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.

中文翻译：

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轴对称几何结构中的微流体逐步乳化

双相步骤乳化（Z.李等人，实验室芯片，2015，15，1023）为有前途的微流体技术的高通量生产微米和亚微米高度单分散的液滴。步进式乳化剂由浅（Hele-Shaw）微通道组成，该微通道与两种同流不混溶的液体共同作用，并突然膨胀（即，步）到一个深而宽的水库。在某些条件下，被同流连续相吞没的分散相的受限物流在该步骤中分解为小的高度单分散的液滴。由于平面装置的复杂几何形状，因此对相应流体力学的理论研究非常复杂，需要采用数值方法。但是，在有限的几何形状中以三维表面张力为主的两相流的直接数值模拟在计算上是昂贵的。在本文中，我们研究了轴对称逐步乳化的模型问题。这种设置包括在圆柱形毛细管中的稳定的核-环形双相流，该毛细管通过与平面阶梯式乳化器的边缘突然膨胀而同轴连接到较大直径的储液管。我们证明，轴对称设置展示了类似于平面设备的液滴生成方案。对基本流体动力学进行详细的参数研究是可行的由于轴向对称性，可以通过廉价的（二维）模拟进行。给出了根据控制无量纲参数量化液滴产生的不同状态的相图。我们表明，与平面设备中的实验定性一致，在逐步乳化过程中产生的液滴尺寸与毛细管数无关，并且几乎对粘度比不敏感。这些发现证实了逐步乳化方式仅受表面张力控制。数值预测与采用轴对称步进式乳化剂进行的内部实验非常吻合。