Hysteresis in the freeze-thaw cycle of emulsions and… — Plain-Language Explanation

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This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are watching a slow-motion movie of winter arriving and then leaving. In nature, when water freezes, it doesn't just turn into ice instantly; a "front" of solid ice pushes forward through the liquid. When spring comes, that ice melts, and the front pulls back.

This paper is like a detective story about what happens to tiny objects—like little oil bubbles or plastic beads—when they get caught in this freezing and thawing dance. The scientists wanted to know: If you freeze something and then thaw it, does it end up exactly where it started, or has it been moved?

Here is the breakdown of their findings using simple analogies:

The Setup: The Ice Conveyor Belt

The researchers set up a tiny, controlled "conveyor belt" made of ice.

Freezing: They push the ice forward toward a single object (like a tiny oil drop or a plastic bead).
Thawing: They pull the ice back, letting the object return to liquid water.

They watched closely to see how the object reacted to the moving edge of the ice.

The Two Characters: The Plastic Bead vs. The Oil Drop

The study looked at two very different types of "victims" in this ice dance:

Polystyrene (PS) Particles: These are hard, solid plastic beads. Think of them as rocks.
Oil Droplets: These are soft, squishy blobs of oil floating in water. Think of them as water balloons.

Act 1: The Freeze (The Push)

When the ice front moves forward:

The Rock (PS Particle): If the ice moves slowly, the rock refuses to get trapped. The ice "pushes" the rock ahead of it, like a snowplow pushing a car. The rock slides along the edge of the ice, getting pushed further and further away from its starting spot.
The Balloon (Oil Drop): The soft oil drop also gets pushed, but because it is squishy, it gets squashed and stretched by the ice as it gets trapped. It changes shape, becoming pointy and tear-like, before finally getting stuck inside the ice block.

Act 2: The Thaw (The Pull)

This is where the magic happens. The scientists reversed the process and melted the ice, pulling the front back.

The Rock (PS Particle): When the ice melts and pulls back, the rock doesn't just sit there. In a surprising twist, the melting ice gives the rock an extra shove in the opposite direction! It's like the ice is saying, "I'm letting you go, but here's a little extra push." As a result, the rock ends up farther away from where it started than it was before the freeze. It never returns home.
The Balloon (Oil Drop): The oil drop behaves differently. As the ice melts and the drop escapes, it seems to get "held back" by the melting front for a moment. It slows down, almost as if the ice is reluctant to let it go. Because of this hesitation, the oil drop drifts back toward its original starting position. By the time it is fully free, it has almost returned to where it began.

The Big Discovery: Hysteresis (The Memory Effect)

The scientists call this difference hysteresis. It's a fancy word for "history matters."

If you take a plastic bead through a freeze-thaw cycle, it ends up in a new location. The path it took to get there is different from the path it took to leave.
If you take an oil drop through the same cycle, it tends to return to its starting spot.

The Shape-Shifter's Secret

One of the coolest findings was about the oil drop's shape.

When the ice froze, the drop got squashed and stretched.
When the ice melted, the drop popped back into a perfect sphere.
The scientists found that this shape-shifting is perfectly reversible. It's like a spring: you compress it, and when you let go, it snaps back to exactly the same shape. The drop didn't get "tired" or damaged; it remembered its original shape perfectly.

Why Does This Happen?

The paper suggests that the difference comes down to how the object interacts with a microscopic layer of water that exists between the object and the ice.

For the hard rock, the physics of this thin water layer creates a force that pushes the rock away as the ice retreats, sending it on a one-way trip.
For the soft oil drop, the interaction is different. The drop seems to get "dragged" back by the melting front, helping it return to its origin.

The Bottom Line

The paper shows that nature isn't always symmetrical. Just because you freeze something and then melt it doesn't mean everything goes back to normal.

Hard objects (like plastic beads) get pushed further away by the cycle.
Soft objects (like oil drops) tend to return to their starting spot and snap back to their original shape.

This helps us understand the complex, invisible forces at play when things freeze and thaw, which is important for understanding everything from how ice forms in nature to how we might preserve materials in the future.

1. Problem Statement

Freeze-thaw cycles are ubiquitous in nature and critical for industrial applications ranging from cryopreservation to the templating of porous materials. While the interaction between objects (particles, droplets, bubbles) and an advancing solidification front (freezing) is well-documented, the behavior during the retracting solidification front (thawing) remains poorly understood.

Key open questions include:

Do objects return to their original positions after a freeze-thaw cycle, or do they experience net displacement?
Is there hysteresis in the interaction dynamics between freezing and thawing?
How does the deformability of the object (soft oil droplets vs. rigid polystyrene particles) influence these dynamics?

2. Methodology

The authors employed a controlled experimental setup to study uni-directional freezing and thawing of isolated spherical objects.

Experimental Setup: A 200 µm thick Hele-Shaw cell was subjected to a fixed thermal gradient ( $G \approx 1 \times 10^4$ K m $^{-1}$ ) created by cooling one side to $-15^\circ$ C and maintaining the other at $18^\circ$ C.
Model Systems:
- Oil-in-water emulsions: Silicone oil droplets (5 cSt) stabilized with TWEEN-80 surfactant. Sizes ranged from $R \approx 50$ µm to $105$ µm.
- Polystyrene (PS) suspensions: Rigid solid particles with radii $R \approx 20$ µm and $70$ µm.
Protocol:
1. Freezing: The cell was moved toward the cold side at a constant velocity $V$ , causing the planar ice front to advance relative to the particle.
2. Thawing: The velocity was reversed, moving the cell toward the warm side, causing the ice front to retract.
Imaging: High-speed microscopy (Nikon D850) captured the particle-front distance $h(t)$ and droplet deformation (aspect ratio $\Gamma(t)$ ) in the frame of reference of the moving front.
Theoretical Comparison: Experimental data were compared against a prior theoretical model (Meijer, Bertin & Lohse, 2025) incorporating Van der Waals disjoining pressure, viscous lubrication, and thermal conductivity mismatches. The model was adjusted to include volume expansion effects during phase change.

3. Key Results

A. Freezing Dynamics (Advancing Front)

Three Regimes: Depending on the approach velocity $V$ $V$ relative to a critical velocity $V_{crit}$ $V_{cr i t}$ , objects exhibit:
1. Fast engulfment: $V > V_{crit}$ ; the object is trapped in the ice with minimal interaction.
2. Indefinite repulsion: $V < V_{crit}$ ; the object is pushed away, creating pure ice.
3. Intermediate interaction: $V \approx V_{crit}$ ; the object interacts for a time $t_{int}$ before being engulfed.
Critical Velocities: PS particles have a significantly higher $V_{crit}$ ( $\approx 1.8$ µm/s) compared to oil droplets ( $\approx 0.4$ µm/s), indicating PS particles are more easily repelled.
Deformation: Oil droplets deform significantly during encapsulation (compressing parallel to the front, elongating perpendicularly), adopting a tear-like shape. Rigid PS particles remain spherical.

B. Thawing Dynamics (Retreating Front)

Hysteresis in Displacement: The behavior during thawing differs fundamentally from freezing and depends on the object type:
- PS Particles (Rigid): Experience an additional push away from their initial position as the front retracts. Even after exiting the ice, they are displaced further in the direction opposite to the front's motion. This results in a non-zero net displacement away from the start point after a full cycle.
- Oil Droplets (Deformable): Experience a retardation effect. As the droplet exits the ice, it is "held back" by the retracting front, slowing its motion. Consequently, the droplet tends to return to its initial position, resulting in near-zero net displacement after a full cycle.
Velocity Dependence: The magnitude of these interactions (both the extra push for PS and the retardation for droplets) diminishes as the thawing velocity increases.

C. Reversibility of Deformation

A striking finding is the perfect reversibility of the oil droplet's shape. The dynamics of deformation during freezing and re-formation (returning to a sphere) during thawing are identical when time is inverted and shifted. The aspect ratio $\Gamma(t)$ follows the same trajectory in reverse, indicating the process is mechanically robust and reversible.

4. Theoretical Interpretation

The authors rationalized these findings using a force-balance model involving:

Disjoining Pressure ( $F_\Pi$ ): Repulsive forces arising from the thin liquid film between the particle and the ice.
Viscous Lubrication ( $F_{vis}$ ): Resistance to motion through the melt.
Volume Expansion Force ( $F_{vol}$ ): An adjustment to the model accounting for the density change of water upon freezing ( $\rho_l > \rho_s$ ).

Model vs. Experiment:

PS Particles: The model successfully predicted the "extra push" during thawing. As the particle exits the ice, the gap narrows, making the repulsive disjoining pressure significant again, pushing the particle further away.
Oil Droplets: The model qualitatively reproduced the return-to-origin behavior. The authors suggest that while disjoining pressure plays a role, the deformability of the droplet and potential thermo-capillary (Marangoni) flows may contribute to the unique "holding back" effect, though the latter was deemed negligible in the absence of observed migration in the melt.

5. Significance and Contributions

Discovery of Hysteresis: The paper establishes that freeze-thaw cycles are not symmetric. The net displacement of an object depends on whether it is rigid or deformable, leading to hysteresis in the particle-front interaction.
Deformability as a Control Parameter: The study highlights that soft, deformable objects (droplets) behave fundamentally differently from rigid ones (particles) during thawing, specifically in their ability to recover their initial position.
Reversibility of Shape: The finding that droplet deformation is perfectly reversible challenges assumptions about irreversible damage during cryopreservation or freezing processes.
Theoretical Advancement: The work extends existing theoretical models to include the "retracting front" scenario, demonstrating that current physics-based models can predict complex hysteresis effects when adjusted for phase-change volume expansion.
Applications: These insights are crucial for optimizing cryopreservation protocols (minimizing cell displacement/damage) and designing directional freezing techniques for creating porous materials with specific microstructures.

In conclusion, the study reveals that the history of a particle's interaction with a solidification front (freezing vs. thawing) dictates its final position, with rigid particles migrating further away and deformable droplets returning to their origin, driven by complex interfacial forces and volume expansion effects.

Hysteresis in the freeze-thaw cycle of emulsions and suspensions