🔬 condensed matter

Shear and bulk viscosities of water up to 1.6 GPa and anomaly in the structural relaxation time

Using combined light scattering techniques and simulations, researchers discovered that water's shear viscosity increases faster than its bulk viscosity under high pressure, while its structural relaxation time reaches a minimum near 0.5 GPa due to a structural anomaly that accelerates hydrogen bond equilibration.

Original authors: Jan Eichler, Johannes Stefanski, José Martin Roca, Isabelle Daniel, Bruno Issenmann, Chantal Valeriani, Frédéric Caupin

Published 2026-03-19

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CC BY 4.0

Original authors: Jan Eichler, Johannes Stefanski, José Martin Roca, Isabelle Daniel, Bruno Issenmann, Chantal Valeriani, Frédéric Caupin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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 water not just as the stuff you drink or swim in, but as a shy, complex character that changes its personality depending on how much you squeeze it.

This paper is about a team of scientists who decided to play "squeeze" with water, but not just a little bit. They crammed it into a tiny, high-tech pressure chamber (a diamond anvil cell) and squeezed it with a force 16,000 times stronger than the atmosphere pressing down on you right now. That's the kind of pressure found deep inside the Earth's crust or inside the icy moons of Jupiter.

Here is the story of what they found, explained simply:

1. The Two Types of "Stickiness"

When we talk about water being "thick" or "sticky," we usually mean Shear Viscosity. Think of this as the resistance you feel when you try to stir honey with a spoon. It's how hard it is to slide layers of liquid past each other.

But water has a secret second type of stickiness called Bulk Viscosity. Imagine trying to squeeze a sponge. If the sponge is very "spongy," it resists being squished down. Bulk viscosity is how much the water resists being compressed or expanded.

The Discovery:
Usually, when you squeeze a liquid, both types of stickiness go up. But the scientists found something weird with water:

As they squeezed harder, the "stirring stickiness" (Shear) went up fast.
The "squeezing stickiness" (Bulk) went up, but slower.
The Result: The ratio between them dropped by half. Water became much more like a solid that resists sliding, but less like a sponge that resists being squished.

2. The "Relaxation" Mystery

To understand why this happens, the scientists looked at something called the Structural Relaxation Time.

The Analogy:
Imagine a crowded dance floor where everyone is holding hands in a specific pattern (hydrogen bonds). If the music stops, everyone has to let go and find a new spot. The time it takes for them to settle into a new, comfortable arrangement is the "relaxation time."

In normal liquids: If you squeeze the dance floor (increase pressure), the dancers get packed tighter. It becomes harder to move, so it takes longer to find a new spot. The relaxation time goes up.
In Water: The scientists found that at first, squeezing the dance floor actually made the dancers move faster. They found a new, faster way to rearrange themselves!
The Minimum: This speed-up happened until the pressure reached about 0.5 GPa (roughly 5,000 times normal pressure). At this exact point, the water was rearranging itself at its absolute fastest (about 1 picosecond, which is a trillionth of a second). After that point, it started slowing down again like a normal liquid.

3. Why Does This Happen? (The Two-Face Water)

The paper suggests that water is like a person with two different outfits it can wear:

Outfit A (Low Density): A loose, open, tetrahedral structure (like a pyramid shape) held together by strong hydrogen bonds. This is what water looks like at normal pressure.
Outfit B (High Density): A tighter, more chaotic, squished structure.

At low pressure, water loves Outfit A. At very high pressure, it's forced into Outfit B.
The Magic Moment: At that specific pressure of 0.5 GPa, the water is in a "sweet spot" where it can switch between Outfit A and Outfit B incredibly easily. It's like a dancer who has found the perfect rhythm to switch costumes instantly. This rapid switching makes the water "relax" faster than it ever has before or after.

4. Why Should We Care?

You might think, "Who cares about water under extreme pressure?" But this matters for:

Life on Earth: There are microbes living miles underground in rocks. They live in water under high pressure. If the water gets too thick or behaves strangely, it could change how these tiny creatures move and survive.
Life in Space: Moons like Ganymede (a moon of Jupiter) have oceans of liquid water hidden under miles of ice. To understand if these oceans can support life or how they move heat around (convection), we need to know exactly how "thick" that water is under that much pressure.
Oil Recovery: When companies pump water deep underground to push oil out of the ground, they need to know how that water will behave under that pressure to do it safely and efficiently.

The Bottom Line

This paper is a detective story about water's hidden personality. By squeezing it harder than ever before, the scientists discovered that water doesn't just get "thicker" under pressure. Instead, it hits a "sweet spot" where its internal structure rearranges itself with surprising speed, revealing a fundamental anomaly that makes water truly unique in the universe.

They confirmed this with computer simulations, showing that even our best digital models of water can predict this strange "speed-up" before it happens, giving us confidence that we are finally understanding the deep secrets of our most common liquid.

1. Problem Statement

Water exhibits unique anomalous properties (e.g., density maximum, negative thermal expansion) driven by its open, tetrahedral hydrogen-bond network. While it is known that water's viscosity initially decreases with pressure at ambient temperature before increasing, the behavior at high pressures (Gigapascal range) remains poorly characterized.

Knowledge Gap: Existing data on water's shear viscosity above 1 GPa is scarce and shows significant discrepancies between different experimental methods (e.g., rolling ball vs. optical tweezers).
Unresolved Questions:
- How do shear ( $\eta$ ) and bulk ( $\eta_b$ ) viscosities evolve independently at high pressures?
- Does the anomalous decrease in structural relaxation time ( $\tau$ ) persist at high pressures, or does water eventually behave like a "simple" liquid?
- What are the implications for geophysics (Earth's crust, subsurface life) and planetary science (icy moons like Ganymede)?

2. Methodology

The authors employed a multi-technique approach combining Differential Dynamic Microscopy (DDM) and Brillouin Light Scattering (BLS) within a Diamond Anvil Cell (DAC) at approximately 295 K.

Shear Viscosity ( $\eta$ ) via DDM:
- Principle: Measured the Brownian motion of sub-micrometer polystyrene spheres suspended in water.
- Innovation: Adapted DDM for high-pressure DAC environments. Unlike previous high-pressure studies using single trapped particles (optical tweezers) or rolling balls, this method tracks the collective diffusion of many free-floating spheres.
- Calibration: Addressed the compressibility of polystyrene spheres and the changing sample chamber height (gasket squeeze) by deriving a pressure-dependent hydrodynamic radius correction based on literature data.
Bulk Viscosity ( $\eta_b$ ) via Brillouin Spectroscopy:
- Principle: Measured the inelastic scattering of light caused by density fluctuations (sound waves).
- Derivation: The linewidth of the Brillouin peak provides the sound attenuation coefficient ( $\alpha$ ). Using the relation $\alpha/f^2 \propto (4/3\eta + \eta_b)$ , and combining it with the independently measured shear viscosity ( $\eta$ ) and sound velocity ( $w$ ), the authors isolated the bulk viscosity ( $\eta_b$ ).
Visco-Elastic Modeling:
- The experimental data ( $\eta$ , $\eta_b$ , and sound velocity) were analyzed using a visco-elastic model to extract the structural relaxation time ( $\tau$ ) and elastic moduli ( $K_0, K_\infty, G_\infty$ ).
Molecular Dynamics (MD) Simulations:
- Simulations using the TIP4P/2005 water model were performed to validate experimental trends and explore the microscopic origins of the observed anomalies.

3. Key Contributions

Simultaneous Measurement: First simultaneous, high-precision measurement of both shear and bulk viscosities of water up to 1.6 GPa at room temperature.
Resolution of Discrepancies: The study clarifies conflicting literature data, supporting results from optical tweezers and rolling ball methods while identifying systematic errors in previous DDM attempts (attributed to particle sedimentation).
Discovery of a Relaxation Time Minimum: The identification of a distinct minimum in the structural relaxation time ( $\tau$ ) at high pressure, a phenomenon not previously reported for water in this regime.
Structural Anomaly Link: Proposing that the minimum in $\tau$ corresponds to a structural anomaly where the interconversion rate between local low-density (tetrahedral) and high-density (disordered) water structures is maximized.

4. Key Results

A. Shear Viscosity ( $\eta$ )

Trend: $\eta$ shows a shallow minimum near ambient pressure (consistent with cooling trends) and then increases monotonically and rapidly with pressure.
Magnitude: At 1.6 GPa, $\eta$ reaches approximately 4 mPa·s (roughly 4 times the ambient value).
Comparison: The data aligns well with optical tweezer measurements but deviates significantly from previous DDM data (which were too low) and the IAPWS formulation (which underestimates viscosity above 1 GPa).

B. Bulk Viscosity ( $\eta_b$ ) and Ratio

Trend: $\eta_b$ also increases with pressure but at a slower rate than $\eta$ .
The Ratio ( $\eta_b/\eta$ ): This ratio decreases significantly, dropping by a factor of two from 0 to 1.6 GPa.
- At 0 GPa: $\eta_b/\eta \approx 2.7$ .
- At 1.6 GPa: $\eta_b/\eta \approx 1.3$ .
Significance: This indicates a decoupling of shear and bulk relaxation mechanisms under high compression.

C. Structural Relaxation Time ( $\tau$ )

The Anomaly: Contrary to most liquids where $\tau$ increases monotonically with pressure, water's $\tau$ initially decreases.
The Minimum: $\tau$ reaches a minimum of approximately 1 picosecond (ps) at 0.5 GPa.
Recovery: Above 0.5 GPa, $\tau$ begins to increase, signaling a return to "normal" liquid behavior where pressure hinders molecular motion.
Interpretation: The minimum represents the point of fastest equilibration of hydrogen bonds. It is interpreted as a structural anomaly where the energy barrier for interconverting between local structural motifs (tetrahedral vs. collapsed) is minimized.

D. Elastic Moduli

The infinite-frequency bulk ( $K_\infty$ ) and shear ( $G_\infty$ ) moduli increase with pressure.
$K_\infty$ and $G_\infty$ in liquid water follow similar pressure trends to hexagonal ice ( $I_h$ ) but are lower by ~20% and ~50%, respectively, reflecting the less developed tetrahedral network in the liquid phase.

5. Significance and Implications

Fundamental Physics: The results support the "cascade of anomalies" hypothesis. The minimum in $\tau$ (a dynamic property) occurs at a higher pressure than the minima in shear viscosity or self-diffusion, suggesting a nested hierarchy of structural, dynamic, and thermodynamic anomalies. This minimum serves as a proxy for the structural anomaly line (maximal disordering of the hydrogen bond network).
Geophysics and Planetary Science:
- Earth: The findings are crucial for modeling fluid flow in the deep crust (up to 25 km depth, ~0.7 GPa) and the habitability of subsurface microbial life, where viscosity affects cell motility and nutrient transport.
- Icy Moons: For moons like Ganymede, where subsurface oceans exist under pressures up to ~1.6 GPa, accurate viscosity data is essential for convection models. The study suggests that convection models using fixed viscosity values may be inaccurate; the pressure dependence is non-linear and significant.
Methodological Impact: The successful adaptation of DDM to high-pressure DACs provides a robust, reliable tool for measuring viscosity in other complex fluids and extreme conditions, overcoming limitations of previous techniques.

In conclusion, this paper provides a comprehensive map of water's viscous behavior under extreme pressure, revealing a complex interplay between shear and bulk relaxation that peaks in "fluidity" (minimum $\tau$ ) at 0.5 GPa before water transitions toward simple liquid behavior at higher pressures.