Drop flow in rectangular microchannels has been utilized extensively in microfluidics. However, the pressure-gradient versus flow-rate relation is still not well understood. We study the motion of a long drop in a rectangular microchannel in the limit the capillary number , the contact-line drag is negligible and the corner fluid is stationary. Thus, the drop moves as a leaky piston. We extend our model to a train of long drops, and compare our model predictions with published experiments.

The motion of long drops in rectangular microchannels at low capillary numbers

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and nonlinear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. Deriving a conservation law along the thread, we can calculate the stress inside the thread from a measurement of the thread thickness. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Non-Newtonian shear-thinning droplet formation mechanism in a T-junction microchannel is experimentally investigated using aqueous solutions of xanthan gum as the dispersed phase and mineral oil as the continuous phase. Influences of both phase flow rates and polymer concentration on flow regime transition are explored. It is observed that the initial vertical expansion stage is present only for the Newtonian and lower shear-thinning systems. Droplet evolution rate shows the influence of continuous phase flow rate and shear-thinning properties on the dynamics of necking stages, viz. squeezing, transition, pinch-off, and filament thinning. Analysis of Ohnesorge number (Oh) reveals that inertial force dominates in the squeezing stage, whereas viscous and interfacial force control in the filament thinning stage. Longer and stable filament generation is detected as a discerning feature for non-Newtonian systems that appears more prominent with increasing dispersed phase shear-thinning properties. The results also indicate an inverse relation of droplet length with continuous phase flow rate and xanthan gum concentration, while the droplet formation frequency and its polydispersity vary directly with those parameters.

Insights into the dynamics of non-Newtonian droplet formation in a 
T-junction microchannel

In this paper we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidences. In addition, it permits to investigate in detail the hydrodynamic phenomena occurring during the breakup stages. Finally, a suitable deformation parameter is introduced and analyzed to characterize the state of deformation of the system by inspecting pairs of interacting droplets flowing in the narrow channel.

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Deformation and breakup dynamics of droplets within a tapered channel

In gas-driven flow focusing, mechanical disturbance is applied to modulate formation of droplets under the condition that the jet breaks at a high speed. By changing the conditions of jet generation, a systematic experimental study of the relevant parameters is carried out. In the axisymmetric mode, the diameter and velocity of the jet are affected by changing the flow rate and pressure drop condition. The results show that the jet can be regulated in a very large range, and the size of the generated droplets can also be accurately predicted. For viscous liquids, mechanical disturbances can also be used to make them break uniformly within a certain range. Due to the high frequency and precise controllability of droplet preparation in the experiment, these findings can be extended to more fields for practical applications.

Parametric study on breakup of liquid jet in a gas-driven flow focusing process upon external excitation

Using micro-particle image velocimetry (μPIV), the convective flow inside a silicone oil droplet was investigated in detail during its formation in coaxial capillaries under co-flow in a water/glycerol mixture continuous phase. The analysis of μPIV measured flow field revealed that two characteristic flow areas exist in the droplet in formation: an inflow zone and a circulation zone. The intensity of vortex flow in these zones was estimated by calculating the average angular velocity of these vortices under the condition of no shear for different dispersed phase and continuous phase flow rates and for different viscosity ratios between the two phases. The evolution of the vortex flow pattern inside the droplet was investigated thoroughly all the way from the step of their formation to the step of the free-moving droplet. The results of this study are important for understanding the mixing processes inside the droplet at different stages of its formation.

Vortex flow evolution in a growing microdroplet during co-flow in coaxial capillaries

This work is focused on the mechanisms of the dripping and jetting flow modes of viscoelastic semi-dilute polyacrylamide aqueous solutions co-flowing with silicone oil in co-axial capillaries. A phase diagram of the dripping, jetting, and intermediate flow modes is established. It was found that in the dripping mode, the elongation velocity of the filament between the terminal droplet and the inner capillary is controlled solely by the continuous phase rate. At the same time, the decrease in the filament diameter is due to both stretching and outflow of the polymer solution into the terminal droplet. In the jetting mode, the thread diameter was found to evolve in three stages. In the first stage, the average jet velocity increases, whereas in the second and third stages, it becomes constant and corresponds to the velocity of the continuous phase. The transition from the second to the third stage is defined by the appearance of capillary waves resulting in the formation of the beads-on-string structure. In the third stage, the filament diameter between the neighbor beads decreases exponentially and is governed by the relaxation time, which strongly depends on polymer concentration, but does not depend on the continuous phase flow rate. A simple physical model was proposed for describing the evolution of dimensions of filaments and beads during development of jet capillary instability. The universal character of the evolution of filaments and beads sizes, which is independent of concentration of semi-diluted polymer solutions and flow rates of the continuous phase, is revealed.

D. Funfschilling

Papers

Vortex flow evolution in a growing microdroplet during co-flow in coaxial capillaries

Dripping and jetting of semi-dilute polymer solutions co-flowing in co-axial capillaries