Impact dynamics of particle-coated droplets

We present findings from an experimental study of the impact of liquid marbles onto solid surfaces. Using dual-view high-speed imaging, we reveal details of the impact dynamics previously not reported. During the spreading stage it is observed that particles at the surface flow rapidly to the periphery of the drop, i.e., the lamella. We characterize the spreading with the maximum spread diameter, comparing to impacts of pure liquid droplets. The principal result is a power-law scaling for the normalized maximum spread in terms of the impact Weber number, $D_{max}/D_0\sim {\text{We}}^{\alpha }$, with $\alpha \approx 1/3$. However, the best description of the spreading is obtained by considering a total energy balance, in a similar fashion to Pasandideh-Fard et al. [Phys. Fluids 8, 650 (1996)]. By using hydrophilic target surfaces, the marble integrity is lost even for moderate impact speeds as the particles at the surface separate and allow liquid-solid contact to occur. Remarkably, however, we observe no significant difference in the maximum spread between hydrophobic and hydrophilic targets, which is rationalized by the presence of the particles. Finally, for the finest particles used, we observe the formation of nonspherical arrested shapes after retraction and rebound from hydrophobic surfaces, which is quantified by a circularity measurement of the side profiles.

Figure 1

Schematic representation of the experimental setup used for liquid marble impact.

Figure 2

Photographs of liquid marbles resting on a glass plate. The particle sizes are $d_p=170\mu \mathrm{m}$ (left) and $d_p=25\mu \mathrm{m}$ (right). The dashed boxes indicate the location of the cropped inset in each image. Scale bar is 1 mm.

Figure 3

Side and bottom views of the impact of a liquid marble onto a hydrophilic glass plate. The particle diameter is $d_p=204\mu \mathrm{m}$ and the impact speed is $V_0=1.08$ m/s ($\text{We}=61$). Images shown are at times $t=-0.2$, 1, 2.2, 4.8, and 46.8 ms from impact. The scale bar in each image set is 2 mm long.

Figure 4

Side and bottom views of the impact of a liquid marble onto a hydrophobic glass plate. The particle diameter is 170 $\mu \mathrm{m}$ and the impact speed is $V_0=1.1$ m/s. Images shown are at times $t=-0.2$, 1, 2.2, 4.8, 10.8, and 46.8 ms from impact. The scale bars in each image set are 2 mm long.

Figure 5

Cracks form early on during the spreading stage at (a) 0.8 ms, whilst particles are trapped in the central region directly below the impact site at (b) 2.2 ms. The scale bars are (a) 1 mm and (b) 2 mm long. $d_p=62\mu \mathrm{m}$; $V_0=0.98$ m/s.

Figure 6

Snapshots of liquid marbles during the spreading stage for (a) $d_p=25\mu \mathrm{m}$ and (b) $d_p=170\mu \mathrm{m}$. The impact speed is $V_0=1.1$ m/s and the scale bar is 2 mm long.

Figure 7

(a) Normalized maximum spread, $D_{max}/D_0$, versus impact Weber number, $\rho D_0{V}_0^2/\sigma$ for pure water droplets on both hydrophilic (blue data points) and hydrophobic (red data points) surfaces. (b) Normalized maximum spread, $D_{max}/D_m$, vs impact Weber number, ${\rho }_m{D}_m{V}_0^2/\sigma$, for liquid marbles on both hydrophilic (open data points) and hydrophobic surfaces (filled data points). The legend indicates mean particle size in micrometers.

Figure 8

Comparison between experimental and theoretical normalized maximum spread, $D_{max}/D_0$ for $d_p=118\mu \mathrm{m}$. The open symbols points represent the hydrophilic substrate and filled symbols represent the hydrophobic substrate. The dashed lines are computed using Eqs. (5) and (8).

Figure 9

Comparison between experimental and theoretical normalized maximum spread, $D_{max}/D_0$. The black data points encompass all the liquid marble trials, whilst the blue and red data points represent pure water droplets onto hydrophilic and hydrophobic surfaces, respectively. The theoretical values are computed using Eq. (8). The black line indicates parity.

Figure 10

Snapshots of liquid marbles at maximum spread on hydrophilic surfaces for (a) $d_p=62\mu \mathrm{m}$, (b) $d_p=170\mu \mathrm{m}$, and (c) $d_p=204\mu \mathrm{m}$. In all cases $V_0\approx 0.98$ m/s. The scale bar is 2 mm long.

Figure 11

(a) Image sequence showing the axis switching during the impact of an elliptical arrested-shape liquid marble. The red arrows in the first and fifth images indicate the orientation of the major axis. $D_0=\sqrt{4A/\pi }=3.5$ mm, $d_p=170\mu \mathrm{m}$, $V_0=1.04$ m/s, and $C=0.86$. (b) Sketch showing the axis switching during the impact of liquid marbles with nonspherical arrested shapes.

Figure 12

Formation of arrested shapes after impact and rebound of liquid marbles ($D_0\approx 3$ mm; $d_p=25\mu \mathrm{m}$) from a hydrophobic surface with impact speed (a) $V_0=0.96$ m/s and (b) $V_0=1.39$ m/s. The scale bars are 2 mm long.

Figure 13

(a),(b) Comparison of image profiles and circularity before and after impact. These images correspond to the sequences shown in Fig. 12. (c) Plot of circularity vs impact speed showing circularity both before and after impact. In all cases, $D_0\approx 3$ mm and $d_p=25\mu \mathrm{m}$.