Experimental Insights into Droplet Behavior on Van der Waals and Non-Van der Waals Liquid-Impregnated Surfaces

This study utilizes high-speed imaging to demonstrate that the properties of infused lubricants (silicone oil vs. hexadecane) have an insignificant effect on the spreading and rebound dynamics of droplets impacting liquid-impregnated surfaces with varying micro-textures across a wide range of Weber numbers.

The Gist

Imagine you are holding a water balloon and you drop it onto a surface. What happens next depends entirely on what that surface is made of. Does the balloon splat and stick? Does it bounce off like a rubber ball? Or does it shatter into a million tiny droplets?

This paper is a deep dive into that exact question, but with a scientific twist. The researchers are studying what happens when water droplets hit a special kind of surface called a Liquid-Impregnated Surface (LIS).

Think of an LIS like a sponge that has been soaked in oil. Instead of a dry, rough surface, you have a surface where the tiny gaps are filled with a slippery liquid (lubricant). The goal is to see how water behaves when it hits this "oily sponge."

Here is the story of their experiment, broken down into simple concepts:

1. The Two Types of "Oily Sponges"

The researchers created two different versions of these surfaces using square pillars (like tiny Lego blocks) spaced apart. They filled the gaps with two different oils:

• The "Sticky" Oil (Silicone Oil): This oil loves the surface. It clings tightly to the pillars and even forms a super-thin, invisible blanket over the very tops of the pillars. The scientists call this a Van der Waals surface.
• The "Slippery" Oil (Hexadecane): This oil doesn't love the surface as much. It fills the gaps between the pillars, but it leaves the very tops of the pillars exposed to the air. The scientists call this a Non-Van der Waals surface.

2. The Experiment: Dropping the Water

They dropped water droplets onto these surfaces from different heights to change how hard they hit (measured by something called the Weber number, which is basically a score for "how much energy is in the splash").

• Low Energy: A gentle drop.
• High Energy: A hard, fast smash.

3. The Big Discovery: The "Oil Blanket" Matters Most

The most surprising finding was that the type of oil mattered way more than the spacing of the pillars.

Scenario A: The "Sticky" Oil (Van der Waals)
When the water hit the surface with the silicone oil, it acted like a superhero bouncing off a trampoline.

• No matter how hard they dropped the water, the droplet always bounced off completely.
• Why? Because the oil formed a perfect, continuous blanket over the pillars. The water never actually touched the solid surface; it only touched the oil. The oil was so happy to be there that the water couldn't push it away. It was like trying to push a balloon off a sheet of ice—the balloon just slides right off.

Scenario B: The "Slippery" Oil (Non-Van der Waals)
When the water hit the surface with the hexadecane, the results were messy and unpredictable.

• Sometimes the water bounced. Sometimes it stuck. Sometimes it splashed.
• Why? Because the oil didn't cover the tops of the pillars. When the water hit hard, it smashed through the oil, hit the solid pillars, and got stuck in the gaps (like a car getting stuck in mud). The water "wet" the surface, making it hard to bounce back.

4. The "Cloaking" Effect

The researchers also noticed something cool with the "Sticky" oil. Before the water even hit the surface, the oil actually wrapped itself around the water droplet like a tiny raincoat. This is called "cloaking." It meant the water was already wearing an oil suit before it even touched the ground, which helped it bounce even better. The "Slippery" oil didn't do this; it stayed put on the surface.

5. The "High-Speed" Chaos

When they dropped the water really hard (high speed), the "Sticky" oil surface showed a weird phenomenon. As the water tried to pull back up after hitting, the edge of the water became unstable and broke into tiny satellite droplets, like a ring of water shattering into beads. Even though it broke apart, the main droplet still managed to bounce away!

The Bottom Line

This study teaches us that how a liquid interacts with a surface isn't just about the surface texture; it's about the chemistry of the liquid filling that texture.

• If you want a surface that always repels water (great for self-cleaning windows or anti-icing planes), you need an oil that loves the surface and forms a complete, unbroken film.
• If the oil doesn't love the surface enough, the water will eventually break through, get stuck, and ruin the effect.

In short: To make a surface that water can't stick to, you don't just need a rough texture; you need a lubricant that hugs that texture tightly, creating a perfect, slippery shield that water can't penetrate.

Technical Summary

1. Problem Statement

Droplet impact dynamics are critical for applications ranging from inkjet printing to anti-icing and cooling systems. While Superhydrophobic (SHPo) surfaces are known for their water-repellency, they suffer from a "Cassie-to-Wenzel" transition under high dynamic pressure (e.g., droplet impact), causing the air layer to collapse and the surface to lose repellency.
Liquid-Impregnated Surfaces (LIS) offer a solution by replacing the trapped air with a lubricating oil. However, the stability and dynamic behavior of LIS during high-speed droplet impact are not fully understood. Specifically, there is a lack of comparative research on:

• Van der Waals (vdw) LIS: Where the lubricant strongly adheres to the substrate, forming a continuous thin film over surface textures.
• Non-Van der Waals (nvdw) LIS: Where the lubricant has lower affinity, leaving the texture posts exposed.
• The influence of lubricant properties (affinity, viscosity, spreading coefficient) and surface geometry (post spacing) on impact outcomes like spreading, rebound, and oil stability.

2. Methodology

The researchers conducted controlled experimental investigations using high-speed imaging to analyze water droplet impacts on engineered LIS.

• Surface Fabrication:
  • Substrate: Silicon wafers with square micro-textures fabricated via lithography.
  • Geometry: Square posts with a fixed height of 10 µm and three varying post spacings (edge-to-edge): 5 µm, 20 µm, and 30 µm.
  • Functionalization: Surfaces were coated with Octadecyl trichlorosilane (OTS) to create a low-energy, non-polar surface.
• Lubricant Selection: Two lubricants were infused to create distinct LIS types:
  1. Silicone Oil (SO-5cSt): High affinity for OTS, forming a vdw LIS (continuous thin film).
  2. Hexadecane: Lower affinity for OTS, forming an nvdw LIS (posts exposed).
• Impact Setup:
  • Water droplets (2.8 mm diameter) were released from varying heights to achieve impact velocities between 0.88 m/s and 3.70 m/s.
  • This corresponded to a Weber number ($We$) range of 28 to 495.
  • Dynamics were captured using a Phantom VEO 410 high-speed camera (5000 fps).
• Characterization:
  • Stability Analysis: Measured contact angles, spreading coefficients ($S_{ow(a)}$), and calculated effective Hamaker constants to determine film stability.
  • Roll-off Angle Tests: Used to assess the ease of droplet sliding and oil layer integrity.
  • Energy Scaling: Analyzed maximum spreading diameter ($\beta_{max}$) against Weber numbers.

3. Key Contributions

• Differentiation of LIS Types: The study explicitly categorizes and compares the dynamic behavior of vdw LIS (oil-coated posts) versus nvdw LIS (exposed posts) under impact.
• Stability Mechanism Elucidation: It provides a thermodynamic and mechanical explanation for why SO-5cSt forms a stable thin film (negative Hamaker constant, positive spreading coefficient) while Hexadecane does not (positive Hamaker constant, negative spreading coefficient).
• Rebound Regime Mapping: The authors established a comprehensive regime map linking Weber numbers, post spacing, and lubricant type to specific outcomes (complete rebound, partial rebound, sticking, or splashing).
• Disjoining Pressure Analysis: The paper quantifies the energy barrier required to penetrate the thin oil film on vdw LIS, explaining why droplets rebound even at high impact velocities where nvdw LIS fails.

4. Key Results

A. Surface Stability and Oil Behavior

• vdw LIS (SO-5cSt): Exhibits a negative spreading coefficient ($S > 0$) and a negative Hamaker constant, leading to a stable, continuous thin oil layer that cloaks the water droplet and covers the post tops. This results in a very low roll-off angle.
• nvdw LIS (Hexadecane): Exhibits a negative spreading coefficient ($S < 0$) and a positive Hamaker constant. The oil does not cloak the droplet, and the post tops remain exposed to the water. This results in a higher roll-off angle and higher contact angle hysteresis.

B. Droplet Impact Dynamics

• Spreading: The maximum spreading diameter ($D_{max}$) scales with the Weber number as $\beta_{max} \sim We^{1/4}$ for all surfaces, consistent with existing scaling laws for low-viscosity liquids.
• Rebound Behavior (The Critical Finding):
  • vdw LIS (SO-5cSt): Droplets exhibited complete rebound across the entire Weber number range (28–495) for all post spacings. The strong oil-substrate interaction prevents the oil from being displaced, maintaining a lubricating layer that prevents water-solid contact.
  • nvdw LIS (Hexadecane): Behavior was highly dependent on $We$ and spacing.
    • At low $We$: Partial rebound or sticking.
    • At mid $We$: Complete rebound (kinetic energy overcomes viscous resistance).
    • At high $We$: Sticking, splashing, or partial rebound. The impact pressure ruptures the oil layer, allowing water to penetrate the texture and adhere to the solid posts.
• Oil Entrapment: On nvdw LIS, the impact displaces oil, which can become entrapped within the water droplet as a small sphere. On vdw LIS, no oil entrapment occurs because the oil layer remains intact.

C. Influence of Post Spacing

• Solid Fraction: Smaller post spacing (5 µm) has a higher solid fraction, offering more resistance to droplet movement on nvdw surfaces.
• Critical Velocity: Theoretical calculations of critical velocity (where dynamic pressure overcomes capillary pressure) matched experimental observations for nvdw LIS but failed for vdw LIS. The discrepancy is explained by the disjoining pressure of the thin oil film on vdw LIS, which requires a Weber number > 700 to break (beyond the experimental limit of 495).

D. Unique Phenomena

• Rayleigh-Plateau Instability: On vdw LIS at high Weber numbers ($We \ge 245$), the receding rim became unstable, forming filaments that broke into satellite droplets, yet the main droplet still rebounded.
• Residual Marks: After impact, nvdw surfaces showed persistent residual oil patches (oil displacement), whereas vdw surfaces showed self-healing behavior where the oil flowed back to the impact site.

5. Significance and Implications

• Design Guidelines: The study provides clear design criteria for creating robust LIS. To ensure droplet repellency under high-impact conditions (e.g., rain, spray cooling), the lubricant must have a strong affinity for the substrate (vdw LIS) to maintain a continuous film.
• Application Potential: These findings are vital for developing:
  • Anti-icing coatings: Where preventing water adhesion is critical.
  • Drag reduction: Maintaining a stable lubricant layer in fluid flow.
  • Microfluidics and inkjet printing: Controlling droplet rebound and spreading.
• Theoretical Advancement: The work bridges the gap between static wetting theory and dynamic impact phenomena, highlighting that lubricant-substrate affinity is a more critical parameter than lubricant viscosity for impact stability.

In conclusion, the paper demonstrates that while both LIS types are stable in static conditions, vdw LIS (strong oil-substrate affinity) is superior for dynamic applications involving droplet impact, as it prevents water penetration and ensures consistent rebound, whereas nvdw LIS is prone to failure at higher impact energies.