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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.

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Gas bubble formation from a submerged orifice under constant-flow conditions in a quiescent high-density liquid metal, lead-bismuth eutectic (LBE), at high Reynolds numbers was investigated numerically. The numerical simulation was carried out using a coupled level-set and volume-of-fluid method governed by axisymmetric Navier-Stokes equations. The ratio of liquid density to gas density for the system of interest was about 15,261. The bubble formation regimes varied from quasi-static to inertia-dominated and the different bubbling regimes such as period-1 and period-2 with pairing and coalescence were described. The volume of the detached bubble was evaluated for various Weber numbers, We, at a given Bond number, Bo, with Reynolds number Re ) 1. It was found that at high values of the Weber number, the computed detached bubble volumes approached a 3/5 power law. The different bubbling regimes were identified quantitatively from the time evolution of the growing bubble volume at the orifice. It was shown that the growing volume of two consecutive bubbles in the period-2 bubbling regime was not the same whereas it was the same for the period-1 bubbling regime. The influence of grid resolution on the transition from period-1 to period-2 with pairing and coalescence bubbling regimes was investigated. It was observed that the transition is extremely sensitive to the grid size. The transition of period-1 and period-2 with pairing and coalescence is shown on a Weber-Bond numbers map. The critical value of Weber number signalling the transition from period-1 to period-2 with pairing and coalescence decreases with Bond number as We $ Bo 21 , which is shown to be consistent with the scaling arguments. Furthermore, comparisons of the dynamics of bubble formation and bubble coalescence in LBE and water systems are discussed. It was found that in a high Reynolds number bubble formation regime, a difference exists in the transition from period-1 to period-2 with pairing and coalescence between the bubbles formed in water and the bubbles formed in LBE. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 3996-4012, 2015

A numerical method for modeling and understanding the dynamics of bubble oscillations subjected to fast variations in the ambient pressure is proposed under low Mach number conditions. In the present work, the method uses a single-fluid continuum formalism of weakly compressible axisymmetric Navier-Stokes equations for the numerical simulation of liquid-gas flows with surface tension and adopts the interface capturing approach based on a coupled level set and volume of fluid (CLSVOF) method for describing the moving and deformed interfaces. To demonstrate the efficacy of the proposed method, first, the numerical results of the radial oscillations of a spherical gas bubble are tested with the numerical solutions of Rayleigh-Plesset equation. Then, the numerical method is applied to reproduce the growth and subsequent collapse of a bubble in an infinite liquid medium observed in experiments. Finally, the numerical simulation of the interaction of two oscillating bubbles at small separation distance is evaluated in response to a moderate step change in the ambient pressure. It is shown that two deformable bubbles undergo coupled radial and oscillatory translational motions which eventually results in the bubbles' attraction and coalescence caused by the secondary Bjerknes forces. The numerical predictions show very good accuracy with the experimental and numerical results reported in the literature.