The flow topology transition of liquid–liquid Taylor flows in square microchannels

This work investigates the change of the flow topology of Taylor flow and qualitatively relates it to the excess velocity. Ensemble-averaged 3D2C-$$\upmu$$ μ PIV measurements simultaneously resolve the flow field inside and outside the droplets of a liquid–liquid Taylor flow that moves through a rectangular horizontal microchannel. While maintaining a constant Capillary number Ca = 0.005, the Reynolds number ($$0.52 \le {\text{Re}} \le 2.14$$ 0.52 ≤ Re ≤ 2.14 ), the viscosity ratio ($$0.24 \le \lambda \le 2.67$$ 0.24 ≤ λ ≤ 2.67 ) and surfactant concentrations of sodium dodecyl sulfate (0–3 CMC) are varied. We experimentally identified the product of the Reynolds number Re and the viscosity ratio $$\lambda$$ λ to indicate the momentum transport from the continuous phase (slugs) into the droplets (plugs). The position and size of the droplet’s main vortex core as well as the flow topology in the cross section of this vortex core changed with increased momentum transfer. Further, we found that the relative velocity of the Taylor droplet correlates negatively with the evoked topology change. A correlation is proposed to describe the effect quantitatively. Graphical abstract

Structural Analysis of Couette-Taylor Flow With Periodic Oscillation of the Inner Cylinder in Different Flow Regimes

The structures of flow in laminar Couette-Taylor flow with periodic oscillation of the inner cylinder rotation velocity (which linearly increases from zero to a fixed maximum value and then goes to zero again in each period) for different three regimes; Couette flow, Taylor vortex and wavy vortex, with the effect of the Womersley number, Wo, for different periods and the critical Taylor number are investigated numerically. The Wo varies between. 0.38 ≤ Wo ≤ 8.59. To understand how the flow responds to a given boundary conditions, the critical Taylor number is calculated and the structure of vortices which formed in the flow field is investigated. The results show that if Wo is increased, i.e. when the slope of rotational velocity of inner cylinder is increased, more delay in changing the flow regime compare to the steady state (when the inner cylinder rotates with constant velocity) is observed. Also for large values of Wo, due to the inertia, the flow does not follow the given boundary condition so for the higher value of the Womersley number, Wo = 8.59, there is a time lag and vortices do not appear until the second period of the inner cylinder oscillations. The reason is that the time scale of the dynamics of flow is less than the time scale that is associated with the flow instability, thus the flow regime behaves like a laminar Couette flow at the initial period. Comparing the present results with that of steady state, it is appeared that for a minimum value of Wo used in this paper, i.e. Wo = 0.38, the primary critical Taylor number is 50% higher than that of steady state.