Liquid metal droplets bouncing higher on thicker water layer

The study addresses how to enhance the mobility and rebound behavior of gallium (Ga) and Ga-based eutectic liquid metal (LM) droplets, which are crucial for applications in flexible electronics, soft robots, liquid marbles, nanomedicines, and thermal management. Unlike conventional liquids, LM droplets suffer from immediate oxidation in ambient conditions, forming a thin Ga2O3 skin that mechanically restrains flow and strongly adheres to most solid surfaces, reducing mobility. Furthermore, the high density of LM makes gravitational and inertial effects significant. Prior strategies to enhance droplet mobility have commonly focused on modifying solid surface structures, tuning liquid properties, or changing ambient conditions, but these are challenging for LMs due to oxidation-driven adhesion. The paper proposes and investigates a counterintuitive approach: using a thin, low-viscosity water layer as a lubrication film on a solid substrate to enable complete rebound of oxidized LM droplets and to examine how water layer thickness modulates the restitution coefficient and contact time.

The authors contrast LM droplet dynamics with conventional droplet mobility enhancements achieved via surface texturing, liquid property tuning, or environmental changes. They note that LM’s oxide skin leads to strong adhesion on solids and restricts internal flow, complicating mobility. Previous observations with viscous interfacial layers (e.g., oil) showed suppressed bouncing and increased energy dissipation. Prior work on droplet impacts includes studies on thin air film-mediated bouncing and superhydrophobic or slippery liquid-infused surfaces, typically emphasizing viscous dissipation effects. Modulations of LM behavior via electrochemical control, magnetic fields, vapor control, encapsulation, fuel feeding, textured structures, and underwater environments have been reported, but differ from the current low-viscosity water lubrication mechanism enabling complete rebound. The present work also builds on theoretical and experimental insights into minimum film thickness, Ohnesorge and Weber number scaling, and spreading dynamics relevant to interfacial films.

Experiments investigated oxidized LM droplets impacting glass substrates covered with aqueous layers of controlled thickness. LM material: EGaIn (75% Ga, 25% In). Liquids for layers: deionized water and glycerin–water mixtures (10–40 wt%) to vary viscosity while maintaining similar interfacial tensions. Physical properties (density, viscosity, surface/interfacial tensions) were measured via pendant drop method. Substrate preparation: oxygen plasma-treated glass to render superhydrophilic; liquid layers formed by dispensing water or glycerin solution to spontaneously spread; layer thickness controlled by volume and measured by a probe method with 1 µm accuracy. Droplet generation: LM droplets (radius R ≈ 1.5 mm; volume ≈ 14 µL) released from a polyethylene tube (ID 0.38 mm) at a controlled flow rate (0.06 sccm). Exposure to air (~15 s) ensured surface oxidation before impact. Impact conditions: typical drop height h0 = 40 mm; Weber number We = ρm u^2 R/γma ≈ 10.7; water layer thickness h varied 20–1000 µm (also tests up to h = 10 mm). Imaging: high-speed cameras (Photron FASTCAM SA4 / Fastcam Nova S) at 6000–8000 fps; inverted microscope for bottom-view contact line dynamics; reflection interference contrast microscopy (RICM) for visualizing the presence of a continuous water lubrication film under the impacting droplet. Metrics: restitution coefficient e (ratio of post- to pre-impact velocity), contact time, bouncing height, and presence of residuals. Additional tests: core-shell droplets (LM core with water shell) to emulate an effective lubrication thickness H = (h + hs)/R; viscosity effects studied with glycerin solutions at large H (plateau region of e) while keeping We ≈ 10.7. Theoretical analysis: energy-based model including gravitational and surface energy, negative capillary pressure-induced suction through a water meniscus (capillary force Fc ≈ −πR^2 γwa/h), viscous dissipation within LM and in the lubrication film via lubrication approximation; predictions for e as functions of dimensionless layer thickness H and film Ohnesorge number Ohf; comparison to experiments.

• LM droplets on bare glass spread and adhere due to oxide-induced adhesion; no rebound observed.
• With a water layer (e.g., h = 89 µm), LM droplets completely bounce with negligible adhesion; thicker layers (e.g., h = 298 µm) yield higher rebound heights (hr ≈ 4.6 mm at 89 µm; hr ≈ 5.1 mm at 298 µm; R = 1.5 mm, We ≈ 10.7).
• Bottom-view imaging shows expansion and recoil without residue on the substrate when a water layer is present; RICM confirms a continuous water cushion persists throughout impact.
• The theoretically estimated minimum water film thickness at We = 10.7 is hm ≈ 0.37 µm, exceeding the rupture threshold (<0.1 µm), consistent with preserved lubrication.
• Restitution coefficient e increases monotonically with dimensionless thickness H = h/R for H ≤ Hc, then plateaus at e ≈ 0.35 for H > Hc, with Hc ≈ 0.15. e decreases with increasing We.
• Contact time decreases by about 23% as H increases (from 15.4 ms to 11.8 ms).
• Core-shell experiments (effective H = (h + hs)/R, with hs ≈ 313 µm, H ≥ 0.21) yield the same e–H trend and plateau value, confirming the lubrication role of the water shell.
• Theoretical model incorporating negative capillary pressure in the water meniscus and viscous dissipation predicts e(H) in quantitative agreement with experiments; fitted parameters C1 = 0.2 and C2 = 0.535.
• Viscosity effects: for large H (plateau regime), e follows a predicted dependence on the film Ohnesorge number Ohf; when Ohf > 0.004, droplets do not bounce (e = 0), validated with a highly viscous aqueous layer (Ohf = 0.0043).
• Applications: a water strider-like robot equipped with LM droplets exhibits enhanced locomotion on a water-lubricated surface, achieving a jumping height of 2.61 mm and sliding velocity of 0.34 mm s−1, which are ~3.5× and ~1.5× higher than without LM droplets, respectively.

Findings demonstrate that a thin, low-viscosity water layer acts as an effective lubrication film, preventing direct contact between oxidized LM droplets and the solid substrate and minimizing viscous dissipation, thereby enabling complete rebound. Increasing the water layer thickness enhances rebound (larger e) until a plateau, indicating reduced capillary suction and dissipation effects at larger H. The mechanism contrasts with prior observations on slippery oil-infused surfaces where high viscosity leads to significant energy loss and no bounce. The negative capillary pressure arising from spontaneous spreading of water over LM during impact introduces a downward suction that modulates e; as H increases, this effect diminishes, consistent with the plateau behavior. The combined experimental and theoretical results extend understanding of complex droplet–film interactions and suggest routes to on-demand control of LM droplet mobility for applications requiring low-adhesion transport and impact resilience.

The study reveals a counterintuitive regime where oxidized LM droplets fully rebound from water-coated solid surfaces, with the restitution coefficient increasing with water layer thickness before reaching a plateau (~0.35). The rebound arises from a continuous, low-viscosity water lubrication film that prevents droplet–solid contact and from the modulation of e by negative capillary pressure due to water’s spontaneous spreading on LM. Experiments, including core-shell droplets and viscosity variation using glycerin solutions, align closely with a theoretical energy-based model. The results advance the fundamental understanding of LM droplet dynamics and enable practical strategies for fluid control, exemplified by enhanced jumping and sliding in a LM-equipped soft robot on water-lubricated surfaces.

• Experimental conditions primarily center on droplets of radius R ≈ 1.5 mm and We ≈ 10.7, with supplementary tests at higher We; e decreases with increasing We.
• The theoretical model employs fitted parameters (C1, C2) and assumptions such as r ≈ h for the meniscus curvature and lubrication approximations.
• Bouncing ceases when the lubrication film’s Ohnesorge number exceeds a threshold (Ohf > 0.004), indicating sensitivity to liquid-layer viscosity.
• While robustness across a range of water layer thicknesses was shown (20 µm to 10 mm), broader parameter spaces (e.g., varied droplet sizes, wider We ranges, other substrates) are not exhaustively covered in the presented data.