Dynamics of Droplets Impacting on Aerogel, Liquid Infused, and Liquid-Like Solid Surfaces

Abstract

Droplets impacting superhydrophobic surfaces have been extensively studied due to their compelling scientific insights and important industrial applications. In these cases, the commonly reported impact regime was that of complete rebound. This impact regime strongly depends on the nature of the superhydrophobic surface. Here, we report the dynamics of droplets impacting three hydrophobic slippery surfaces, which have fundamental differences in normal liquid adhesion and lateral static and kinetic liquid friction. For an air cushion-like (super)hydrophobic solid surface (Aerogel) with low adhesion and low static and low kinetic friction, complete rebound can start at a very low Weber (We) number (∼1). For slippery liquid-infused porous (SLIP) surfaces with high adhesion and low static and low kinetic friction, complete rebound only occurs at a much higher We number (>5). For a slippery omniphobic covalently attached liquid-like (SOCAL) solid surface, with high adhesion and low static friction similar to SLIPS but higher kinetic friction, complete rebound was not observed, even for a We as high as 200. Furthermore, the droplet ejection volume after impacting the Aerogel surface is 100% across the whole range of We numbers tested compared to other surfaces. In contrast, droplet ejection for SLIPs was only observed consistently when the We was above 5-10. For SOCAL, 100% (or near 100%) ejection volume was not observed even at the highest We number tested here (∼200). This suggests that droplets impacting our (super)hydrophobic Aerogel and SLIPS lose less kinetic energy. These insights into the differences between normal adhesion and lateral friction properties can be used to inform the selection of surface properties to achieve the most desirable droplet impact characteristics to fulfill a wide range of applications, such as deicing, inkjet printing, and microelectronics.

Keywords: SLIPS; SOCAL; adhesion; aerogel; droplet impact; friction; superhydrophobic.

Figure 1

(a) Image of the custom droplet impact imaging stage. (b) Close-up of the needle holder, sample stage, and height rail. (c) Image of the tilting stage equipment used to carry out droplet kinetic friction measurements. (d) Diagram showing the front and back contact angles of a droplet sliding on an inclined surface at an arbitrary velocity.

Figure 2

Comparison of the (a) static contact angle, θ_s, and (b) contact angle hysteresis, θ_hysteresis, of DI water droplets deposited on all four surfaces tested (PDMS, SLIPS, SOCAL, and Aerogel). A 1 mm scale bar is provided in the first image of subfigure (a), and each CA value is provided as a mean ± std. (c) Comparison of values of πw sin θ_e = πw (sin θ_F + sin θ_B)/2 for each surface, where θ_F and θ_B are defined in Figure 1d. (d) Comparison of the droplet kinetic friction quantified using μ_k/k, for all four surfaces. * represents a student’s t test p-value <0.05, ** < 0.001, and *** < 0.0001. The kinetic friction of Aerogel presented in (d) was calculated using angles measured from both the compressed and relaxed stages of droplet bouncing (see Video S1 of Aerogel bouncing in the Supporting Information).

Figure 3

Representative images showing the different impact regimes encountered in this study. (a) The “no rebound” regime where no part of the droplet loses contact with the surface after impact. In this regime, the droplet displays damped oscillation between a changing maxima and minima spread until it eventually comes to rest. (b) The “partial rebound” regime where, after receding from maximum spreading, a portion of the droplet is ejected vertically while the base of the droplet remains pinned to the surface. (c) The “complete rebound” regime where the whole droplet rebounds from the surface following impact. (d) The “receding breakup and rebound” regime where satellite droplets are ejected radially outward while the main drop recedes from the maximum spread and rebounds from the surface. For each regime (a–d), photos from left to right show a progression in time after impact.

Figure 4

Evolution of impact regime against droplet Weber and Reynold’s numbers for each surface. Each surface is presented in a separate graph to improve clarity (there is significant overlap between curves).

Figure 5

Evolution of the droplet bouncing ratio and several images of droplet ejection at intermediate We (30 < We < 40). (a) Graphs of the bouncing ratio evolution of droplets impacting on plain PDMS, SLIPS, SOCAL, and Aerogel for intermediate We. Droplet ejection occurred on all surfaces except plain PDMS. (b) Droplet ejection images from SLIPS, SOCAL, and Aerogel surfaces. A 2 mm scale bar is provided in the left image. For SOCAL, the secondary droplet curve is shown to separate from the primary curve: this is when the secondary droplet is ejected from the primary droplet.

Figure 6

Evolution of the droplet bouncing ratio and several images of droplet ejection at high Weber numbers (150 < We < 205). (a) Graphs of the bouncing ratio evolution of droplets impacting on plain PDMS, SLIPS, SOCAL, and Aerogel for high We. Droplet ejection occurred on all surfaces including PDMS. (b) Droplet ejection images from SLIPS, SOCAL, and Aerogel surfaces. A 2 mm scale bar is provided in the left image and any breaks in bouncing curves are due to ejected droplets leaving the frame of the captured video.

Figure 7

Bar plot showing the proportion of the impacting droplet that is ejected from each surface at each drop height. For clarity, error bars show the max and min measurements instead of the measurements’ standard deviation.

Figure 8

(a) Graph showing the droplet contact time plotted against Weber number. (b) Ratio of spreading time over the contact time for a wide range of We. It appears that such a time ratio decreases with the We number. The three rebounding SLIPS points shown in Figure 4 (We < 10) were not included in fittings as they were present in a region of nonconsistent droplet rebound (see Figure 4).

Figure 9

Droplet spreading dynamics at low Weber number (1 < We < 4) corresponding to a drop height of 15 mm. (a) Selected snapshots of impacting droplets on each of the surfaces tested in this study (the first four images show droplet spreading, and the final image shows droplet retraction). A 2 mm scale bar is provided in the upper left image. (b) Comparison of the spreading ratio evolutions of droplets impacting each of the four surfaces tested.

Figure 10

Droplet spreading dynamics at intermediate Weber number (30 < We < 40) corresponding to a drop height of 100 mm. (a) Selected snapshots of impacting droplets on each of the surfaces tested in this study (the first three images show droplet spreading, and the final image shows droplet retraction). A 2 mm scale bar is provided in the upper left image. (b) Comparison of the spreading ratio evolutions of droplets impacting each of the four surfaces tested.

Figure 11

Droplet spreading dynamics at low Weber number (150 < We < 250) corresponding to a drop height of 550 mm. (a) Selected snapshots of impacting droplets on each of the surfaces tested in this study (the first four images show droplet spreading, and the final image shows droplet retraction). A 2 mm scale bar is provided in the upper left image. (b) Comparison of the spreading ratio evolutions of droplets impacting each of the four surfaces tested.

Figure 12

Comparison of β_max fittings using the model derived by Pasandideh-Fard et al. (eq 9) and present study (eqs 10a and 10b).