_s/R_0-1$ of the shell as a function of the plate temperature $T_p$ for various values of Young's modulus $E$. The ratio of shell thickness $e_0$ to droplet radius $R_0$ is taken equal to $\epsilon$, which decreases with $T_p$, leading to a slight increase of $\delta$. Here $p_0=1$ atm, $T_0=373\mathrm{K}$, and the nucleation temperature is taken (for illustration) to be $T_n=525\mathrm{K}$, i.e., $50\mathrm{K}$ lower than the homogeneous nucleation limit $T_k$. The zone between $E={10}^3$ and ${10}^5$ Pa corresponds to hydrogels, thought to be representative of our SDS shells. Note that this diagram is independent of the values of $V_i$ and $N_i$, due to the self-similarity of the concentration evolution discussed above.