Droplet formation in microfluidic T-junction generators operating in the transitional regime. II. Modeling

Abstract

This is the second part of a two-part study on the generation of droplets at a microfluidic T-junction operating in the transition regime. In the preceding paper [Phys. Rev. E 85, 016322 (2012)], we presented our experimental observations of droplet formation and decomposed the process into three sequential stages defined as the lag, filling, and necking stages. Here we develop a model that describes the performance of microfluidic T-junction generators working in the squeezing to transition regimes where confinement of the droplet dominates the formation process. The model incorporates a detailed geometric description of the drop shape during the formation process combined with a force balance and necking criteria to define the droplet size, production rate, and spacing. The model inherently captures the influence of the intersection geometry, including the channel width ratio and height-to-width ratio, capillary number, and flow ratio, on the performance of the generator. The model is validated by comparing it to speed videos of the formation process for several T-junction geometries across a range of capillary numbers and viscosity ratios.

Parallelization of microfluidic flow-focusing devices

“…Similarly, the size of drops formed in junctions with θ = 90° is nearly independent of the viscosity of the inner phase for q i > 400 µL/h, as shown in Figure 3c. By contrast, significant differences are observed for higher values 30 of q i . At these flow rates, the drop formation becomes much more stable at higher fluid flow rates if the viscosity of the inner phase is 8 mPa s or higher, such that their size does not increase abruptly at q i = 400 µL/h.…”

“…Hence, in these junctions, drop formation is only stable at > 700 µL/h. 30 Drops produced in junctions with θ = 90° are significantly smaller than those made in the other junctions we tested, if formed at equal injection flow rates. We assign this difference to a change in the time required to initiate necking: If θ = 90°, the pressure 35 build-up in the outer phase is much faster, such that the necking is initiated earlier, when the drop precursor volume is smaller.…”

“…In this regime, the dynamics of drop breakup is entirely controlled by the flow rate of the 25 outer phase, 8 such that the drop size depends on the flow rate of the outer phase, 6, 9 its viscosity and surface tension, 10 and the channel geometry. 7,11,12 However, the necking process, which eventually leads to drop formation, is slow, limiting the maximum drop 30 generation frequency and hence the throughput. The drop generation frequency can be increased if an additional thin orifice is added after the crossjunction.…”

“…In devices with θ = 135°, the inner fluid is pushed back if the local underpressure at the meniscus of the inner fluid, caused by the drop pinch-off, is higher than the pressure at which 80 fluid is injected in the liquid inlet. 30 The distance the meniscus is pushed back increases with increasing viscosity of the outer phase and with decreasing viscosity of the inner phase. 30 In devices with θ = 135°, the pushback is enhanced because the y-component of the outer 85 fluid contributes to this push-back.…”

“…30 The distance the meniscus is pushed back increases with increasing viscosity of the outer phase and with decreasing viscosity of the inner phase. 30 In devices with θ = 135°, the pushback is enhanced because the y-component of the outer 85 fluid contributes to this push-back. Hence, if we increase the viscosity of the outer phase 10-fold, this push-back is much more pronounced in devices with θ = 135°.…”