Strong alignment of prolate ellipsoids in Taylor–Couette flow

Abstract

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$ ) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$ , $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$ , respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$ . Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$ . This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ( $\textit {Ta}=6\times 10^5$ ) and we explain why.

Interfacial-dominated torque response in liquid–liquid Taylor–Couette flows

“…For high We = 400 (figure 3a-e), the secondary phase is highly fragmented, preferentially remains in the bulk region, and adopts unique repeating flow patterns in the axial (z) direction. The clustering trend of the dispersed phase in the bulk region is also observed for rigid particle suspensions for the Taylor vortex regime (Majji & Morris 2018; Assen et al 2022), which is caused by the linear shear gradient driving the suspended object towards the centre of the channel (Majji & Morris 2018). In our case, although the droplets are deformable and a free-slip boundary condition is imposed on the surface (instead of a no-slip condition, which is enforced on the particles), a similar mechanism might induce the migration of the droplets.…”

“…They revealed that the equilibrium positions were changed drastically for different flow regimes, starting from the centre of the channel (circular Couette flow regime), followed by circular regions in the r-z plane (Taylor vortex flow regime), and eventually distributing uniformly (wavy vortex flow regime). Assen et al (2022) analysed numerically the motions of finite-sized elliptic objects in Taylor-Couette flows from the Taylor vortex flow regime to the turbulent regime. They observed that the behaviour of particles (e.g.…”

“…However, compared to single-phase or particle-laden TC flows, quantitative discussions and physical insights on the two-liquid flows are still limited, and no high-fidelity numerical simulations have been reported, to the best of our knowledge. Here, we will discuss the basic dynamics of two-liquid flows in TC flow obtained by a high-performance direct numerical simulation tool 'AFiD' (van der Poel et al 2015), which is based on a second-order-accurate finite-difference method (Verzicco & Orlandi 1996) and has been used to study various turbulent TC flows (Ostilla-Mónico, Lohse & Verzicco 2016;Spandan et al 2018;Zhu et al 2018;Assen et al 2022). In order to describe the interfacial motions, the method is combined with a state-of-the-art volume-of-fluid method (Ii et al 2012;Xie & Xiao 2017).…”

“…Assen et al. (2022) analysed numerically the motions of finite-sized elliptic objects in Taylor–Couette flows from the Taylor vortex flow regime to the turbulent regime. They observed that the behaviour of particles (e.g.…”

“…2018; Assen et al. 2022). In order to describe the interfacial motions, the method is combined with a state-of-the-art volume-of-fluid method (Ii et al.…”