By tracking particle orientation and macroscopic vortices on the same millisecond timescale, researchers tested whether nanoscale constituents move in step with the flow around them.
Paper: Multiscale transitional flow in anisotropic nanoparticle suspensions revealed by time-resolved X-ray scatter microscopy. AI-generated abstract conceptual image created using ChatGPT/OpenAI
A recent Nature Physics paper developed time-resolved X-ray scattering microscopy to reveal multiscale transitional flow in anisotropic nanoparticle suspensions.
Importance of multiscale structural characterization
In classical physics, the transition from laminar to turbulent flow in complex fluids is a longstanding multiscale problem, characterized by strong coupling among length scales that span several orders of magnitude.
In continuum mechanics, fluid elements follow complex trajectories, producing secondary flows in the form of macroscopic vortices. For anisotropic nanoparticle suspensions, particle orientation also matters. Taylor–Couette flow occurs in fluid confined between concentric cylinders; in this experiment, the inner cylinder rotated while the outer cylinder remained stationary.
Interactions between anisotropic particles, vorticity, and velocity gradients produce distinct orientations and rotations in Newtonian laminar flow. Secondary-vortex flow fields in transitional Taylor–Couette flow can produce complex, position-dependent orientations of suspended anisotropic particles.
The rotational Péclet number (Pe?) provides a convenient measure for analysis. In the limit of small Pe?, particles are expected to show nearly isotropic orientation distributions, and Brownian motion dominates; in the limit of large Pe?, dispersed particles are expected to adopt orientations set by the underlying flow field, and rotational advection dominates.
At moderate Pe? ~ 1, competition between diffusion and rotational advection can produce more complex nanoparticle orientation. To test this hypothesis experimentally, multiscale structural characterization is needed to resolve both nanoscale particle orientation and macroscopic flow patterns on a common timescale.
Flow visualization and particle image velocimetry routinely resolve the macroscopic flow field, but these approaches cannot directly access the orientational motion of suspended nanoparticles and often operate at length scales far larger than the particles themselves.
The proposed approach
In this work, researchers developed a multiscale method that integrates small-angle X-ray scattering (SAXS) microscopy with polarized light imaging (PLI) to bridge seven orders of magnitude in length scales. The measurements were compared on a common millisecond timescale, but PLI and SAXS used different geometrical configurations, and the study collected the PLI data separately.
They achieved millisecond temporal resolution in SAXS microscopy using frequency-domain analysis and the extreme X-ray flux from diffraction-limited synchrotron sources.
SAXS microscopy can map preferential orientation, shape, and size of nanoscale constituents. This technique can be applied to complex in situ experiments and various sample aggregation states.
SAXS is the X-ray counterpart of static light scattering, with high transmission and low multiple scattering, enabling experiments in Taylor–Couette geometry.
Pioneering SAXS microscopy experiments in Taylor–Couette flow on platelet-like clay nanoparticle suspensions determined the time-averaged orientation of the nanoparticle director (the average orientation axis) and its effect on the onset of instabilities.
The team also quantified the macroscopic patterns of Taylor–Couette flow and their time dependence using PLI, which measures flow-induced birefringence in nanoparticle suspensions. The study examined whether replacing an idealized fluid element with an anisotropic nanoparticle would produce the same spatiotemporal behavior at nanoscopic and macroscopic scales.
Results from the approach
The team tested the method in Taylor–Couette flow, a classical transitional flow problem, using platelet-like graphene oxide (GO) and rod-like cellulose nanocrystal (CNC) suspensions.
The two materials also affected instability onset differently: GO caused Taylor vortex flow to appear at a lower Reynolds number than in the Newtonian reference fluid, while CNC shifted its onset to a higher Reynolds number, though the flow patterns above the instability threshold in both remained similar to those of a Newtonian fluid.
The results revealed particle-specific spectral behavior during transitional Taylor–Couette flow, in line with the Pe?-based argument.
While the platelet-like particles followed the macroscopic motion of the secondary flows, consistent with high Pe?, the rod-like particles showed characteristic high-frequency orientational motion at moderate Pe?. A simple kinematic model found the CNC frequency consistent with the vortex turnover frequency, rather than proving a unique assignment.
Rod-like CNCs (3 wt%, Pe? of order 1) demonstrated high-frequency orientational motion, while platelet-like GO (0.7 wt%, Pe? of order 10²) tracked the macroscopic wavy vortices.
Significance
The distinct multiscale spatiotemporal behavior of platelet-like GO and rod-like CNC suspensions can be partly understood through the competition between Brownian rotational diffusion and flow-induced rotational motion driven by macroscopic wavy modes.
The authors also define a supercritical-flow rotational Péclet number comparing wave frequency with rotational diffusion, effectively comparing the vortex-wave timescale with how quickly particles lose orientational memory. It is about 10¹ for GO and 10-¹ for CNC, which helps explain why GO tracks the vortex wave while CNC loses orientational memory many times within a single wave cycle.
The Péclet-number interpretation alone cannot explain the distinct nanoscale spectral peaks observed in CNC suspensions across different instabilities, including time-invariant Taylor vortex flow, but excluding laminar Couette flow.
GO suspensions behaved differently, with nanoscopic motion primarily driven by macroscopic vortex motion. The higher reduced number density of CNC implied stronger interparticle interactions than in GO, which could further influence nanoparticle orientation.
In the simple model, experimentally estimated rotational diffusion suppressed the coherent CNC peak. The mismatch with experiment points to a possible role for interactions not represented in the model.
Still, the detailed role of this multiscale behavior in flow stability, and its relationship to classical macroscopic effects such as elasticity and shear thinning, remains unresolved.
Experimental access to this multiscale behavior, combined with future first-principles simulations, could help researchers investigate the flow–microstructure coupling underlying the pattern-formation process.
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