Rebound of self-lubricating compound drops

Abstract

Drop impact on solid surfaces is encountered in numerous natural and technological processes. Although the impact of single-phase drops has been widely explored, the impact of compound drops has received little attention. Here, we demonstrate a self-lubrication mechanism for water-in-oil compound drops impacting on a solid surface. Unexpectedly, the core water drop rebounds from the surface below a threshold impact velocity, irrespective of the substrate wettability. This is interpreted as the result of lubrication from the oil shell that prevents contact between the water core and the solid surface. We combine side and bottom view high-speed imaging to demonstrate the correlation between the water core rebound and the oil layer stability. A theoretical model is developed to explain the observed effect of compound drop geometry. This work sets the ground for precise complex drop deposition, with a strong impact on two- and three-dimensional printing technologies and liquid separation.

Fig. 1. Impact of a compound drop of water with volume fraction α = 0.3 on a hydrophilic surface.

(A) Black and white image sequence of an impact from an impact height of h = 0.33 m (impact velocity V = 2.4 m/s, We = 659). (B) Color image sequence for h = 0.39 m (We = 772). The water was dyed through addition of a fluorescein salt to distinguish it from the oil. Images were postprocessed to remove spots due to dust on the sensor. (C) Schematic vertical cross sections of an impacting compound drop, illustrating horizontal splashing of oil, the formation and collapse of a cavity, the ejection of a vertical oil jet, the entrapment of oil in the core, and rebound of the core.

Fig. 2. Map of the rebound behavior after impact on a hydrophilic surface as a function of the water volume fraction α and the impact height h (left axis) and Weber number We (right axis), for compound drops produced with the coaxial needle method.

Closed squares, no rebound; closed triangles, rebound (core-shell rebound); open triangles, core-substrate contact, transition zone; open squares, core-substrate contact, no rebound. Shaded area: This region (α = 0.3) refers to the investigation detailed in Figs. 3 and 4. Magnified symbols correspond to the images on the right. The solid line indicates the height from which the water core can sink to the bottom of the drop, obtained by numerical integration of Eqs. 1 and 2. The We axis corresponds to α = 0.3 but is representative for all α since the dependence on α is small.

Fig. 3. Core-substrate contact.

Impact of coaxially produced drops (α = 0.3) on a hydrophilic surface. (A and B) For h = 45 cm (We = 871), the water core spreads on top of the lubricating oil layer without wetting the glass and recoils smoothly (A, bottom view reflection), resulting in core rebound (B, side view). (C and D) For h = 48 cm (We = 922), the lubricating oil layer ruptures, causing the water core to stick to the hydrophilic surface (C), suppressing the recoil, and resulting in a strongly reduced rebounded volume (D). In the bottom view reflection images (A and C), oil-substrate contact is recognizable as darker areas and water-substrate contact as lighter areas. The contrast of the magnified images in the bottom rows of (A) and (C) was enhanced during postprocessing. Overexposed areas in these images correspond to secondary reflections due to the liquid-air interface being parallel to the substrate, as is clearly visible at 3.9 ms, when the drop reaches maximum spreading.

Fig. 4. Effect of substrate wetting properties.

(A) Total rebounded volume Ω_reb (water and oil) as a function of impact height h (approximately ∝ We), normalized by total impacting volume Ω₀, for compound drops produced using the coaxial needle method, with water volume fraction α = 0.3. Three regimes can be distinguished as follows: At low impact speeds, only a single drop rebounds; at intermediate impact speeds, two or more drops rebound; and at higher speeds, core-substrate contact is established, and rebound is suppressed. The core-substrate contact threshold is indicated by the dashed line. (B) Bottom reflection images for h = 54 cm on a hydrophobic (in red) and hydrophilic (in blue) substrate, showing rupture of the lubricating oil layer. On a hydrophobic substrate the core-substrate contact area remains confined, whereas on a hydrophilic substrate the core-substrate contact area rapidly expands. The image contrast was enhanced during postprocessing. (C) Position of the water core as a function of impact height, h. The water core appears larger than it is, as the oil shell acts as a magnifying lens. The actual size of the core is indicated by the dashed circle.

Fig. 5. Effect of the injection method.

(A) Total rebounded volume Ω_reb (water and oil) as a function of the impact height h (approximately ∝ We), normalized by the total impacting volume Ω₀, for compound drops produced by the injection method with water volume fraction α = 0.3. The core-substrate contact threshold (dashed line) is substantially lower for drops produced by the injection method than for drops produced by the coaxial method. (B) Bottom view reflection images for h = 24 cm (We = 490), above the threshold. Core-substrate contact is visible. The image contrast was enhanced during postprocessing.