Taylor–Couette (TC) flow, the flow between two independently rotating and coaxial cylinders, is commonly used as a canonical model for shear flows. Unlike plane Couette flow, pinned secondary flows can be found in TC flow. These are known as Taylor rolls and drastically affect the flow behaviour. We study the possibility of modifying these secondary structures using patterns of stressfree and noslip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of narrowgap TC flow with pure innercylinder rotation at four different shear Reynolds numbers up to $Re_s=3\times 10^4$ . We find that onedimensional azimuthal patterns do not have a significant effect on the flow topology, and that the resulting torque is a large fraction ( $\sim$ 80 %–90 %) of torque in the fully noslip case. Onedimensional axial patterns decrease the torque more, and for certain pattern frequency disrupt the rolls by interfering with the existing Reynolds stresses that generate secondary structures. For $Re\geq 10^4$ , this disruption leads to a smaller torque than what would be expected from simple boundary layer effects and the resulting effective slip length and slip velocity. We find that twodimensional checkerboard patterns have similar behaviour to azimuthal patterns and do not affect the flow or the torque substantially, but twodimensional spiral inhomogeneities can move around the pinned secondary flows as they induce persistent axial velocities. We quantify the roll's movement for various angles and the widths of the spiral pattern, and find a nonmonotonic behaviour as a function of pattern angle and pattern frequency.
more »
« less
Flow instability and transitions in Taylor–Couette flow of a semidilute noncolloidal suspension
Flow of a semidilute neutrally buoyant and noncolloidal suspension is numerically studied in the Taylor–Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction ${\phi _b} = 0.1$ , the radius ratio $(\eta = {r_i}/{r_o} = 0.877)$ and two particle size ratios $\mathrm{\epsilon }\,( = \; d\textrm{/}a) = 60,\;200$ , where d is the gap width ( $= {r_o}  {r_i}$ ) between cylinders, a is the suspended particles’ radius and $r_i$ and $r_o$ are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counterrotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of $\mathrm{\epsilon } = 200$ , the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of nonaxisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of $\mathrm{\epsilon } = 60$ ; thus, the transitions occur following the sequence of CCF → SVF → WSVF → WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow.
more »
« less
 Award ID(s):
 1854376
 NSFPAR ID:
 10278347
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 916
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


The seminal study by G. I. Taylor (1923) has inspired generations of work in exploring and characterizing Taylor–Couette (TC) flow instabilities and laid the foundation for research of complex fluid systems requiring a controlled hydrodynamic environment. Here, TC flow with radial fluid injection is used to study the mixing dynamics of complex oilinwater emulsions. Concentrated emulsion simulating oily bilgewater is radially injected into the annulus between rotating inner and outer cylinders, and the emulsion is allowed to disperse through the flow field. The resultant mixing dynamics are investigated, and effective intermixing coefficients are calculated through measured changes in the intensity of light reflected by the emulsion droplets in fresh and salty water. The impacts of the flow field and mixing conditions on the emulsion stability are tracked via changes in droplet size distribution (DSD), and the use of emulsified droplets as tracer particles is discussed in terms of changes in the dispersive Péclet, Capillary and Weber numbers. For oily wastewater systems, the formation of larger droplets is known to yield better separation during a water treatment process, and the final DSD observed here is found to be tunable based on salt concentration, observation time and mixing flow state in the TC cell.more » « less
This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal
Philosophical Transactions paper (part 2)’. 
We investigate the effect of particle inertia on the merger of corotating dusty vortex pairs at semidilute concentrations. In a particlefree flow, the merger is triggered once the ratio of vortex core size to vortex separation reaches a critical value. The vortex pair separation then decreases monotonically until the two cores merge together. Using Eulerian–Lagrangian simulations of corotating particleladen vortices, we show substantial departure from the vortex dynamics previously established in particlefree flows. Most strikingly, we find that disperse particles with moderate inertia cause the vortex pair to push apart to a separation nearly twice as large as the initial separation. During this stage, the drag force exerted by particles ejected out of the vortex cores on the fluid results in a net repulsive force that pushes the two cores apart. Eventually, the two dusty vortices merge into a single vortex with most particles accumulating outside the core, similar to the dusty Lamb–Oseen vortex described in Shuai & Kasbaoui (J. Fluid Mech., vol 936, 2022, p. A8). For weakly inertial particles, we find that the merger dynamics follows the same mechanics as that of a singlephase flow, albeit with a density that must be adjusted to match the mixture density. For highly inertial particles, the feedback force exerted by the particles on the fluid may stretch the two cores during the merger to a point where each core splits into two, resulting in inner and outer vortex pairs. In this case, the merger occurs in two stages where the inner vortices merge first, followed by the outer ones.more » « less

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor–Couette flow. The flows of interest rotate differentially with the inner cylinder faster than the outer, but are linearly stable against Rayleigh’s inviscid centrifugal instability. At shear Reynolds numbers as large as 10 6 , hydrodynamic flows of this type (quasiKeplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretiondisc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor–Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery of some interesting inductionless cousins of SMRI, and with the recently reported success in demonstrating SMRI itself using conducting axial boundaries. Some outstanding questions and nearfuture prospects are discussed, especially in connection with astrophysics. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 2)’.more » « less

Expandable graphite (EG) and fewlayer graphene (FLG) have proven to be instrumental materials for various applications. The production of EG and FLG has been limited to batch processes using numerous intercalating agents, especially organic acids. In this study, a Taylor−Couette reactor (TCR) setup is used to expand and exfoliate natural graphite and produce a mixture of EG and FLG in aqueous solutions using an amphiphilic dispersant and a semiflexible stabilizer. Laminar Couette flow structure and high shear rates are achieved via the rotation of the outer cylinder while the inner cylinder is still, which circumvents vortex formation because of the suppression of centrifugal forces. Our results reveal that the level of expansion and exfoliation using an aqueous solution and a TCR is comparable to that using commercial EG (CEG) synthesized by intercalating sulfuric acid. More importantly, the resultant EG and FLG flakes are more structurally homogeneous than CEG, the ratio of FLG to EG increases with increasing shearing time, and the produced FLG sheets exhibit large lateral dimensions (>10 μm). The aqueous solutions of EG and FLG are wetspun to produce ultralight fibers with a bulk density of 0.35 g/cm3. These graphene fibers exhibit a mechanical strength of 0.5 GPa without any modification or thermal treatment, which offers great potential in lightweight composite applications. KEYWORDS: graphene, graphite, Taylor−Couette, exfoliation, expansion, fibermore » « less