Particle-laden Taylor–Couette flows: higher-order transitions and evidence for azimuthally localized wavy vortices

We extend upon the known flow transitions in neutrally buoyant particle-laden Taylor–Couette flows by accessing higher suspension Reynolds numbers $(Re_{{susp}} \sim O(10^3))$ in a geometry with radius ratio $\eta = 0.917$ and aspect ratio $\varGamma = 21.67$. Flow transitions for several particle volume fractions ($0 \leq \phi \leq 0.40$) are investigated by means of flow visualization experiments, in a flow driven by a rotating inner cylinder. Despite higher effective ramp rates, we observe non-axisymmetric patterns, such as spirals, in the presence of particles. A novel observation in our experiments is the azimuthally localized wavy vortex flow, characterized by waviness present on a fraction of the otherwise axisymmetric Taylor vortices. The existence of this flow state suggests that in addition to the already established, destabilizing effect of particles, they may also inhibit the growth of instabilities. Flow topologies corresponding to higher-order transitions in particle-laden suspensions appear to be qualitatively similar to those observed in single-phase flows. A key difference, however, is the visible reduction in the appearance of a second, incommensurate frequency at higher particle loadings, which could have implications for the onset of chaos. Simultaneous torque measurements allow us to estimate an empirical scaling law between the Nusselt number ($Nu_{\omega }$), the Taylor number ($Ta$) and the relative viscosity ($\chi ^{e}): Nu_{\omega } \propto Ta^{0.24} \chi ^{e \, 0.41}$. The scaling exponent of $Ta$ is non-trivially independent of the particle loading. Apparently, particles do not trigger a qualitative change in the nature of angular momentum transfer between the cylinders.