Droplet splashing on rough surfaces

When a droplet hits a surface fast enough, droplet splashing can occur: Smaller secondary droplets detach from the main droplet during impact. While droplet splashing on smooth surfaces is by now well understood, the surface roughness also affects at which impact velocity a droplet splashes. In this paper, the influence of the surface roughness on droplet splashing is investigated. By changing the root-mean-square roughness of the impacted surface, we show that the droplet splashing velocity is only affected when the droplet roughness is large enough to disrupt the spreading droplet lamella and change the droplet splashing mechanism from corona to prompt splashing. Finally, using Weber and Ohnesorge number scaling models, we also show that the measured splashing velocity for both water and ethanol on surfaces with different roughnesses and water-ethanol mixtures collapses onto a single curve, showing that the droplet splashing velocity on rough surfaces scales with the Ohnesorge number defined with the surface roughness length scale.

Figure 1

Surface roughness profiles of the sandpaper surfaces [(a) grit 2000, $R_{\text{rms}}=4.6\pm 0.3\mu \mathrm{m}$; (b) grit 80, $R_{\text{rms}}=78\pm 7\mu \mathrm{m}$] and glass surfaces [(c) smooth, $R_{\text{rms}}=0.0075\pm 0.0006\mu \mathrm{m}$; (d) sandblasted, $R_{\text{rms}}=7\pm 1\mu \mathrm{m}$] as measured with a Keyence VK-X1000 laser scanning confocal microscope. The surface roughness profiles shown in (c) and (d) are for untreated glass slides. The color coding indicates the height or depth of the peaks and valleys with respect to a reference plane of the roughness profile, with the legend shown in the top left of each image.

Figure 2

High-speed images of an ethanol droplet impacting (a) a smooth silanized glass slide ($R_{\text{rms}}=0.03\pm 0.03\mu \mathrm{m}$) and (b) grit 80 sandpaper ($R_{\text{rms}}=78\pm 7\mu \mathrm{m}$) (b) at the same impact velocity ($v>v_{\text{sp}}$). For the smooth surface, satellite droplets are formed from the rim of the lifted sheet of liquid (corona splash), whereas for rough surfaces the satellite droplets are formed from fingerlike structures (prompt splash).

Figure 3

Measured splashing velocity as function of the surface roughness plotted on a log-log scale for ethanol impacting sandpaper (blue circles), and untreated (yellow squares) and silanized (green diamonds) glass slides. The red line gives the theoretical prediction for corona splashing [14]. The splashing velocity measurements for ethanol impacting stainless steel (purple downward triangle) and parafilm (open brown circle) from the study of de Goede et al. [10] are added for comparison. The vertical gray dashed line shows the transition roughness calculated with Eq. (2).

Figure 4

(a) Measured splashing velocity of water and ethanol for different surface roughnesses on sandpaper, and untreated and silanized glass slides plotted on a log-log scale. The dashed lines give the theoretical prediction for corona splashing [14]. No splashing was observed for droplet impact on the smooth untreated glass surface. (b) Measured contact angles of water as a function of the root-mean-square roughness of the sandpaper (blue circles), and untreated (yellow squares) and silanized glass slides (green diamonds). The contact angle of parafilm from Ref. [10] (red square) is added to this graph as well.

Figure 5

(a) Calculated critical Weber number as a function of $2R_{\text{rms}}/D_0$ for the water (blue circles) and ethanol (yellow squares) measurements shown in Figs. 3 and 3, together with measurements of water-ethanol mixtures on rough glass (brown pentagons). Data for water-ethanol mixtures on stainless steel (downward green triangles), parafilm (upward red triangles), and smooth glass (purple diamonds) from de Goede et al. [10] are included. The red and green solid lines are the critical Weber numbers calculated using the splashing model of Riboux and Gordillo [14] for water and ethanol, respectively. The black dashed line is given by ${\mathrm{We}}_c\ge K_2\left(cos{\theta }_0\right){\left(2R_{\text{rms}}/D_0\right)}^{-3/5}$ [Eq. (1)]. (b) Ratio $v_{\text{sp}}/v_{\text{RG}}$ as a function of the Ohnesorge number with $R_{\text{rms}}$ as the characteristic length scale $\text{Oh}\left(R_{\text{rms}}\right)$ for the water and ethanol measurements on different surfaces (blue circles and yellow squares, respectively) and water-ethanol mixtures on a rough glass slide (brown pentagons). Data for water-ethanol mixtures on stainless steel (green triangles), smooth glass (purple diamonds), and parafilm (red triangles) from de Goede et al. [10] are included. The red line gives the prediction of the splashing model of Riboux and Gordillo, and the black line is the best fit of ${\text{Oh}}^{2/3}$.