🔬 condensed matter

Elastic turbulence in highly entangled polymers and wormlike micelles

This paper provides the first theoretical simulation evidence that linearly unstable two-dimensional perturbations in highly entangled polymeric fluids and wormlike micelles can lead to elastic turbulence, occurring not only in fluids with non-monotonic constitutive curves but also in shear-thinning fluids with monotonic curves, thereby offering a potential explanation for experimentally observed rheo-chaotic states.

Original authors: Theo A. Lewy, Suzanne M. Fielding, Peter D. Olmsted, Rich R. Kerswell

Published 2026-02-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Theo A. Lewy, Suzanne M. Fielding, Peter D. Olmsted, Rich R. Kerswell

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 you are stirring a thick, sticky pot of honey or a giant batch of melted plastic. Usually, when you stir something like this, it flows smoothly, even if it's slow. But sometimes, if you stir it fast enough, something strange happens: the fluid starts to wiggle, churn, and act chaotic, even though there's no heavy machinery or fast-moving parts to cause it. Scientists call this "Elastic Turbulence."

For a long time, we knew this happened in thin, watery solutions of polymers (like hair gel). But this new paper asks a big question: Does this chaotic behavior happen in thick, gooey, highly concentrated polymers (like melted plastic or toothpaste) too?

The answer, according to this study, is a resounding YES.

Here is a simple breakdown of what the researchers found, using some everyday analogies:

1. The Setup: The "Stirring Pot"

The researchers used computer simulations to model two types of flow:

Couette Flow: Imagine two parallel plates with gooey fluid between them. You slide the top plate to the right and the bottom plate to the left. It's like sliding your hands past each other with lotion in between.
Poiseuille Flow: Imagine pushing fluid through a pipe or a channel, like squeezing toothpaste out of a tube.

They used two different "rulebooks" (mathematical models) to describe how these thick fluids behave: the Johnson-Segalman model and the Rolie-Poly model. Think of these as two different ways to predict how a rubber band snaps back or stretches.

2. The Surprise: Chaos Without Curvature

In the past, scientists thought elastic turbulence needed "curved" paths (like stirring in a round bowl) to happen. They thought the "hoop stress" (the tension trying to snap a rubber band back into a circle) was the culprit.

The Discovery: This paper shows that even in a straight, flat channel (no curves at all), the fluid can still go crazy.

The Analogy: Imagine a line of people holding hands walking in a straight hallway. Usually, they walk in a straight line. But if they are holding very stretchy rubber bands between them, and they walk fast enough, the whole line might suddenly start zig-zagging, bunching up, and splitting apart, even though the hallway is perfectly straight.

3. The "Shear Banding" Mystery

Thick fluids often like to split into layers. Some layers move fast, and some move slow. This is called Shear Banding.

Old View: Scientists used to think these layers were like calm, static stripes. One stripe moves fast, the next moves slow, and they sit there peacefully next to each other.
New View: This paper shows that the "fast" stripe isn't calm at all. It's actually turbulent and chaotic.
The Analogy: Think of a highway. The old theory said the fast lane and the slow lane were just two distinct lines of cars moving at steady speeds. The new theory says the fast lane is actually a mosh pit. The cars (molecules) are crashing, merging, splitting, and swirling wildly, while the slow lane remains a calm, orderly line of traffic.

4. The "Monotonic" Surprise

The most surprising part is that this chaos happens even when the fluid should be stable.

Some fluids get thinner (less sticky) the faster you stir them.
Some fluids have a weird "S-curve" where they get unstable at certain speeds.
The researchers found that even the fluids that look perfectly stable on paper (the ones that don't have that weird "S-curve") can still turn into a chaotic mess if you look at them in 2D (side-to-side) rather than just 1D (top-to-bottom).

5. What Does This Mean for the Real World?

This isn't just a math game. It changes how we understand:

Industrial Processes: When factories mold plastic or extrude materials, they might be dealing with hidden chaos that causes defects or uneven products.
Biological Fluids: Many biological fluids (like mucus or the stuff inside our cells) are concentrated polymers. This might explain why they sometimes behave erratically.
Wormlike Micelles: These are soap-like molecules that form long chains. Experiments have shown them acting "chaotic" (rheo-chaos), and this paper suggests it's because the fast-moving part of the fluid has turned into a turbulent storm, not just a simple layer.

The Bottom Line

The researchers proved that thick, sticky fluids can become turbulent without needing to be stirred in a circle or having a weird chemical reaction.

If you stir a thick polymer fluid fast enough, it doesn't just flow; it fights back. It breaks into narrow, chaotic bands that constantly merge and split, creating a "turbulent storm" inside a fluid that looks calm from the outside. This is the first time we've seen this happen in simulations of these specific, thick materials, and it suggests that nature is much more chaotic than our simple 1D models predicted.

1. Problem Statement

Viscoelastic fluids, particularly concentrated polymeric solutions and melts, exhibit complex nonlinear flow phenomena that significantly impact industrial processes like extrusion and molding. While Elastic Turbulence (ET)—a chaotic flow state driven by elastic forces at negligible Reynolds numbers—is well-documented in dilute polymer solutions (often driven by hoop stresses in curved geometries), its existence in concentrated systems remains under-explored.

In concentrated systems, the primary instability mechanism is often shear banding, where a homogeneous flow spontaneously separates into coexisting bands of high and low shear rates. This typically occurs when the constitutive curve (shear stress vs. shear rate) is non-monotonic. Historically, these banding states were interpreted via one-dimensional (1D) models predicting stationary, flat interfaces between bands. However, experiments often reveal chaotic, turbulent dynamics ("rheo-chaos") within the high-shear bands, which 1D models fail to capture. The central question addressed by this paper is whether 2D linear instabilities can trigger elastic turbulence in concentrated, shear-thinning fluids, even in the absence of hoop stresses or base-state stress gradients.

2. Methodology

The authors employ a combination of linear stability analysis and direct numerical simulations (DNS) to investigate this problem.

Constitutive Models: Two widely used models for entangled polymers are studied:
1. Johnson-Segalman (JS) Model: A phenomenological model capable of shear banding via a slip parameter $a$ .
2. Rolie-Poly (RP) Model: A microscopically motivated model incorporating reptation and constraint release, capable of capturing shear thinning and banding.
Flow Geometries: Simulations are performed in two rectilinear geometries where hoop stresses are absent in the base state:
1. Planar Couette Flow (pCf): Homogeneous base stress; driven by moving plates.
2. Planar Poiseuille Flow (pPf): Heterogeneous base stress; driven by a pressure gradient.
Stability Analysis: The authors analyze the stability of a homogeneous base state against small perturbations. They distinguish between:
- 1D Perturbations: Variations only in the flow-gradient direction ( $y$ ).
- 2D Perturbations: Variations in both flow ( $x$ ) and gradient ( $y$ ) directions.
  Growth rates ( $\omega$ ) are calculated to determine if perturbations grow ( $\omega > 0$ ).
Nonlinear Simulations: Direct 2D simulations are performed to evolve unstable modes to finite amplitude. A ramp-down protocol is used to trace flow curves and observe the transition from laminar to turbulent states.

3. Key Contributions

First Numerical Evidence of ET in Concentrated Fluids: This work provides the first direct simulation evidence of elastic turbulence in highly entangled polymeric fluids and wormlike micelles.
2D Instability in Monotonic Regimes: The authors demonstrate that ET arises not only in fluids with non-monotonic constitutive curves (shear banding) but also in shear-thinning fluids with monotonic constitutive curves. In these monotonic cases, the 1D base state is stable, yet 2D perturbations grow, leading to turbulence.
Mechanism Identification: They identify a route to ET via the linear instability of an initially rectilinear base state, distinct from the hoop-stress mechanisms found in dilute solutions.
Reinterpretation of Rheo-Chaos: The findings suggest that experimentally observed "rheo-chaos" in shear-banding systems is likely the result of a coexistence between a laminar low-shear band and an elastically turbulent high-shear band, rather than complex 1D interface dynamics.

4. Key Results

A. Linear Stability Analysis

Instability Regimes: In both JS and RP models, the authors found regimes where 2D perturbations are more unstable than 1D perturbations ( $\omega_{2D} > \omega_{1D}$ ).
Monotonic Curves: Crucially, they identified 2D instabilities in regions where the constitutive curve has a positive slope (stable in 1D).
- In the JS model, this occurs on the high-shear branch.
- In the RP model, this occurs on both high and low shear branches, even at low entanglement numbers where the curve is strictly monotonic.
Instability Types:
- At lower Weissenberg numbers ( $W$ ), the instability is a bulk constitutive instability (global, large-scale).
- At higher $W$ in the JS model, the instability transitions to a Polymer Diffusive Instability (PDI), which is small-scale and confined to the boundary. The RP model exhibits only bulk constitutive instability.

B. Nonlinear Simulations (Elastic Turbulence)

Turbulent States: Direct simulations confirm that the 2D instability evolves into a chaotic state (ET).
Two Types of ET States (in JS model):
1. Type A ( $W > 4.2$ ): Multiple shear bands dynamically coalesce, split, and interact across the domain. The stress signal is highly chaotic with large fluctuations.
2. Type B ( $W < 4.2$ ): Distinct bands localized near the walls. The number of bands is constant, and stress fluctuations are smaller (quasi-periodic or low-amplitude chaos).
Robustness: ET was observed across various parameters:
- Different solvent viscosity ratios ( $\delta$ ).
- Different stress diffusion coefficients ( $\epsilon$ ).
- Both pCf (homogeneous base stress) and pPf (heterogeneous base stress).
- Both non-monotonic (JS) and monotonic (RP) constitutive curves.

C. Comparison with Experiments

The authors argue that their results explain experimental observations in wormlike micelles (e.g., CTAB/NaNO $_3$ ) where the high-shear band appears turbid and chaotic. They suggest that in low-curvature Taylor-Couette flows (where hoop stresses are weak), the constitutive instability identified here is the dominant mechanism, leading to a turbulent high-shear band coexisting with a laminar low-shear band.

5. Significance

Fundamental Physics: This work fundamentally alters the understanding of flow instabilities in concentrated viscoelastic fluids. It proves that shear thinning alone, without hoop stresses or 1D shear banding, is sufficient to generate elastic turbulence via 2D instabilities.
Industrial Relevance: Since many industrial processes involve concentrated polymer melts and shear-thinning behavior, these findings suggest that unexpected turbulent states and flow instabilities can occur even in simple geometries (like Couette flow), impacting processing stability and product quality.
Experimental Guidance: The paper provides a theoretical framework to interpret "rheo-chaos" in experiments. It suggests that researchers should look for the coexistence of laminar and turbulent bands rather than assuming complex 1D interface dynamics.
Model Validation: The robustness of ET across two distinct constitutive models (JS and RP) and two geometries (pCf and pPf) strengthens the conclusion that this is a generic feature of concentrated viscoelastic fluids, not an artifact of a specific model.

In summary, Lewy et al. demonstrate that elastic turbulence is a generic, robust phenomenon in concentrated polymeric fluids, driven by 2D linear instabilities that can destabilize even shear-thinning fluids with monotonic constitutive curves, offering a new explanation for chaotic flow states observed in both polymers and wormlike micelles.