Flow transition of liquid–liquid two-phase Taylor–Couette flow with axial flow

• A flow transition in liquid–liquid two-phase Taylor–Couette flow was investigated. • Several concentrations of glycerol solution were used as the continuous phase. • Flow patterns were classified using Reynolds and Weber numbers. • A stable banded structure was observed at higher Reynolds and Weber numbers. • Droplet inertia plays a key role in the formation of the banded structure. A liquid–liquid two-phase Taylor–Couette flow is of fundamental and practical importance in multiphase flow systems. This study investigates the flow transitions in such a system with constant axial flow and gradually increased rotation of the inner cylinder. To clarify the effect of continuous-phase viscosity on flow transitions, several concentrations of glycerol–water solutions were employed as the continuous phase, while soybean oil was used as the dispersed phase. Visualization experiments revealed that the flow undergoes a cascade of transitions: stratified flow, disturbed stratified flow, transitional droplet flow, unstable banded flow, and stable banded flow. A flow map was constructed using two dimensionless parameters, rotational Reynolds number ( Re rot ) and Weber number ( We ). The transitions from disturbed stratified to unstable banded flow (TR I) and from unstable to stable banded flow (TR II) were found to be approximately expressed by a power-law relation of the form We ∼ Re rot A , where A is a fitting exponent. For TR I, A showed no clear dependence on continuous-phase viscosity, suggesting that the transition is governed by the combined effects of inertia, viscosity, and interfacial tension. In contrast, A decreased with increasing viscosity in TR II, becoming nearly zero at high glycerol concentration. Furthermore, to clarify the mechanism of stable banded flow formation, the droplet inertia was evaluated using the Stokes number ( St ). It was revealed that the stable banded structure results from the loss of droplet inertia, associated with droplet fragmentation under higher rotation and the increasing inertia of the continuous phase.