Hydrodynamic Characterization of Phase Separation in Devices with Microfabricated Capillaries

Capillary microseparators have been gaining interest in downstream unit operations, especially for pharmaceutical, space, and nuclear applications, offering efficient separation of two-phase flows. In this work, a detailed analysis of the dynamics of gas–liquid separation at the single meniscus level helped to formulate a model to map the operability region of microseparation devices. A water–nitrogen segmented flow was separated in a microfabricated silicon-glass device, with a main channel (width, W = 600 μm; height, H = 120 μm) leading into an array of 276 capillaries (100 μm long; width = 5 μm facing the main channel and 25 μm facing the liquid outlet), on both sides of the channel. At optimal pressure differences, the wetting phase (water) flowed through the capillaries into the liquid outlet, whereas the nonwetting phase (nitrogen) flowed past the capillaries into the gas outlet. A high-speed imaging methodology aided by computational analysis was used to quantify the length of the liquid slugs and their positions in the separation zone. It was observed that during stable separation, the position of the leading edge of the liquid slugs (advancing meniscus), which became stationary in the separation zone, was dependent only on the outlet pressure difference. The trailing edge of the liquid slugs (receding meniscus) approached the advancing meniscus at a constant speed, thus leading to a linear decrease of the liquid slug length. Close to the liquid-to-gas breakthrough point, that is, when water exited through the gas outlet, the advancing meniscus was no longer stationary, and the slug lengths decreased exponentially. The rates of decrease of the liquid slug length during separation were accurately estimated by the model, and the calculated liquid-to-gas breakthrough pressures agreed with experimental measurements.


Design and operation of the microfabricated gas-liquid separation devices
Two designs were employed with an array of tapered capillaries on both sides of a separation channel. The capillaries were trapezoidal shaped with a rectangular cross-section increasing in width along the length of the capillaries (as shown in Figure S1) and the corresponding dimensions are shown in Table S1. Upon fabrication of the devices, observation of gas-toliquid and liquid-to-gas breakthrough pressures was performed in the experimental set-up shown in Figure 1 of the article. The system was first pressurised only with gas (dispersed phase) followed by the initiation of slug-flow with the wetting phase (water). The outlet pressures were then adjusted, so as to have a slightly higher gas outlet pressure than the liquid-outlet pressure, as shown in Figure S2. Once stable separation was established, the breakthrough pressures were monitored by adjusting the pressure of only one outlet with a back pressure regulator, while keeping the pressure of the other outlet constant. To study liquid-to-gas breakthrough, the pressure of the gas outlet was lowered (i.e., outlet pressure difference ΔPGL was lowered), whereas for the gas-to-liquid breakthrough measurements, ΔPGL was increased by lowering the liquid outlet pressure.  Figure S1: Schematic representation of the microseparator design with the relevant geometrical parameters of the capillaries annotated (from Table S1). Images are not to scale. Figure S2: Automated pressure sensing via LabView showing the operating procedure followed to measure: (a) liquid-to-gas breakthrough pressure (ΔPL>G) and (b) gas-to-liquid breakthrough pressure (ΔPG>L). Data labels in the graphs show each step: [1] gas-only flow to pressurise the system, [2] start the flow of liquid, [3] slug-flow established, [4] adjust outlet pressures PG or PL for stable separation, [5] vary the pressure difference, ΔPGL by adjusting the outlet pressures PG or PL to observe breakthrough, [6] point of breakthrough.

Image pre-processing via morphological reconstruction
A series of high-speed images was recorded to observe the dynamic nature of liquid slugs during separation, which were then processed by an algorithm in Python programming language 1 . Images were analysed using this script to track the positions of the advancing and the receding menisci, as mentioned in the "High-speed imaging and computational image analysis" section of the article. Due to the hydrophilicity of the channels, water from the trailing edge of the liquid film coalesced to form droplets of water on the surfaces of the main channel. Consequently, this affected the meniscus profile of the advancing meniscus and additionally posed a problem for an accurate edge detection based identification and tracking of the advancing meniscus. To remove these droplets a morphological reconstruction step was implemented in the image analysis code to selectively identify the droplets and robustly remove them without afflicting any pixel-based morphological changes to the gas-liquid menisci. An erosion filter based morphological reconstruction step was adapted from Robinson and Whelan, 2004 2 and the resulting image is shown in Figure S3. Once this preprocessing step was completed, only the gas-liquid menisci were selected and their positions tracked, as shown in the attached Supplementary Movie 1.

Measurement of the initial liquid slug length, number of active capillaries, and bubble frequency during separation
The initial length of liquid slugs, L0, has been observed to affect the gas-liquid separation process and is a key parameter in the modified Hagen-Poiseuille equation for the estimation of liquid-to-gas breakthrough pressures 3,4 . The length of the slugs was measured upstream of the separation zone of the device during gas-liquid separation at stable separation pressures ( Figure S4a and S4b). Images recorded with the high-speed camera were analysed manually using the ImageJ software 5 . Pressure fluctuations in the separation zone of the device and possible expansion of the gas bubbles in the main channel affected the formation of slug-flow upstream of the device at the T-junction 6 . Results from the manual analysis indicated that the number of active capillaries varied as a function of the gas-liquid pressure difference, ΔPGL ( Figure S4c). At higher liquid flow rate, fluctuations in the position of the advancing meniscus were observed possibly due to pressure instabilities in the liquid slug inside the separation zone ( Figure S4d).

S6
Additionally, the periodic nature of the segmented flow was quantified in the main channel, upstream of the separation zone, by measuring the bubble frequency in the device. Warnier et al. 7 defined the bubble formation frequency as the number of unit cells (one liquid slug + one gas bubble) travelling past a defined location in the channel per unit time. The experimentally measured frequencies were observed to increase linearly with increasing liquid flow rates ( Figure S5).

Tracking the entry of the advancing meniscus in the separation zone at stable separation conditions
Despite issues with the coalescence of water droplets with the liquid slugs, the position of the advancing meniscus, xa, was tracked and compared with the theoretical value from Equation (11) in the article. As expected, the velocity of the advancing meniscus decreased as it entered the separation zone (due to outflow through the capillaries) and gradually became pinned (i.e., stationary) before the receding meniscus entered the separation zone ( Figure S6). The dotted line in Figure S6 shows the noise from the edge-detection step in the image analysis script, which is a direct result of the varying pixel gradients occurring during the coalescence of the water droplet with the advancing meniscus. The receding meniscus entered the separation zone at t = l0/qT, (only after xa reached xp), moving at a constant speed governed by the total flow rate QT.

Quantification of slug lengths in the A-2 device at varying pressure differences
The capability of the theoretical model to estimate the liquid-to-gas breakthrough pressures in another microfabricated separation device (A-2) was also tested, as detailed in the "Phase separation in separator A-2" section of the article. Experiments were performed to measure the decrease in the length of the slugs at varying ΔPGL ( Figure S8), along with the pinning positions ( Figure 9a in the article). Results showed that the rate of decrease in the liquid slug lengths was independent of variations in ΔPGL, while the pinning location of the advancing meniscus decreased with increasing ΔPGL.