Multiscale transitional flow in anisotropic nanoparticle suspensions revealed by time-resolved x-ray scatter microscopy

Abstract

Complex fluids transition from laminar to transitory flow above a critical control parameter, akin to their Newtonian counterparts. In a continuum mechanics sense, fluid elements follow the ensuing complex trajectories, giving rise to secondary flows in terms of macroscopic vortices and patterns thereof. However, if we replace idealized fluid elements with actual anisotropic nanoparticles, would their trajectories still reveal the same spatiotemporal behavior as the macroscopic flow field? This question is fundamental for complex fluids, where fully developed turbulence is suppressed by high viscosities and where understanding particle-flow coupling is central to transport, processing, and structure formation. To address this question, we develop small-angle x-ray scatter microscopy of unprecedented temporal resolution combined with polarized light imaging, thereby bridging seven orders of magnitude in lengtscales. Proof-of-principle is demonstrated on a classical stability problem, Taylor-Couette flow, of platelet-like graphene oxide nanoparticle and rod-like cellulose nanocrystal suspensions. The analysis shows hitherto hidden, markedly different multiscale dynamics underlying flow stability; while the platelet-like particles follow the wavy motion of the macroscopic, secondary flow field, the rod-like particles exhibit high-frequency motion that is uncorrelated with the vortex instabilities.

Figures (9)

• Figure 1: Custom Taylor-Couette experimental setup for multiscale analysis of nanoparticle suspensions in supercritical flows. a, Illustration of the PLI visualization setup consisting of transparent concentric cylinders and cross-polarizer setup illuminated from the background with LED lights (not shown) and as viewed from the optical visualization camera (not shown), exemplifying wavy vortex flow. b, Tangential configuration (denoted by a circled T) of the SAXS experiment on the same flow cell, during which a set of fourteen SAXS time series are collected as function of position along the vorticity direction. b, Accessible length and time scales of the present PLI-SAXS study (green), compared to previous state-of-the-art PLI ghanbari24 and SAXS philippe12 experiments in Taylor-Couette flow. The velocity gradient and vorticity directions are denoted by $\nabla \mathbf{v}$ (or 2) and $\nabla \times \mathbf{v}$ (or 3), respectively, where $\mathbf{v}$ is the velocity vector (direction denoted by 1), positioned orthogonally to the planes formed by the afore mentioned axes.
• Figure 2: Summary of multiscale data analysis of TC-PLI-SAXS experiments. a, PLI video recordings processed as a sequence of frames wherefrom a line of 1 pixel is extracted along the vertical ($z$) axis of the cylinders. b, Example of PLI space-time diagram constructed from the individual frames for modulated wavy vortices (MWV) in a CNC suspension. Following two-dimensional Fourier analysis, the macroscale characteristic wavenumber (spatial periodicity) and frequency(ies) (temporal periodicity), $\{\kappa, f\}$, of the MWV can be determined. c, SAXS data processing, starting from azimuthal integration of time series of scattering patterns over a range of scattering vector moduli $q$. d, From the azimuthally integrated data, the scattered intensity $I(\it\Phi,z,t)_{q_0}$ can be determined for each $z=ct.$ scan. Thereafter, for each time step the scattering anisotropy was determined using the Hermans orientation parameter $P_2$, with Fourier analysis thereof yielding nanoscopic, characteristic spatial and temporal frequencies.
• Figure 3: Multiscale observation of flow transitions. The data present the transition from (a,c) laminar Couette (LCF) to (b,d) Taylor vortex flow (TVF) for (a,b) the GO and (c,d) the CNC suspension. Each figure compares PLI visualization (left), temporally averaged azimuthally integrated SAXS data $\langle I(\it\Phi,z)_{q_0}\rangle_t$ (middle), and a schematic picture of nanoparticle alignment based on the above data (right). Data collected in tangential configuration are highlighted with a circled T.
• Figure 4: Multiscale spatiotemporal analysis of transitional flow in anisotropic nanoparticle suspensions. Data are presented for (a) GO and (b) CNC suspensions subjected to modulated wavy vortex flow (MWV). The left panel presents the macroscopic space-time plot obtained by PLI (top) and the spatiotemporally resolved nanoscopic Hermans orientation parameter $P_2(z,t)$ determined by SAXS (bottom). The middle and right panels display spatially resolved $S(z,f)$ and averaged $\langle S(f)\rangle_z$ power spectral densities at both macroscopic (top) and nanoscopic lengthscales (bottom), determined by Fourier analysis from the data of the left panel. The rotational frequency $f_\Omega$ of the Taylor-Couette cell and the characteristic frequency $f_n$ (pentagon) are also depicted in the right panel. Note the common spatial scale for both PLI and SAXS.
• Figure 5: Multiscale dynamics of nanoparticle suspensions subjected to transitional flow. Both nanoscopic (SAXS) and macroscopic (PLI) data are presented for (a) GO and (b) CNC as the characteristic frequencies $f_n$ versus Reynolds number $Re$. The dashed line depicts the rotational frequency $f_{\Omega}$ of the Taylor-Couette cell. Note the different scale on the frequency axes for the GO and CNC data.