🔬 condensed matter

Shear-driven memory effects in carbon black gels

This study utilizes ultra-small angle X-ray scattering to demonstrate that carbon black gels retain a strong structural memory of their shear history, revealing that their rheological behavior is fully determined by a double-fractal microstructure governed by the ratio of viscous to attractive forces.

Original authors: Julien Bauland, Thomas Gibaud

Published 2026-06-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Julien Bauland, Thomas Gibaud

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 a jar of thick, black goo made of tiny carbon particles floating in oil. To the naked eye, it looks like a solid jelly, but if you stir it hard enough, it turns into a liquid. This is a colloidal gel.

The big question this paper asks is: Does this goo remember how you stirred it?

The answer is a resounding "yes." Just like a piece of clay that holds the shape of your thumbprint, these gels hold onto a "memory" of the forces applied to them. Even after you stop stirring, the internal structure of the gel remains changed, and this change dictates how stiff or soft the gel feels.

Here is the story of how the researchers discovered this, explained through simple analogies.

The Two Ways to Stir: The "Mason Number"

The researchers found that the gel reacts differently depending on how hard you push it. They use a special ratio called the Mason number to describe this. Think of this as a tug-of-war between two forces:

The Viscous Drag: The force of the oil trying to drag the particles apart (like wind blowing leaves).
The Attraction: The sticky force holding the particles together (like Velcro).

The paper identifies two distinct "worlds" based on who wins this tug-of-war:

1. The "High-Speed" World (Strong Wind)

When you stir the gel very fast (high Mason number), the wind is so strong that it breaks the particles apart into small, uniform clumps.

The Analogy: Imagine a crowd of people holding hands. If a strong wind blows, it breaks the big groups apart, leaving only small pairs or trios.
The Result: When you stop stirring, these small groups quickly rebuild into a neat, uniform network. The "memory" here is stored in the size of these small groups. If you stirred faster, the groups are smaller, and the final gel is softer. If you stirred slower (but still fast), the groups are bigger, and the gel is stiffer.

2. The "Low-Speed" World (Weak Wind)

When you stir the gel very slowly (low Mason number), the sticky "Velcro" wins. The wind isn't strong enough to break the clumps apart.

The Analogy: Imagine the same crowd of people, but now the wind is a gentle breeze. Instead of breaking them apart, the breeze just pushes the existing big groups closer together, making them denser and more tangled.
The Result: The gel becomes a messy, lumpy structure with big, dense clumps and empty spaces (voids) in between.
The Twist: In this world, time matters. If you keep stirring slowly for a long time, the clumps get even denser and the gel gets weaker. It's like letting a sponge sit in water; eventually, it changes its internal structure completely.

The "Goldilocks" Zone

The most surprising discovery was that the gel's stiffness doesn't just go up or down as you change the stirring speed. It goes down, then up.

If you stir very fast, the gel is stiff.
If you slow down to a "medium" speed, the gel becomes surprisingly weak (the weakest point).
If you slow down even further to a "very slow" speed, the gel gets stiff again.

The researchers found that this "weakest point" happens exactly when the wind force and the sticky force are perfectly balanced. It's a sweet spot where the structure is most vulnerable.

How They Saw the Invisible

You can't see these tiny changes with your eyes. To solve this, the scientists used a giant, super-powerful X-ray machine (called USAXS) at a European lab.

They shone X-rays through the gel while it was being stirred and right after they stopped.
The "Flash Photo": The X-rays acted like a high-speed camera, taking a picture of the microscopic structure.
The Discovery: They saw that the structure formed while the gel was being stirred was frozen in place the moment the stirring stopped. The gel didn't just relax back to its original state; it kept the "shape" of the flow.

The Big Picture

This paper tells us that these "smart" gels are like sponges that remember their history.

Fast stirring creates a neat, uniform sponge made of small bricks.
Slow stirring creates a messy, lumpy sponge made of giant, dense rocks.
The memory is written into the size and density of these bricks and rocks.

By understanding this, scientists can now "program" these gels. If they want a soft gel, they stir it at a specific speed. If they want a stiff gel, they stir it at a different speed. They don't need to change the ingredients; they just need to change the "story" of how they moved the material.

In short: The gel is a storyteller. The way you move it (the flow history) writes a story into its microscopic structure, and that story determines how strong the gel feels when you touch it later.

Technical Summary: Shear-driven memory effects in carbon black gels

Problem Statement
Particulate colloidal gels are promising candidates for "smart" materials due to their ability to adapt mechanical properties under physical stimuli. While shear flow is a known method for tuning these properties and imprinting a "rheological memory" (retaining structural changes after flow cessation), the precise relationship between flow history and viscoelastic response remains unclear. This lack of clarity stems largely from limited structural characterization of these disordered systems during and after flow. Existing literature presents conflicting observations regarding how shear rate affects gel elasticity, with some studies suggesting monotonic trends and others non-monotonic behaviors, often without a unified structural explanation.

Methodology
The authors investigated carbon black (CB) gels dispersed in mineral oil at low volume fractions ( $\phi_{r0}$ between 1.2% and 3.2%). The study employed a combined approach of rheometry and ultra-small angle X-ray scattering (USAXS) at the ESRF ID02 beamline.

Rheometry: A stress-controlled rheometer was used to perform step-flow experiments. Samples underwent a "rejuvenation" step at a high shear rate ( $\dot{\gamma} = 1000 \text{ s}^{-1}$ ) followed by a pre-shear step at various rates ( $\dot{\gamma}_0$ ) for 200 seconds. Flow was then ceased, and the evolution of elastic ( $G'$ ) and viscous ( $G''$ ) moduli was monitored.
Structural Characterization: USAXS was used to probe the microstructure both during flow and after cessation. The scattering intensity $I(q)$ was analyzed to identify hierarchical structural levels: primary particles ( $r_0$ ), small clusters ( $\xi_1$ ), and the percolated network ( $\xi_2$ ).
Modeling: The data were analyzed using a hierarchical fractal model and a cluster-of-clusters approach. The Mason number ($Mn$), defined as the ratio of viscous drag to attractive forces, was calculated to distinguish between different flow regimes.

Key Results

Non-monotonic Elasticity: The gel's crossover modulus ( $G_c$ ), used as a metric for elasticity, exhibits a non-monotonic dependence on the pre-shear rate. $G_c$ reaches a minimum at a critical shear rate $\dot{\gamma}^* \approx 40 \text{ s}^{-1}$ . At very low shear rates ( $\dot{\gamma}_0 < 7 \text{ s}^{-1}$ ), elasticity drops significantly due to antithixotropic restructuring.
Structural Memory: USAXS reveals a strong structural memory where the microstructure formed under shear is retained after flow cessation. The scattering curves after cessation closely resemble those measured during flow at the same shear rate.
Two Distinct Regimes: The authors identify two mechanisms governing structural memory based on the Mason number ($Mn$):
- Hydrodynamic Regime ($Mn > 1$, $\dot{\gamma}_0 \gtrsim 100 \text{ s}^{-1}$ ): The size of small clusters ( $\xi_1$ ) scales inversely with shear rate ( $\xi_1 \propto \dot{\gamma}_0^{-0.5}$ ), while their fractal dimension ( $d_{f1} \approx 2.5$ ) remains constant. Upon cessation, these clusters form a homogeneous, open network with a mesh size $\xi_2$ and fractal dimension $d_{f2} \approx 2$ .
- Elasto-plastic Regime ($Mn < 1$, $\dot{\gamma}_0 \lesssim 40 \text{ s}^{-1}$ ): Viscous forces are insufficient to prevent attractive forces from dominating. Small clusters densify and form larger, denser agglomerates. The network fractal dimension ( $d_{f2}$ ) increases (up to 2.9), and the structure becomes heterogeneous. Mass conservation analysis suggests the existence of large voids at length scales beyond USAXS resolution.
Antithixotropy: At very low shear rates ( $\dot{\gamma} < 7 \text{ s}^{-1}$ ), the system exhibits antithixotropy, where prolonged shearing leads to a slow decay in stress and a drastic reduction in gel elasticity. This results in a "partial memory loss" where the final structure becomes independent of the specific pre-shear rate, consisting of large, dense, loosely connected agglomerates.
Double-Fractal Architecture: The gels exhibit a double-fractal structure spanning over two orders of magnitude in length scale (from primary particles to mesh sizes in the tens of microns). The authors demonstrate that the gel elasticity is fully determined by this microstructure.

Significance and Claims
The paper claims to provide a physical explanation for how memory is encoded in colloidal gels as a function of shear rate. By correlating rheological data with USAXS structural data, the authors show that:

Rheological memory is not a single phenomenon but is governed by two distinct mechanisms depending on the balance of viscous and attractive forces (Mason number).
In the high shear regime, memory is encoded in the size of the building blocks (clusters), which dictates the homogeneity of the resulting gel.
In the low shear regime, memory is encoded through the densification of the network and the duration of shearing, leading to heterogeneous structures.
The Mason number serves as a unifying metric to predict the transition between these regimes.

The authors conclude that these findings offer strategies to tune the shear sensitivity of colloidal gels and design smart materials without altering formulation or volume fraction. They suggest that the broad range of length scales over which these materials self-organize is a key factor enabling their strong sensitivity to shear history. The work highlights the necessity of structural measurements during and after flow to fully understand the link between structure and rheology in disordered materials.