A study of particle paths in non-axisymmetric Taylor–Couette flows

Abstract

We study the paths of fluid particles in velocity fields modelling rigidly rotating velocity fields that occur in the concentric Taylor problem. We set up velocity fields using the model of Davey, DiPrima & Stuart (1968) based on small-gap asymptotics. This allows a numerical study of the Lagrangian properties of steady flow patterns in a rotating frame. The spiral and Taylor vortex modes are integrable, implying that in these cases almost all particle paths are confined to two-dimensional surfaces in the fluid. For the case of Taylor vortices the motion on these surfaces is quasi-periodic, whereas for spirals the particles propagate up or down the cylinder on these surfaces.The non-axisymmetric modes we consider are wavy vortices, spirals, ribbons and twisted Taylor vortices. All of these flows have the property that they are steady flows when examined in a rotating frame of reference. For all non-axisymmetric modes with the exception of spirals, we observe the existence of regions of chaotic mixing within the fluid. We discuss mixing of the fluid by these flows with reference to the pattern of stagnation points and some of the periodic trajectories within the fluid and on the boundary.

Intensified and attenuated waves in a microbubble Taylor–Couette flow

“…The mechanisms that generate the organized inhomogeneous bubble distribution, however, have not been discussed and are still unknown. Fluid particles experience periodic accelerations and pressure fluctuations in the waviness of WVF 44 in the Lagrangian-frame. The voidage wave, i.e., the fluctuation in the number density of microbubbles, in the azimuthal direction might be related to the integration of the drift due to the small but unignorable slip velocity in the periodically accelerated wavy flow.…”

Visualization of Three-Dimensional Chaos

“…Even though the first theoretical example of chaotic advection was a 3D flow (IS), the number of theoretical studies addressing chaos and mixing in such flows is small (16)(17)(18). One problem is that an experimentally tractable 3D system that allows for detailed experimental and computational investigation had not been available.…”

“…probably with reduced intensity if the number of near neighbors of a given type IS lower. but perhaps with enhanced intensity if the resonant excited ler el is a mole delocalized magnetic dichroism effects, or both, in these resonances, yielding a probe of near-neighbor inagnetic order 17 Most chaotic mixing experiments have been restricted to two-dimensional, time-periodic flows, and this has shaped advances in theory as well. A prototypical, bounded, three-dimensional flow with a moderate Reynolds number is presented; this system lends itself to detailed experimental observation and allows for high-precision computational inspection.…”

Hydrodynamic stability of a suspension in cylindrical Couette flow

“…Although not directly related to the stability of a suspension, there recently has been substantial interest in tracking particle motion in both nonwavy and wavy Taylor-Couette flow. [32][33][34][35][36][37] This work has focused on particle paths and enhanced diffusion without regard to the effect of the particles in the suspension on the stability of the flow. Finally, Dominguez-Lerma et al detected a nonperiodically time-dependent nonuniformity in the size of the vortices when a low concentration of flakes was used to visualize Taylor-Couette flow in vertical apparatus, but they did not note how the flakes affected the critical Taylor number.…”