Microchemical systems for continuous-flow synthesis

Microfluidics for studying the deep underground biosphere: from applications to fundamentals

In this review, selected examples are presented to demonstrate how microfluidic approaches can be utilized for investigating microbial life from deep geological environments, both from practical and fundamental perspectives. Beginning with the definition of the deep underground biosphere and the conventional experimental techniques employed for these studies, the use of microfluidic systems for accessing critical parameters of deep life in geological environments at the microscale is subsequently addressed (high pressure, high temperature, low volume). Microfluidics can simulate a range of environmental conditions on a chip, enabling rapid and comprehensive studies of microbial behavior and interactions in subsurface ecosystems, such as simulations of porous systems, interactions among microbes/microbes/minerals, and gradient cultivation. Transparent microreactors allow real-time, noninvasive analysis of microbial activities (microscopy, Raman spectroscopy, FTIR microspectroscopy, etc.), providing detailed insights into biogeochemical processes and facilitating pore-scale analysis. Finally, the current challenges and opportunities to expand the use of microfluidic methodologies for studying and monitoring the deep biosphere in real time under deep underground conditions are discussed.

Microfluidic Laser-Induced Nucleation of Iron (II,III) Oxide Nanoparticle-Doped Supersaturated Aqueous KCl Solutions

A capillary-based microfluidic system designed for nonphotochemical laser-induced nucleation (NPLIN) studies coupled with real-time microscopy was used to study NPLIN of iron (II,III) oxide doped aqueous KCl solutions. Supersaturation was achieved by lowering the solution temperature using thermoelectric cooling, and heating was used for the dissolution of crystals downstream to prevent clogging during the flow. The effect of nanoparticle concentration, supersaturation, laser intensity, and filtration was studied. We report laser-induced nucleation using laser intensities as low as 1 MW/cm2 with nanoparticle number densities of ∼109 particles per mL of solution at KCl supersaturations from 1.06 to 1.08. The number of crystals increased with increasing laser intensity, supersaturation, and nanoparticle concentration. We discuss our results with respect to the colloidal impurity-heating mechanism hypothesis and propose a semiempirical model based on the nanoparticle heating and bubble formation due to the absorption of laser energy.

Vibrational manipulation of dry granular materials in lab-on-a-chip devices

We present vibrational techniques to pump, mix, and separate dry granular materials using multifrequency vibrations applied to a solid substrate with a standard audio system. The direction and velocity of the granular flow are tuned by modulating the sign and amplitude, respectively, of the vibratory waveform, with typical pumping velocities of centimeters per second. Different granular materials are mixed by combining them at Y-shaped junctions, and mixtures of granules with different friction coefficients are separated along straight channels by judicious choice of the vibratory waveform. We demonstrate that the observed velocities accord with a theory valid for sufficiently large or fast vibrations, and we discuss the implications for using vibrational manipulation in conjunction with established microfluidic technologies to combine liquid and dry solid handling operations at sub-millimeter length scales.

Synthesis of nanoparticles via microfluidic devices and integrated applications

In recent years, nanomaterials have attracted the research intervention of experts in the fields of catalysis, energy, biomedical testing, and biomedicine with their unrivaled optical, chemical, and biological properties. From basic metal and oxide nanoparticles to complex quantum dots and MOFs, the stable preparation of various nanomaterials has always been a struggle for researchers. Microfluidics, as a paradigm of microscale control, is a remarkable platform for online stable synthesis of nanomaterials with efficient mass and heat transfer in microreactors, flexible blending of reactants, and precise control of reaction conditions. We describe the process of microfluidic preparation of nanoparticles in the last 5 years in terms of microfluidic techniques and the methods of microfluidic manipulation of fluids. Then, the ability of microfluidics to prepare different nanomaterials, such as metals, oxides, quantum dots, and biopolymer nanoparticles, is presented. The effective synthesis of some nanomaterials with complex structures and the cases of nanomaterials prepared by microfluidics under extreme conditions (high temperature and pressure), the compatibility of microfluidics as a superior platform for the preparation of nanoparticles is demonstrated. Microfluidics has a potent integration capability to combine nanoparticle synthesis with real-time monitoring and online detection, which significantly improves the quality and production efficiency of nanoparticles, and also provides a high-quality ultra-clean platform for some bioassays.

A versatile non-fouling multi-step flow reactor platform: demonstration for partial oxidation synthesis of iron oxide nanoparticles

In the last decade flow reactors for material synthesis were firmly established, demonstrating advantageous operating conditions, reproducible and scalable production via continuous operation, as well as high-throughput screening of synthetic conditions. Reactor fouling, however, often restricts flow chemistry and the common fouling prevention via segmented flow comes at the cost of inflexibility. Often, the difficulty of feeding reagents into liquid segments (droplets or slugs) constrains flow syntheses using segmented flow to simple synthetic protocols with a single reagent addition step prior or during segmentation. Hence, the translation of fouling prone syntheses requiring multiple reagent addition steps into flow remains challenging. This work presents a modular flow reactor platform overcoming this bottleneck by fully exploiting the potential of three-phase (gas-liquid-liquid) segmented flow to supply reagents after segmentation, hence facilitating fouling free multi-step flow syntheses. The reactor design and materials selection address the operation challenges inherent to gas-liquid-liquid flow and reagent addition into segments allowing for a wide range of flow rates, flow ratios, temperatures, and use of continuous phases (no perfluorinated solvents needed). This "Lego®-like" reactor platform comprises elements for three-phase segmentation and sequential reagent addition into fluid segments, as well as temperature-controlled residence time modules that offer the flexibility required to translate even complex nanomaterial synthesis protocols to flow. To demonstrate the platform's versatility, we chose a fouling prone multi-step synthesis, i.e., a water-based partial oxidation synthesis of iron oxide nanoparticles. This synthesis required I) the precipitation of ferrous hydroxides, II) the addition of an oxidation agent, III) a temperature treatment to initiate magnetite/maghemite formation, and IV) the addition of citric acid to increase the colloidal stability. The platform facilitated the synthesis of colloidally stable magnetic nanoparticles reproducibly at well-controlled synthetic conditions and prevented fouling using heptane as continuous phase. The biocompatible particles showed excellent heating abilities in alternating magnetic fields (ILP values >3 nH m² kg_Fe^-1), hence, their potential for magnetic hyperthermia cancer treatment. The platform allowed for long term operation, as well as screening of synthetic conditions to tune particle properties. This was demonstrated via the addition of tetraethylenepentamine, confirming its potential to control particle morphology. Such a versatile reactor platform makes it possible to translate even complex syntheses into flow, opening up new opportunities for material synthesis.

Rapid and Replaceable Luminescent Coating for Silicon-Based Microreactors Enabling Energy-Efficient Solar Photochemistry

The sun is the most sustainable source of photons on the earth but is rarely used in photochemical transformations due its relatively low and variable intensity, broad wavelength range, and lack of focus. Luminescent solar concentrator-based photomicroreactors (LSC-PMs) can be an answer to all these issues, but widespread adoption is plagued by challenges associated with their complicated manufacturing. Herein, we developed a new strategy to accelerate and ease the production of LSC-PMs by depositing a thin luminescent film on commercially and widely available silicon-based microreactors. The protocol is fast and operationally simple, and the luminescent coating can be easily removed and replaced. This enables rapid tuning of the luminescent coating to fit the requirements of the photocatalytic system and to increase the photon flux inside the microreactor channels.

Capillary Microreactor for Initial Screening of Three Amine-Based Solvents for CO2 Absorption, Desorption, and Foaming

Microreactor is a very attractive laboratory device for screening conditions and solvents in an efficient, safe and fast manner. Most reported work on microreactors for CO2 capturing deals with absorption and mass transfer performance with a limited number of studies on solvent regeneration. For the first time, foaming, which is a major operational challenge of CO2 capturing is being studied in combination with absorption and desorption in a capillary microreactor setup. To demonstrate the setup capabilities, three known amine-based solvents (MEA, MDEA, and AMP) were selected for the screening and evaluation studies. MEA had the highest CO2 absorption efficiency while MDEA had the lowest one. CO2 absorption efficiency increased with temperature, liquid flow rate, and amine concentration as per the literature. During the absorption work, the Taylor flow regime was maintained at the reactor inlet. CO2 desorption of loaded amine solutions was investigated at different concentrations and temperatures up to 85°C. MDEA solution had the highest desorption efficiency, followed by AMP and the least desorption efficiency was that of MEA. Foaming experimental results showed that MEA had a larger foaming region compared to AMP. However, more foaming happened with AMP at higher gas and liquid flow rates. A plug flow mathematical reactor model was developed to simulate the MEA-CO2 system. The model captured well the performance and trends of the studied system, however the absolute prediction deviated due to uncertainties in the used physical properties and mass transfer correlation. Selecting a solvent for chemical absorption depends on many more factors than these three studied parameters. Still, microreactor proves a valuable tool to generate experimental results under different conditions, with the least amount of consumables (less than 1 L solvents were used), in a fast manner, combined with a knowledge insight because of the uniqueness of the Taylor flow regime.

Liquid Phase Oxidation of Hydrocarbons to High-Value Chemicals in Microfluidic Reactors - Prospects and Challenges

Liquid phase oxidation (LPO) of hydrocarbon is an industrially important process to produce petrochemicals and pharmaceuticals. It follows a free radical path having initiation, propagation and termination. The initiation step is slow while the propagation and termination steps are fast. The main challenge of such process is to control product selectivity at an appreciable conversion level. With the advancement of microfluidic reactor technology, it is possible to control the free radical steps. The present contribution critically reviewed the reaction engineering aspects of LPO of hydrocarbon, the influence of microfluidic reactor design and operation on reaction mechanism, conversion and product selectivity. It also outlines the challenges associated with microfluidic reactor operation, and prospects to apply the understanding from microfluidic reactors in few sectors. The understanding from the free radical oxidation process can also be applied to any other free radical processes.

Numerical study of a fractal-like tree node micromixer based on Murray’s law

This article focuses on the influence of fractal-like tree node (FTN) on the mixing efficiency and pressure drop of the micromixer. The mixing efficiency of FTN micromixers with different branch angle δ = 30°, 60° and 90° are compared at six kinds of Reynolds (Res). We can get that the micromixer with δ = 90° has higher mixing efficiency at any Re. The mixing results of the center FTN and the stagger FTN micromixer show that the center FTN has better mixing effect. The angle of FTN and the number of FTN are the key to improve the mixing efficiency. They are also the key to change the pressure drop in the microchannel. The FTN can slow down the pressure drop and maintain the stable pressure drop between two adjacent FTNs. The way to obtain a more stable pressure range is to increase the distance between two adjacent FTN. This provides a reliable reference for maintaining a stable pressure in the microchannel.

Understanding flow chemistry for the production of active pharmaceutical ingredients

Multi-step organic syntheses of various drugs, active pharmaceutical ingredients, and other pharmaceutically and agriculturally important compounds have already been reported using flow synthesis. Compared to batch, hazardous and reactive reagents can be handled safely in flow. This review discusses the pros and cons of flow chemistry in today’s scenario and recent developments in flow devices. The review majorly emphasizes on the recent developments in the flow synthesis of pharmaceutically important products in last five years including flibanserin, imatinib, buclizine, cinnarizine, cyclizine, meclizine, ribociclib, celecoxib, SC-560 and mavacoxib, efavirenz, fluconazole, melitracen HCl, rasagiline, tamsulosin, valsartan, and hydroxychloroquine. Critical steps and new development in the flow synthesis of selected compounds are also discussed.

Anionic polymerizations in a microreactor

Anionic polymerizations in a microreactor enable fast mixing, high-level control, and scale-up synthesis of polymers.

Non-Invasive Manipulation of Two-Phase Liquid-Liquid Slug Flow Parameters Using Magnetofluidics

Liquid-liquid slug flow in a microcapillary, with its improved heat and mass transfer properties and narrow residence time, plays a vital role in process intensification. Knowledge of the flow properties in microchannels along variables' controllability (e.g., phase ratio, slug length along with classical variables, such as pressure, temperature, and flow velocity) during operation is crucial. This work aids in this by using magnetofluidics to manipulate these parameters. A ferrofluid with reproducible properties is produced and, together with another phase, stable slug flow is generated. Micro-gear pumps and syringe pumps, with their traditional mechanical components, result in parts degrading over time due to fatigue caused by pressure differentials and corrosive chemicals. The microflow is also disturbed by the invasive nature of these pumps. A considerably energy-efficient, non-invasive alternative, with reduced mechanical interfacing is suggested in this work. It uses magnetic gradients to manipulate two-phase flow, one of which is a magnetically active phase. Conveying concepts using permanent magnets in the immediate vicinity of the flow are investigated. To operate this pump continuously and to be able to regulate the phase ratio, an electromagnetic non-invasive valve is developed. Phase separation is also carried out with an existing decanter design, modified using electromagnetism to work without a selective membrane, usually necessary for phase separation at this scale. This pump is then compared with similar pumps developed in the past.

Study on the Technology of Monodisperse Droplets by a High-Throughput and Instant-Mixing Droplet Microfluidic System

In this study, we report a novel high-throughput and instant-mixing droplet microfluidic system that can prepare uniformly mixed monodisperse droplets at a flow rate of mL/min designed for rapid mixing between multiple solutions and the preparation of micro-/nanoparticles. The system is composed of a magneton micromixer and a T-junction microfluidic device. The magneton micromixer rapidly mixes multiple solutions uniformly through the rotation of the magneton, and the mixed solution is sheared into monodisperse droplets by the silicone oil in the T-junction microfluidic device. The optimal conditions of the preparation of monodisperse droplets for the system have been found and factors affecting droplet size are analyzed for correlation; for example, the structure of the T-junction microfluidic device, the rotation speed of the magneton, etc. At the same time, through the uniformity of the color of the mixed solution, the mixing performance of the system is quantitatively evaluated. Compared with mainstream micromixers on the market, the system has the best mixing performance. Finally, we used the system to simulate the internal gelation broth preparation of zirconium broth and uranium broth. The results show that the system is expected to realize the preparation of ceramic microspheres at room temperature without cooling by the internal gelation process.

Continuous Flow Synthesis of a ZSM-5 Film in Capillary Microchannel for Efficient Production of Solketal

This work presented the microfluidic preparation of zeolite film in a capillary microchannel with different length-to-diameter ratios. In the quartz capillary with an inner diameter of 0.53 and 0.32 mm, Zeolite Socony Mobil-5 (ZSM-5) film was prepared by a continuous flow hydrothermal method. Considering the chemically inert surface of quartz capillary and the difficulty of preparing uniform and continuous zeolite film by conventional static synthesis, the ZSM-5 seed layer was precoated as active sites to induce film growth. The parameters of length-to-diameter ratio, seed coating, feed flow rate, and synthesis time were investigated. It revealed that the crystallinity of the ZSM-5 film was significantly affected by the capillary length-to-diameter ratio and seed coating in this flow system. The film morphology and thickness could be precisely controlled by adjusting the feed flow rate and synthesis time. This hydrogen form of the ZSM-5 (HZSM-5) film capillary microreactor was applied in the ketalization reaction of glycerol with acetone to produce solketal. The single-pass yield of solketal could reach ∼30% under mild conditions. This work provided a convenient stratagem of preparing zeolite catalytic coating or other support coatings in closed microchannels with a high length-to-diameter ratio and the potential application in valuable transformation of biomass glycerol.

Catalytic exchange of hydrogen isotopes intensified by two-phase stratified flow in wettability designable microchannels

This work develops a reliable method to achieve stratified flow in squared cross-section microchannels by endowing the four channel walls with very different wettabilities. The gas-liquid flows are studied experimentally in six kinds of microchannels with different wetting partitions on the channel walls, where occurrence of the stratified flow is found to strongly depend on the wetting partition and the individual flow rate of gas or liquid. Among them, the microchannel possessing three hydrophobic and one hydrophilic walls (3S1H) shows great potential in facilitating liquid phase catalytic exchange (LPCE) of hydrogen isotopes. Subsequently, a 3S1H microchannel reactor coated with hydrophobic Pt/activated carbon/polydimethylsiloxane (Pt/AC/PDMS) is fabricated to perform the LPCE at 30-80 °C and in a wide range of flow rates of hydrogen and water. The experimental outcomes not only unveil the relationship of the isotopic exchange performance with the temperature and flow pattern but also exhibit an outstanding isotopic exchange performance under the stratified flow.

O. Microfluidic Point-of-Care Devices: New Trends and Future Prospects for eHealth Diagnostics

Point-of-care (PoC) diagnostics is promising for early detection of a number of diseases, including cancer, diabetes, and cardiovascular diseases, in addition to serving for monitoring health conditions. To be efficient and cost-effective, portable PoC devices are made with microfluidic technologies, with which laboratory analysis can be made with small-volume samples. Recent years have witnessed considerable progress in this area with "epidermal electronics", including miniaturized wearable diagnosis devices. These wearable devices allow for continuous real-time transmission of biological data to the Internet for further processing and transformation into clinical knowledge. Other approaches include bluetooth and WiFi technology for data transmission from portable (non-wearable) diagnosis devices to cellphones or computers, and then to the Internet for communication with centralized healthcare structures. There are, however, considerable challenges to be faced before PoC devices become routine in the clinical practice. For instance, the implementation of this technology requires integration of detection components with other fluid regulatory elements at the microscale, where fluid-flow properties become increasingly controlled by viscous forces rather than inertial forces. Another challenge is to develop new materials for environmentally friendly, cheap, and portable microfluidic devices. In this review paper, we first revisit the progress made in the last few years and discuss trends and strategies for the fabrication of microfluidic devices. Then, we discuss the challenges in lab-on-a-chip biosensing devices, including colorimetric sensors coupled to smartphones, plasmonic sensors, and electronic tongues. The latter ones use statistical and big data analysis for proper classification. The increasing use of big data and artificial intelligence methods is then commented upon in the context of wearable and handled biosensing platforms for the Internet of things and futuristic healthcare systems.

A Novel Approach to Functionalization of Aryl Azides through the Generation and Reaction of Organolithium Species Bearing Masked Azides in Flow Microreactors

A novel straightforward method for aryl azides having functional groups based on generation and reactions of aryllithiums bearing a triazene group from polybromoarenes using flow microreactor systems was achieved. The present approach will serve as a powerful method in organolithium chemistry and open a new possibility in the synthesis of polyfunctional organic azides.

3D-printed PEEK reactors and development of a complete continuous flow system for chemical synthesis

This paper presents the development of milli- and microfluidic reactors made of polyether ether ketone (PEEK) and 3D-printed equipment for a complete continuous flow system.

Microfluidic processing of HZSM-5 films in a capillary microreactor for the continuous acetalisation reaction of glycerol with acetone

This work presented microfluidic processing of zeolite films in a capillary microreactor and its potential application for biomass conversion.

Continuous flow synthesis of phase transition-resistant titania microparticles with tunable morphologies

Titania microspheres have attracted substantial attention for a variety of applications, including ion scavenging, catalysis, and energy generation, though most synthetic techniques are limited to a few basic morphologies and narrow size ranges. Here, an intensified microfluidic strategy for continuous synthesis of anatase titania microspheres is presented. In-flow photo crosslinking, incorporated with a flow reactor and polar aprotic solvent, enables access to precursor compositions up to an order of magnitude higher than those previously reported, with size tunability approaching two orders of magnitude. Morphological and surface area effects associated with precursor composition are explored, resulting in hollow, yolk–shell, macroporous, and dense titania microspheres containing no detectable rutile phase and possessing surface areas exceeding 350 m² g⁻¹ post calcination. Furthermore, effects of calcination temperature and time on the surface area, crystallinity and phase composition, and morphology of the synthesized titania microspheres are studied in detail. The synthesized microspheres are shown to remain completely in the anatase phase, even at temperatures up to 900 °C, far beyond the expected phase transition temperature. Thus, the breadth of attainable morphologies, specific surface areas, and phase compositions present a variety of intriguing substrate candidates for such applications as heterogeneous (photo) catalysis, adsorption and ion capture, electrochemistry, and photovoltaics.

A flow chemistry strategy for synthesis of anatase titania microparticles utilizing a flow-focusing microreactor integrated with a collimated UV LED is presented. The synthesized microparticles possess a wide variety of morphologies and high surface areas (up to 362 m² g⁻¹).

Anodic bonding of mid-infrared transparent germanate glasses for high pressure - high temperature microfluidic applications

High pressure/high-temperature microreactors based on silicon-Pyrex® microfabrication technologies have attracted increasing interest in various applications providing optical access in high-pressure flow processes. However, they cannot be coupled to infrared spectroscopy due to the limited optical transparency (up to ~2.7 μm in the infrared region) of the Pyrex® glass substrate employed in the microreactor fabrication. To address this limitation, the alternative approach proposed in this work consists in replacing the Pyrex® glass in the microreactor by a mid-infrared transparent glass with thermal and mechanical properties as close as possible or even better to those of the Pyrex®, including its ability for silicon-wafers coupling by the anodic bonding process. Glasses based on germanate GeO₂, known for their excellent transmission in the mid-infrared range and thermal/thermo-mechanical properties, have been thus evaluated and developed for this purpose. The optical, mechanical, thermal and electrical conductivity properties of adapted glass compositions belonging to five vitreous systems have been systemically investigated. The glass composition 70GeO₂-15Al₂O₃-10La₂O₃-5Na₂O (mol.%) was defined as the best candidate and produced in large plates of 50 mm diameter and 1 mm thickness. Anodic bonding tests with Si-wafers have been then successfully conducted, paving the way for the development of fully mid-infrared transparent silicon-glass microreactors.

Oxo-Thiolation of Cationically Polymerizable Alkenes Using Flow Microreactors

The present study describes the cationic oxo-thiolation of polymerizable alkenes by using highly reactive cationic species generated by anodic oxidation. These highly reactive cations were able to activate alkenes before their polymerization. Fast mixing in flow microreactors effectively controlled chemoselectivity, enabling higher reaction temperatures.

Generation and Reaction of Functional Alkyllithiums by Using Microreactors and Their Application to Heterotelechelic Polymer Synthesis

Flow microreactors enabled the successful generation of various functional alkyllithiums containing electrophilic functional groups, as well as the use of these alkyllithiums in subsequent reactions. The high reactivity of these series of reactions could be achieved by the extremely accurate and selective control of residence time. Moreover, integrated flow microreactor systems could be used to successfully synthesize heterotelechelic polymers with two functionalities, one at each end, via a process involving controlled anionic polymerization initiated by functional alkyllithium compounds, followed by trapping reactions with difunctional electrophiles.

Pulsed ultrasound for temperature control and clogging prevention in micro-reactors

Ultrasonic micro-reactors are frequently applied to prevent micro-channel clogging in the presence of solid materials. Continuous sonication will lead to a sizeable energy input resulting in a temperature increase in the fluidic channels and concerns regarding microchannel degradation. In this paper, we investigate the application of pulsed ultrasound as a less invasive approach to prevent micro-channel clogging, while also controlling the temperature increase. The inorganic precipitation of barium sulfate particles was studied, and the impact of the effective ultrasonic treatment ratio, frequency and load power on the particle size distribution, pressure and temperature was quantified in comparison to non-sonicated experiments. The precipitation reactions were performed in a continuous reactor consisting of a micro-reactor chip attached to a Langevin-type transducer. It was found that adjusting the pulsed ultrasound conditions prevented microchannel clogging by reducing the particle size to the same magnitude as observed for continuous sonication. Furthermore, reducing the effective treatment ratio from 100 to 12.5% decreases the temperature rise from 7 to 1 °C.

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 ?m; height, H = 120 ?m) leading into an array of 276 capillaries (100 ?m long; width = 5 ?m facing the main channel and 25 ?m 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.