X-ray microscope reveals how nanoparticles dance to different rhythms in swirling flows

For more than a century, the transition from smooth laminar flow to turbulence has stood as one of the great unsolved puzzles of classical physics. Now a team of Swedish and Swiss researchers has opened a new window onto this problem by watching, in real time and at the nanoscale, how individual anisotropic nanoparticles behave inside one of fluid dynamics’ most celebrated experimental systems. Writing in Nature Physics, Kesavan Sekar of Chalmers University of Technology and colleagues report a technique that combines millisecond-resolution small-angle X-ray scatter microscopy with polarized light imaging, bridging seven orders of magnitude in length scale and revealing that the microscopic world does not always march in step with the macroscopic flow that carries it.

The team’s chosen arena is Taylor–Couette flow, the fluid trapped between two concentric cylinders with the inner one rotating and the outer one held still. This configuration has served as a benchmark for instability studies since G. I. Taylor’s seminal 1923 experiments, and its lineage stretches back even further, to James Clerk Maxwell’s unsuccessful nineteenth-century attempts to observe flow-induced birefringence. As the Reynolds number, the ratio of inertial to viscous forces, is increased, the fluid passes through a well-charted cascade of states. In laminar Couette flow, a fluid element traces a simple circular path. Above a critical Reynolds number, the flow reorganizes through a pitchfork bifurcation into Taylor vortex flow, a pattern of counter-rotating toroidal vortices separated by radial inflow and outflow regions. Further increases in speed trigger a Hopf bifurcation into wavy vortex flow, in which the vortices carry a travelling wave, followed by modulated wavy vortices, chaotic merging and splitting, and eventually turbulent Taylor vortices.

What has remained unknown is whether actual suspended particles, rather than idealized continuum fluid elements, follow the same spatiotemporal choreography as the macroscopic flow field. Anisotropic nanoparticles complicate the picture considerably. Their interactions with velocity gradients and vorticity produce distinct rotational and alignment dynamics, and the secondary vortex flows of transitional flow are expected to impose intricate, position-dependent alignment. The theoretical framework for this question rests on the rotational Péclet number, the ratio of the apparent shear rate to the rotational diffusion coefficient. At large values, flow-driven rotation dominates and particles should align with the flow; at small values, Brownian motion wins and orientations should be nearly isotropic. At moderate values near unity, the interplay between advection and diffusion could produce far more convoluted behaviour, but testing this hypothesis demanded a measurement technique capable of resolving both the macroscopic vortex patterns and the nanoscale orientation of the particles simultaneously.

Existing tools fell short. Flow visualization and particle image velocimetry routinely map macroscopic flow fields, but they operate at length scales far above those of the suspended nanoparticles and cannot access their orientational dynamics directly. Spatially resolved small-angle X-ray scattering, or SAXS microscopy, can map the size, shape, packing and preferential alignment of nanoscale constituents, and pioneering experiments had already identified time-averaged alignment of plate-like clay particles in Taylor–Couette flow. Yet the technique’s temporal resolution, roughly a minute in state-of-the-art implementations, confined it to slow processes such as the assembly of nanoparticle superlattices or the sodiation of battery electrodes. The new work shatters that limitation by exploiting the extreme X-ray flux of diffraction-limited synchrotron sources, achieving millisecond temporal resolution through frequency-domain analysis.

The experimental set-up is a custom Taylor–Couette cell manufactured by Anton Paar and mounted on an MCR702 rheometer, with inner and outer cylinder radii of 20.5 and 22.5 millimetres. Polarized light imaging is performed in the radial configuration, visualizing the flow in the plane defined by the velocity and vorticity directions, while SAXS data are collected in the tangential configuration, probing the plane defined by the velocity gradient and vorticity. Crucially, the use of the suspensions’ intrinsic flow-induced birefringence to determine macroscopic flow patterns eliminates the need for tracer particles, which would otherwise perturb the nanoscale flow being studied. The X-ray measurements were carried out at the ForMAX beamline of the MAX IV Laboratory, using an incident beam of roughly five times ten to the fourteen photons per second at 16.3 kiloelectronvolts, with scattering patterns recorded at 100 hertz by an EIGER2 X 4M photon-counting detector.

To make the macroscopic and nanoscopic observations directly comparable, the researchers developed a common spatiotemporal analysis framework. Lines of single pixels extracted from the polarized light video recordings are assembled into space-time diagrams, whose two-dimensional Fourier transforms yield the characteristic wavenumber and frequencies of each instability mode. On the X-ray side, two-dimensional scattering patterns are azimuthally integrated to construct azimuthal angle–time diagrams, from which a spatiotemporally resolved variant of the Hermans orientation parameter provides an instantaneous, ensemble-averaged and local measure of the nanoparticles’ preferential alignment. Based on Jeffery’s classical result for rigid anisotropic particles in simple shear, a temporal resolution of about one millisecond suffices to resolve single-particle rotation at shear rates up to roughly one thousand per second for the aspect ratios involved.

Two suspensions served as the test subjects: platelet-like graphene oxide nanoparticles, roughly two micrometres across and one nanometre thick, dispersed at 0.7 percent by weight, and rod-like cellulose nanocrystals, about 230 nanometres long and 6 nanometres in diameter, at 3 percent by weight. The validation experiments on the onset of the first instability already revealed striking differences. Graphene oxide destabilizes the flow, with the critical Reynolds number falling below the Newtonian reference value of approximately 184, and the transition initially appears as an elasticity-modified pattern in which Taylor vortices are triggered first in the middle of the flow domain. Cellulose nanocrystals, by contrast, stabilize the flow, pushing the critical Reynolds number above the Newtonian value, while shear-thinning effects yield smaller characteristic vortex wavenumbers. For both suspensions, all supercritical flow patterns remain Newtonian-like in character, although their onsets and ranges differ considerably.

The central result emerges when the two suspensions are compared under modulated wavy vortex flow at similar Reynolds numbers. The graphene oxide platelets, whose rotational Péclet number is large at around one hundred, follow the macroscopic dynamics of the secondary flows exactly as expected: the nanoscale characteristic frequency measured by SAXS matches the main wavy-mode frequency of about 7 hertz identified by polarized light imaging, and the spatial periodicity of the particle alignment mirrors that of the macroscopic flow field. The cellulose nanocrystal rods, operating at a moderate rotational Péclet number near unity, behave entirely differently. Although their director exhibits the same spatial periodicity as the macroscopic flow, it shows no signature of the large-scale wavy dynamics. Instead, the nanoscale dynamics is dominated by a frequency of about 29 hertz, far exceeding the wavy-mode frequencies of roughly 10 and 2.5 hertz and the rotational frequency of the inner cylinder, and correlating instead with the turnover frequency of the vortex instabilities, the rate at which a fluid element circulates within a single Taylor vortex.

The researchers interpret this divergence through a rotational supercritical flow Péclet number, defined as the ratio of the wavy-mode frequency to the rotational diffusion coefficient. For graphene oxide this quantity is of order ten, meaning flow dominates; for cellulose nanocrystals it is of order one-tenth, meaning Brownian de-orientation prevails. In plain terms, a cellulose nanocrystal loses its orientational memory many times within a single vortex wave cycle, its rotational decorrelation time of about 11 milliseconds being far shorter than the roughly 100-millisecond wave period, whereas a graphene oxide platelet, with a decorrelation time of about 6 seconds, tracks the wave faithfully. Yet the Péclet framework alone cannot explain the distinct high-frequency spectral peaks observed for the rods, which are nearly an order of magnitude faster than the extensively studied shear-induced Jeffery orbits. A simple kinematic model shows that rotational diffusion should suppress any coherent spectral peak even in the presence of vortex advection, so the observed peaks suggest a collective orientational mechanism in which interparticle interactions, plausibly stronger in the denser cellulose nanocrystal suspension, sustain coherence against rotational diffusion.

Beyond its immediate findings, the work raises questions that reach to the heart of pattern formation in nonequilibrium systems. The critical transition from laminar flow to Taylor vortices proves to be length-scale and particle-type independent, while the orientational response to the subsequent Hopf bifurcation is particle dependent, revealing a particle-shape-mediated transition in the orientational phase space of the suspension. Which small-scale degrees of freedom genuinely participate in macroscopic pattern formation, and which can be coarse-grained away, remains unresolved, as does the detailed impact of the observed multiscale dynamics on flow stability through elastic and shear-thinning effects. With millisecond-resolved X-ray scatter microscopy now demonstrated, combined with first-principles dynamical simulations, researchers have a powerful new instrument for dissecting the flow–microstructure coupling that underlies one of physics’ oldest and most beautiful instabilities.

Subject of Research: Multiscale orientational dynamics of anisotropic nanoparticles in transitional Taylor–Couette flow

Article Title: Multiscale transitional flow in anisotropic nanoparticle suspensions revealed by time-resolved X-ray scatter microscopy

Article References: Multiscale transitional flow in anisotropic nanoparticle suspensions revealed by time-resolved X-ray scatter microscopy. (n.d.). https://doi.org/10.1038/s41567-026-03467-1

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03467-1

Keywords: fluid dynamics, Taylor–Couette flow, nanoparticles, X-ray scattering, SAXS microscopy, polarized light imaging, flow instabilities, turbulence transition, graphene oxide, cellulose nanocrystals, rotational Péclet number, synchrotron