Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact

Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlying mechanism. An effective viscosity is defined accordingly to quantitatively explain the observations.

Figure 1

Maximum droplet spreading diameter $D_m$ scaled by the initial diameter of the droplet $D_0$ versus the effective Weber number ${\text{We}}^{†}$ (see the text for its definition). The results are plotted for different grain sizes (indicated by colors) and combinations of droplets and granular substrates (denoted by symbols). The inset shows the same data in logarithmic scale.

Figure 2

The maximum droplet spreading diameter $D_m/D_0$ for all hydrophilic impacts of Fig. 1 in a doubly logarithmic plot. The same symbols and colors as in Fig. 1 are used. The data have been compensated in such a way that a transition between a capillary ($\propto {{\text{We}}^{†}}^{1/4}$) and a viscous regime ($\propto {{\mathrm{Re}}^{†}}^{1/5}$) can be observed. The power laws of these two regimes are indicated by dashed lines.

Figure 3

The splashing parameter $K_d^{†}={{\text{We}}^{†}}^{1/2}{{\mathrm{Re}}^{†}}^{1/4}$ as a function of ${\text{We}}^{†}$. Here, ${\text{We}}^{†}$ and ${\mathrm{Re}}^{†}$ are the effective Weber and Reynolds number, respectively, as defined in the text. The same colors and symbols as in Fig. 1 are used to denote various combinations of liquid and wettability of grains, while those impacts resulting in splashing or fragmentation are highlighted with a cross. The dashed line marks the threshold separating deposition and splashing regimes. The top left and bottom right insets show examples of a water droplet with $D_0=2.8\mathrm{mm}$ and $U=5.2\mathrm{m}/\mathrm{s}$ impacting on clean ceramic beads with $d_g=98\mu \mathrm{m}$ and ceramic beads with $d_g=257\mu \mathrm{m}$, respectively.