Instability and stress fluctuations of a probe driven through a worm-like micellar fluid

A particle moving through a worm-like micellar fluid (WLM) shows instability and large fluctuations beyond a threshold \textcolor{black}{velocity/force (depending on the control parameter used)}. Despite many detailed studies, a direct measurement of the time-dependent stress on the probe particle remains unexplored. To address this, we have designed a measuring geometry coupled with a commercial rheometer to study the dynamics of a cylindrical probe through a WLM system of 2 wt.% cetyltrimethyl ammonium tosylate(CTAT) + 100 mM sodium chloride(NaCl) for a wide range of velocity and stress scales. We map out the in-situ velocity distribution using particle imaging velocimetry. Beyond a velocity threshold, we observe large stress fluctuation with gradual stress build-up followed by sudden stress drop indicating storage and release of elastic energy. The length scale constructed from the stress build-up time scale and the probe’s velocity match the length scale of extensile deformation just before the stress drop, confirming the strong correlation of storage and release of energy with the unstable probe motion. Interestingly, the Weissenberg number ($Wi$) for the onset of flow instability obtained from the shear and extensile components remains almost the same. We also find that the turbulent motion of the probe at higher $Wi$ results from the complex mixing of the stick-slip events originating from the partial release of the stored elastic energy. Further, we show that the magnitude of the stick-slip events depends on the detailed micellar structure and dynamics controlled by salt concentration and temperature.

💡 Research Summary

The authors investigate the dynamic response of a cylindrical probe driven through a worm‑like micellar (WLM) fluid composed of 2 wt % cetyltrimethylammonium tosylate (CTAT) and 100 mM NaCl. By integrating a custom pin‑driving geometry with a commercial stress‑controlled rheometer (MCR‑702), they are able to impose either constant velocity or constant force on the probe while simultaneously measuring the instantaneous torque and thus the force acting on the probe. The experimental cell consists of two concentric cylinders forming an annular gap; the probe (diameter 1–5 mm, length 15–20 mm) is driven along the radial direction, and the system temperature is varied between 20 °C and 30 °C. Tracer polystyrene particles (20–50 µm) are added for particle‑imaging velocimetry (PIV), enabling in‑situ mapping of the local velocity field and visualization of flow‑induced turbidity.

Force‑versus‑velocity (F‑v) curves reveal three distinct regimes. At low velocities (v ≲ 10 mm s⁻¹) the relationship is linear, indicating a viscous‑dominated regime. As the velocity increases, a plateau appears where the measured force remains nearly constant despite rising speed. Beyond the plateau (v > 100 mm s⁻¹) the curve becomes linear again, but with a markedly reduced slope, reflecting strong shear‑thinning and a transition to a quasi‑Newtonian response when the deformation time scale becomes shorter than the micellar breaking‑recombination time.

The most striking observation occurs within the plateau region: the force signal exhibits large, irregular fluctuations characterized by a gradual build‑up followed by abrupt drops. This stick‑slip behavior is interpreted as the accumulation of elastic energy in the stretched micelles (extensional deformation) until a critical stress is reached, at which point micellar rupture and partial re‑formation release the stored energy. By multiplying the build‑up time τ_build by the probe velocity, the authors obtain a characteristic length scale L = v τ_build that matches the measured extensional deformation length ahead of the probe from PIV images. This quantitative agreement directly links the temporal stress dynamics to spatial micellar deformation.

Weissenberg numbers based on shear (Wi = λ γ̇) and extension (Wi = λ ε̇) are calculated using the linear‑viscoelastic relaxation time λ obtained from bulk rheology. Both definitions yield essentially the same critical Wi (≈0.8) for the onset of instability, indicating that shear and extensional elasticity are equally important in triggering micellar breakage. At higher Wi the stick‑slip events overlap, producing a chaotic, turbulent‑like motion that the authors refer to as “elastic turbulence.” Unlike classic shear‑banding fluids, bulk Taylor‑Couette measurements on the same CTAT‑NaCl system show no stress plateau and no steady shear bands, confirming that the observed instability is not a conventional shear‑banding phenomenon but is rooted in localized micellar rupture in the probe’s wake.

Systematic variation of salt concentration and temperature demonstrates that the magnitude and frequency of stick‑slip events are highly sensitive to micellar structure. Increased salt lengthens micelles and raises the elastic modulus, leading to larger stress spikes, whereas higher temperature accelerates micellar recombination, suppressing the amplitude of fluctuations. These trends underscore the role of micellar architecture in governing non‑linear flow responses.

Overall, the study provides the first direct, high‑resolution measurement of time‑dependent stress on a probe moving through a WLM fluid, bridging the gap between macroscopic rheology and microscopic micellar dynamics. The custom pin‑driving setup offers a versatile platform for probing a wide range of velocities and forces, enabling detailed statistical analysis of stress fluctuations, validation of two‑species VCM (Vasquez‑Cox‑Marr) models, and exploration of the transition from stick‑slip to elastic turbulence. The findings have implications for industrial processes involving micellar fluids (e.g., enhanced oil recovery, hydraulic fracturing, cosmetics) where small probes or particles experience complex, unstable motions. Future work suggested includes three‑dimensional PIV, high‑speed imaging of micellar rupture, and quantitative comparison with numerical simulations to further elucidate the mechanisms of energy storage, release, and turbulent mixing in worm‑like micellar systems.