A melting mode of frozen sessile droplets with unmelted ice layer deposited at the bottom

This paper identifies a unique melting mode of frozen sessile droplets on superhydrophobic surfaces where the unmelted ice layer remains deposited at the bottom due to upward fluid flow and lubrication effects, a process that significantly accelerates complete melting compared to the traditional floating mode.

The Gist

The Mystery of the Sinking Ice: Why Some Ice Cubes "Sink" Instead of Float

Imagine you are watching an ice cube melt in a glass of water. Common sense tells you that because ice is lighter (less dense) than water, it should always float to the top. If you were watching a tiny, frozen droplet melt on a surface, you’d expect the "ice heart" to bob up to the surface like a cork in a bathtub.

However, researchers from Tianjin University have discovered something that defies this intuition. They found that under certain conditions, the ice doesn't float—it sinks to the bottom and stays there.

Here is a breakdown of how this "impossible" melting works, using some everyday analogies.

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1. The Two Modes: The "Cork" vs. The "Anchor"

The scientists identified two different ways a frozen droplet can melt:

• The Floating Mode (The Cork): This is what we see every day. As the bottom melts, the ice stays buoyant and rides the waves to the top.
• The Deposited Mode (The Anchor): On special "superhydrophobic" (ultra-water-repellent) surfaces, the ice stays pinned to the bottom like an anchor, even as the water around it melts away.

2. The Secret Engine: The "Marangoni Slide"

How does the ice stay down? It’s all about a hidden current called Marangoni convection.

Think of the melting droplet like a tiny, crowded water park slide. As the bottom of the ice melts, it creates a temperature difference. This temperature difference acts like a "gravity" for surface tension. It creates a powerful current that flows along the very top edge of the droplet.

The Analogy: Imagine a crowd of people (the melted water) rushing toward the top of a hill. As they rush past the ice, they create a "wind" or a "current" that pushes against the ice. In this specific "Deposited Mode," the current is so strong and directed that it actually shoves the ice downward, pinning it against the floor. It’s like a heavy gust of wind blowing a beach ball into a corner, preventing it from bouncing back up.

3. The "Greasy Floor" Effect: Lubrication

You might wonder: "If the ice is being pushed down, why doesn't it just get stuck and stop melting?"

The researchers found that a microscopic, incredibly thin layer of water forms between the ice and the surface.

The Analogy: Think of this like a thin layer of oil on a kitchen floor. Even though the ice is being pressed down, this "liquid lubricant" allows the ice to slide and melt smoothly. It’s a "lubrication effect" that keeps the ice in contact with the heat source (the bottom) without getting stuck, allowing it to melt much faster than if it were floating at the top.

4. Why does this matter? (The "De-Icing" Superpower)

Why should we care about a tiny droplet sinking? Because this discovery is a game-changer for anti-icing technology.

If we can control whether ice "floats" or "sinks," we can control how fast it melts. The "Deposited Mode" (the sinking mode) melts the ice 56% faster than the floating mode.

Real-world applications:

• Airplanes: Imagine a coating on wings that forces ice to stay at the bottom and melt rapidly using the engine's heat, rather than letting it build up and float/clump on the surface.
• Wind Turbines: Helping blades shed ice quickly to keep them spinning.
• Electronics: Protecting sensitive components from frost buildup.

Summary Table

Feature	Floating Mode (Normal)	Deposited Mode (The Discovery)
Ice Position	At the top (like a cork)	At the bottom (like an anchor)
Speed	Slower melting	Much faster melting
Main Force	Buoyancy (floating)	Marangoni Flow (pushing down)
Best Conditions	Low heat, rough surfaces	High heat, ultra-smooth/repellent surfaces

Technical Summary

Technical Summary: A Melting Mode of Frozen Sessile Droplets with Unmelted Ice Layer Deposited at the Bottom

1. Problem Statement

In the study of phase-change phenomena, it is a fundamental physical expectation that ice, being less dense than liquid water, should float at the top of a melting droplet (the "floating mode"). This behavior is critical for understanding anti-icing and deicing processes on surfaces like aircraft, wind turbines, and electronic components. However, the researchers identified an unconventional phenomenon where the unmelted ice layer remains deposited at the bottom of the droplet (the "deposited mode"), seemingly defying buoyancy. The core scientific problem addressed is: What physical mechanisms drive this counter-intuitive melting mode and how can it be controlled?

2. Methodology

The researchers employed a combination of experimental visualization, force analysis, and dimensionless scaling models:

• Experimental Setup: Frozen sessile droplets were placed on various substrates: Copper (Cu), Hierarchical-scale Micro-Nano-structured (HMN) superhydrophobic surfaces, and Single-scale Nano-structured (SN) superhydrophobic surfaces.
• Controlled Variables: The study manipulated heating temperatures (20–80 °C), droplet volumes, contact angles, and particle concentrations to observe transitions between melting modes.
• Flow Visualization: High-speed imaging (100 fps) was used to overlay consecutive images, allowing the team to visualize internal flow patterns (Marangoni and natural convection) within the melting droplet.
• Theoretical Modeling: The team developed a simplified scaling model using dimensionless parameters—the thermocapillary-to-buoyancy parameter ($\Pi$) and the ratio of viscous to buoyancy pressure ($\Lambda$)—to quantify the competition between surface tension gradients, buoyancy, and lubrication forces.

3. Key Contributions

• Discovery of the "Deposited Mode": Identification of a specific melting morphology where ice stays at the bottom, significantly accelerating the melting process.
• Mechanistic Elucidation: The paper identifies thermal Marangoni convection as the primary driver. It explains that the flow pattern determines whether the ice floats or sinks.
• Lubrication Theory Application: The study introduces the concept of a thin liquid film between the ice and the heating wall, where viscous forces dominate, creating a "lubrication effect" that prevents the ice from rising.
• Predictive Scaling Model: The introduction of $\Pi$ and $\Lambda$ provides a mathematical framework to predict which melting mode will occur based on temperature, geometry, and fluid properties.

4. Results

• Morphological Differences: On HMN substrates, the ice floats (floating mode). On SN substrates, the ice deposits at the bottom (deposited mode).
• Melting Efficiency: The deposited mode is significantly faster. At 30 °C, the melting time on the SN substrate was approximately 19.61 s, compared to 44.78 s on the HMN substrate—a 56% reduction in melting time.
• Flow Dynamics:
  • In the floating mode, flow rates toward the bottom of the ice ($Q_2$) are higher than toward the top ($Q_1$), allowing buoyancy to push the ice up.
  • In the deposited mode, high-intensity Marangoni convection causes more fluid to bypass the ice and flow toward the top ($Q_1 > Q_2$), exerting a downward force that overcomes buoyancy.
• Parametric Trends: The deposited mode is favored by:
  • Higher heating temperatures (increases $\Delta T$ and Marangoni flow).
  • Larger contact angles (narrows the flow corridor, increasing flow intensity).
  • Lower particle concentrations (reduces damping of the Marangoni flow).

5. Significance

This research provides a new paradigm for controlling phase-change processes. By understanding how to trigger the "deposited mode," engineers can design superhydrophobic surfaces that facilitate much faster deicing. This has direct industrial implications for:

• Aviation Safety: Faster removal of ice from wings and sensors.
• Renewable Energy: Improving the efficiency of wind turbines by preventing ice accumulation.
• Thermal Management: Optimizing phase-change energy storage and 3D printing processes.