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Investigation on two-phase flow in small diameter non-circular channels under low and normal gravity AIP Conf.In this work numerical simulations have been carried out to study the problem of dynamic air bubble formation from a submerged orifice in quiescent liquid, under constant inflow condition, at normal and reduced gravity levels. A coupled level-set and volume-of-fluid method is used to simulate the bubble formation, bubble detachment, and the bubble rise above the orifice. For the described study, the authors have mainly focused on low and medium air flow rate for simulation of bubble formation at the orifice. The employed gravity levels g / g e are in the range of 10 0 , 10 −1 , and 10 −2 . The influence of buoyancy on the bubble shape has been studied. The study includes the bubble volume, formation frequency, pinch-off rate, detached bubble diameter, and the bubble growth history for different air flow rates. Even for the static contact angle s =0 0 , it is observed that at low gravity levels the bubble base spreads along the surface of the orifice plate away from the orifice rim during the expansion stage, and during the detachment stage the bubble base again comes back to the orifice rim. As the air flow rate is increased under normal and low gravity conditions, coalescence between the rising bubbles or between the detached bubble and the forming bubble at the orifice is observed. It is shown that the increasing trend of bubble size at detachment, with increasing air flow rate under normal gravity is reversed in the case of reduced gravity ͑g / g e =10 −2 ͒.

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We proposed the combined numerical and experimental study of the dynamics of droplets generation at shallow microfluidic T-junction, where the flow is strongly confined in the vertical direction. The numerical simulation is performed by employing quasi-2D Hele-Shaw approximation with an interface capturing procedure based on coupled Level-Set and Volume-of-Fluid methods. We investigate the effect of the capillary number, Ca, the channel geometry (cross section aspect ratio, χ), and the flow rate (disperse-to-continuous phases) ratio, Γ, on the dynamics of the droplet breakup. Depending on Ca, three distinct flow regimes are identified: squeezing, tearing and jetting. In the squeezing regime at low Ca, the size of the generated droplets depends on χ and Γ, while it is almost insensitive to Ca in agreement to previous studies. In the tearing regime at moderate Ca, the droplet size decreases as ∼Ca−1/3, while it is only a weak function of χ and Γ. Finally, in the jetting regime, the steady co-flow of both phases takes place at high enough Ca. The numerical predictions based on the Hele-Shaw flow approximation are in excellent agreement with our in-house experimental results, demonstrating that the proposed approach can be effectively used for computationally inexpensive and adequately accurate modeling of biphasic flows in shallow microfluidic devices.

Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of μm and sub-μm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric step-emulsifier.