Abstract

We experimentally investigate the drag modification by neutrally buoyant finite-size particles with various aspect ratios in a Taylor–Couette (TC) turbulent flow. The current Reynolds number, $Re$ , ranges from $6.5\times 10^3$ to $2.6\times 10^4$ , and the particle volume fraction, $\varPhi$ , is up to $10\,\%$ . Particles with three kinds of aspect ratio, $\lambda$ , are used: $\lambda =1/3$ (oblate), $\lambda =1$ (spherical) and $\lambda =3$ (prolate). Unlike the case of bubbly TC flow (van Gils et al., J. Fluid Mech., vol. 722, 2013, pp. 317–347; Verschoof et al., Phys. Rev. Lett., vol. 117, issue 10, 2016, p. 104502), we find that the suspended finite-size particles increase the drag of the TC system regardless of their aspect ratios. The overall drag of the system increases with increasing $Re$ , which is consistent with the literature. In addition, the normalized friction coefficient, $c_{f,\varPhi }/c_{f,\varPhi =0}$ , decreases with increasing $Re$ , the reason could be that in the current low volume fractions the turbulent stress becomes dominant at higher $Re$ . The particle distributions along the radial direction of the system are obtained by performing optical measurements at $\varPhi =0.5\,\%$ and $\varPhi = 2\,\%$ . As $Re$ increases, the particles distribute more evenly in the entire system, which results from both the greater turbulence intensity and the more pronounced finite-size effects of the particles at higher $Re$ . Moreover, it is found that the variation of the particle aspect ratios leads to different particle collective effects. The suspended spherical particles, which tend to cluster near the walls and form a particle layer, significantly affect the boundary layer and result in maximum drag modification. The minimal drag modification is found in the oblate case, where the particles preferentially cluster in the bulk region, and, thus, the particle layer is absent. Based on the optical measurement results, it can be concluded that, in the low volume fraction ranges ( $\varPhi =0.5\,\%$ and $\varPhi = 2\,\%$ here), the larger drag modification is connected to the near-wall particle clustering. The present findings suggest that the particle shape plays a significant role in drag modification, and the collective behaviours of rigid particles provide clues to understand the bubbly drag reduction.

By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor–Couette turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviours, i.e. the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction for O/W or for W/O. However, for W/O it is about $50\,\%$ larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviours are expected to be caused by the presence of surface-active contaminants from the walls of the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry and reach conclusions on emulsions where interfaces are fully covered by the surfactant. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a $-6/5$ scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich (Physicochemical Hydrodynamics, Prentice-Hall, 1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov (Dokl. Akad. Nauk. SSSR, vol. 66, 1949, pp. 825–828). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviours in dynamic emulsification, and connects them.

Emulsions are common in many natural and industrial settings. Recently, much attention has been paid to understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor–Couette flow, mainly focusing on the statistics of the dispersed phase and the global momentum transport of the system. We first study the size distribution and the breakup mechanism of the dispersed droplets for turbulent emulsions with a low volume-fraction (dilute) of the dispersed phase. For systems with a high volume-fraction (dense) of the dispersed phase, we address the detailed response of the global transport (effective viscosity) of the turbulent emulsion and its connection to the droplet statistics. Finally, we will discuss catastrophic phase inversions, which can happen when the volume-fraction of the dispersed phase exceeds a critical value during dynamic emulsification. We end the manuscript with a summary and an outlook including some open questions for future research. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.

Abstract