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Nov 10, 2024

Characterization of the oil water two phase flow in a novel microchannel contactor equipped with helical wire static mixer | Scientific Reports

Scientific Reports volume 14, Article number: 23369 (2024) Cite this article 538 Accesses Metrics details This study investigates an oil/water two-phase system to assess the potential efficacy of a

Scientific Reports volume 14, Article number: 23369 (2024) Cite this article

538 Accesses

Metrics details

This study investigates an oil/water two-phase system to assess the potential efficacy of a novel passive mixer in enhancing the liquid-liquid interfacial area within a micro-channel contactor. In this system, two fluids are introduced into a microchannel with a diameter of 800 μm and a length of 20 cm, which is equipped with a stainless-steel helical wire measuring 250 μm in diameter. Throughout the experiments, both fluids are supplied at equal flow rates, and the dominant forces, including attachment and detachment forces, are examined. The results reveal a critical Weber number of 3.8 × 10−³, at which the first detachment occurs. A comparison between microchannels with and without the passive micromixer demonstrates that greater slug breakup occurs in the system incorporating the helical wire micromixer. This innovative configuration results in a significant reduction in slug/droplet size compared to a microchannel without a barrier, decreasing from approximately 600 μm to 390 μm at a flow rate of 0.8 mL/min. Additionally, a flow map is presented, illustrating three distinct flow regimes: flow contains long slug, Slug-droplet flow, and droplet flow regimes, with the droplet flow regime covering the largest area. The findings indicate that the implementation of this innovative passive mixer substantially increases the interfacial area, providing significant advantages for mass transfer applications.

Microfluidic devices often employ microchannels, which are tiny channels with dimensions typically measured in micrometers. These channels are utilized in a wide range of applications, such as chemical analysis, drug delivery, and heat transfer (Khan and Fartaj17). Microfabrication techniques like photolithography or soft lithography are commonly used to fabricate these channels, which can come in different shapes and sizes. Microchannels have several advantages compared to traditional channels, including lower flow rates, higher surface area-to-volume ratios, and smaller sample volumes (Lee et al.19). These benefits make microchannels an excellent choice for several applications, such as medical diagnostics using lab-on-a-chip devices (Arshavsky-Graham and Segal1), chemical synthesis with microreactors (Watts and Haswell32), and cooling electronic devices via microfluidic heat exchangers (Ramesh et al.26). In essence, the microchannels have paved the way for new possibilities in the field of microfluidic devices and have played a crucial role in the creation of various innovative applications across different industries.

In a micro-scale two-phase system, there is an interaction between the continuous phase and dispersed phase within the microchannel. Interfacial tension as an important physical property plays a significant role, leading to the enhanced control over liquid-liquid two-phase flow in the microchannel. Different flow regimes are observed by changing operating conditions such as slug flow, droplet flow, slug–drop flow, parallel flow, annular flow, deformed interface flow, and some less common patterns in the liquid–liquid two-phase flow system (Ganguli and Pandit8). Each flow pattern within the microchannel has the potential to intensify a process in different applications through its distinctive characteristics. Applications described in various studies include solvent extraction (Hasanpoursorkhdehi and OmidbakhshAmiri12; Wen et al.33), polymerization (Chen and Timperman6; Ghasemzade Bariki et al.9), and chemical and biomedical synthesis (Huang et al. 14; Ma et al.23).

One significant characteristic of microchannels that sets them apart from the conventional contactors is their ability to enhance mixing and mass transfer in processes such as liquid-liquid extraction (LLE). Liquid-liquid extraction is a separation technique used to extract a component from one liquid to another liquid that is immiscible based on its differential solubility in two different phases. The primary factors that influence the liquid-liquid extraction are the interfacial area and mixing. Increasing the interfacial surface area can improve the efficiency of liquid-liquid extraction and consequently enhance the mass transfer rate. The particular design of the microchannel helps to improve the effectiveness of the liquid-liquid extraction system towards achieving its objective (Assmann et al.2]; Xu and He 2007). An example of this is seen in the extractive desulfurization, where the utilization of microchannel leads to significantly higher extraction rates compared to the batch contactors in a shorter residence time (Mahdavi et al.16). Numerous studies have demonstrated that the application of microchannels can facilitate effective contact between two phases by increasing the interfacial area (Karamzadeh et al.15; Tabatabaei et al.29).

Microfluidic systems have made a significant impact on the chemical industries due to the advantages offered by the small-scale flow channels in these systems, which increase the surface-to-volume ratio. However, the Reynolds number of liquid flows in microchannels is very low, often around 0.1 in typical water-based microfluidic systems. This low Reynolds number leads to limited turbulent mixing and a heavy reliance on diffusion, which is a slow process. Therefore, to achieve thorough species mixing within a short mixing channel and preserve the compact nature of the microfluidic devices, effective microfluidic mixing schemes are essential. Additionally, developing efficient mixing schemes caused by increasing the interfacial area is critical for increasing the performance of the microfluidic systems.

Mixing methods typically rely on creating chaotic advection or turbulence, where the fluid motion is irregular and causes pressure and velocity to vary randomly in both space and time. Chaotic advection can be achieved by stirring the flow and is particularly effective at low Reynolds numbers due to the splitting, stretching, folding, and breaking up of the species streams (Lee et al.21). However, advection primarily occurs in a direction parallel to the main flow direction, and is therefore not very useful for enhancing transverse mixing processes. To overcome this problem, various systems are presented for improving the chaotic advection within microchannel including passive (using special microchannel geometries) or active systems (by applying an external driving force such as electrical or pressure) (Bayareh et al.3). The design of micromixers based on chaotic advection is similar to that of macroscopic mixers. The main concept is modifying the channel shape to split, stretch, fold, and break the flow. Although, there is no formal classification, existing microfluidic mixing devices can be broadly classified as high (Re > 100), intermediate (10 < Re < 100), and low (Re < 10) ranges (Lee et al.20).

An efficient approach for improving the inherent characteristics of the microchannels is to incorporate internal parts within them. Internal parts known as barriers can be used as passive mixers in the microchannel to enhance mixing efficiency and reduce the diffusion length of the mixing process (Goovaerts et al.10). Passive micromixers do not require any direct energy input aside from the pressure head that drives fluid flow at a constant speed. The principle behind using barriers as passive mixers is to create the chaotic advection, which is achieved by embedding obstacles or changing the geometry of the channel. In a simple design, a series of obstacles can be introduced along the channel to create vortices and flow instability, which enhances the efficient mixing. For instance, Kurnia et al. suggested that the incorporation of a twisted tape into a microchannel can enhance single-phase mixing, but there hasn’t been any endeavor to address its effectiveness in a two-liquid phase system (Kurnia and Sasmito18).

Optimal mixing performance can be achieved by optimizing the size, shape, and spacing of the obstacles. In the presence of internal obstacles within the microchannels, the flow maintains a laminar state, where the mixing process predominantly depends on the effects of chaotic advection. These effects help to increase the interfacial surface between different flows of species. Another approach is to use a meandering microchannel design such as the herringbone mixer (Hama et al.11), the split-and-recombine mixer (Liu et al.22), and the serpentine mixer (Cao and Chen5), where the channel geometry is intentionally distorted to create the fluid deformation and mixing. This design can induce a high degree of chaotic advection, leading to enhanced mixing even at low Reynolds numbers. It is worth mentioning that all designs are based on different principles, but they all aim to achieve efficient mixing in a compact and easy-to-fabricate design.

Buchegger et al. proposed a horizontal multi-lamination micromixer with wedge-shaped inlet channels that allowed for highly uniform fluid mixing in the low millisecond range (Buchegger et al.4). Similarly, Tofteberg et al. created a passive micromixer that involved a controlled 90-degree rotation of the flow cross-section, followed by a split into several channels. The flow in each channel was rotated through another 90 degrees before being recombined, effectively doubling the interfacial contact area between the two fluids. This splitting and recombination process could be repeated until the desired degree of mixing was achieved (Tofteberg et al.30). Roudgar et al. performed a numerical investigation on the split T-micromixers and found that they achieved better mixing efficiency compared to the conventional T-micromixers, particularly at higher Reynolds numbers (e.g., Re = 100) due to the formation of vortex pairs (Roudgar et al.28). They also discovered that for equal flow rates in the inlet channels, a vertical split induced better mixing of the species compared to a horizontal split, while for strongly unequal flow rates, the reverse was true. In another study, Raza et al. conducted a comparative investigation into various 2D and 3D micromixers. The objective was to determine the effectiveness of different micromixers in achieving adequate mixing under specific conditions. Consequently, they discovered that effective mixing can be achieved even at low Reynolds numbers by using proper configuration (Raza et al.27).

As it is stated, one of the applicable ways to achieve the chaotic advection is to insert obstacles into the mixing channel. Wong et al. investigated the low-Reynolds number mixing behavior in a mixing channel and two static mixing elements. They found that the relatively large size of the outlet channel prevented a complete mixing of the species in the absence of static elements, but with the introduction of two static elements into the channel, a significant improvement in the mixing performance was achieved. They also realized that after 1 millisecond, an almost complete mixing of the two species is obtained (Wong et al.34).

Park et al. designed a micromixer that induces the rotational flow using obstruction-pairs composed of two hexahedron blocks arranged asymmetrically along the base of the mixing channel (Park et al.25). Tseng et al. investigated the mixing performance of a passive micromixer that contained embedded diamond-shaped obstacles and boundary protrusions. Their simulation results indicated that the boundary protrusion regions generated intense vortices and secondary flows in the spanwise planes, resulting in a significant improvement in the mixing efficiency along the microchannel (Tseng et al.31).

Apart from the limited studies focusing on using passive mixers in the microchannel, based on our knowledge, most of them pertain to single-phase systems. For instance, Kurnia et al. (Kurnia and Sasmito18) proposed that adding a twisted tape to a microchannel can improve mixing in single-phase scenarios, but there is no research on its effectiveness in a two-phase system. To enhance mixing efficiency in the two-phase liquid-liquid flow it is important to increase the interfacial area between phases. Thus, this study introduces a novel internal barrier (i.e., helical wire) in the microchannel aimed at enhancing the interfacial area of two phases. The following sections provide a detailed examination of the novel microfluidic mixer, tested in a chemical system with high interfacial tension. Preliminary tests in a circular microchannel revealed that the helical wire significantly disrupted the balance of forces on slugs or droplets, transforming slugs into droplets or deforming droplets, thereby expected to improve mixing and mass transfer. The study focuses on understanding how the helical wire can enhance the interfacial area between phases in terms of size reduction of the dispersed phase after passing through the channel at various flow rates. Overall, the application of barriers as passive mixers in microchannels can substantially enhance mixing efficiency, which is critical for various microfluidic applications including chemical synthesis, biological analysis, and lab-on-a-chip devices.

Cooking oil (frying oil: including 78%, unsaturated fatty acid and 22% saturated acid) and distilled water were provided for creation of a typical immiscible two-phase system. Acetone (> 99%) was also purchased from Dr Mojallali Chemical Complex Company due to the elution of all wetted components of setup. All of the chemicals were used without further purification.

Figure 1 displays the microchannel contactors for the oil/water as an immiscible system. This setup consisted of several components, including two syringe pumps, glass syringes, a T-junction, a microchannel, a plastic tube, a collector, a microscopic camera, helical wire (embedded barrier), and backlight lamps. The SP110 model syringe pump, produced by Soraco in Iran, was utilized. A capillary glass tube with an inside diameter of 0.8 mm and a length of 200 mm was used as the microchannel. Also, a helical wire with a diameter of 0.25 mm and a step length of 2.15 mm is embedded inside the microchannel as a passive mixer (Fig. 2). The material chosen for the helical wire is stainless steel 316 L due to its excellent formability. The conducted experiments were divided into two main sections: one in the presence of a passive mixer and another without it. It should be mentioned that both series of experiments have been carried out under the same conditions. There are important factors that should be considered in the experiments, such as ensuring the sealing of all connection joints, fixing the embedded barrier, and choosing the suitable wire material to prevent deformation.

Schematic of microchannel setup integrated with helical wire.

Schematic of microchannel equipped with helical wire as passive mixer.

In each experimental run, both fluids of the system (i.e., oil and water) enter the proposed microchannel at equal flow rates at room conditions (atmospheric pressure and 25 oC temperature). A digital handheld microscope with a 5.0 MP resolution sensor and 8 fps frame rate manufactured by Celestron in the United States was used to capture the images of the flow patterns within the microchannel. The camera was positioned above the channel, while the light source was placed under the contactor with a 45 mm distance to achieve a clear view of the flow. The flow rate of both fluids in each system was regulated between 0.1 and 0.8 mL/min. After passing through the microchannel, the output was collected in a container. It is important to note that the microchannel was washed with acetone and distilled water after each experiment. Furthermore, to assess the physical characteristics of fluids, such as viscosity and surface/interfacial tension, the Visco Star and KSV sigma 701 (accuracy: ± 1% of the full scale) devices were employed, respectively.

Nowadays, image processing is a beneficial tool that involves techniques such as filtering, segmentation, feature extraction, and pattern recognition to analyze and modify the images. Image processing is widely used in different fields such as medicine, remote sensing, robotics, multimedia, etc. It has various applications, including image enhancement, restoration, compression, object detection, recognition, and tracking (He et al.13). In the present study, the image processing techniques were used to analyze the data to identify the features of each flow pattern. Therefore, it is extremely important to provide precise and understandable images for this purpose. To meet this requirement, a video was initially taken in each segment of the microchannel. Then, after converting the video to consecutive frames, the resulting images underwent analysis. It is highly necessary to capture images when the system is steady. Slug length and average diameter are some of the important parameters, which are measured after image processing. In essence, measuring can be conducted by scaling and aligning measurable parameters. For instance, the internal diameter of the microchannel, which can be measured with a caliper, acts as a reference size for calculating other parameters, such as slug length. In other words, by finding the corresponding pixels for each measurable parameter, others are determined by scaling. At first, the captured image is converted to grayscale. Then, the maximum length and diameter of slug/droplet are determined using edge detection mechanism. At the next stage, the average value of the size in axial and lateral directions are reported as the average diameter of slug/droplet. The entire analysis is conducted using the OpenCV 4.10.0 software.

In addition, further observations and analyses were performed in order to identify the traits of the fluid being studied and track various flow patterns to explore how the physical properties of fluids impact them. For instance, contact angle, viscosity, and surface/interfacial tension are significant parameters that are effective in the hydrodynamic evaluation of the proposed systems. The applicable properties of all two fluids involved in the experiment are included in Table 1.

The formation of oil-in-water (O/W) or water-in-oil (W/O) emulsions in microchannels can be influenced by various factors, including interfacial tension, flow conditions, channel geometry, and priority of fluid entry into the microchannel. The interfacial tension between the oil and water phases plays a significant role in the emulsion formation. In microchannels, where the droplet size is typically small, a lower interfacial tension between oil and water promotes the formation of O/W emulsions. This is because the lower interfacial tension allows for easier breakup of the dispersed phase into smaller droplets. The flow conditions within the microchannels can also influence the emulsion formation. Factors such as flow rates, shear rates, and mixing conditions can impact the breakup and coalescence of the dispersed phase. For example, higher shear rates may favor the formation of smaller droplets, while lower shear rates may lead to the formation of larger droplets or phase separation.

The geometry of the microchannel is another effective factor, where narrower channels can induce higher shear rates, promoting droplet breakup and enhancing the formation of smaller droplets. Conversely, wider channels with lower shear rates may favor larger droplet formation or phase separation. In the case of oil and water, the oil molecules do not dissolve in water due to differences in the polarity. Oil is generally nonpolar or has low polarity, while water is highly polar. The cohesive forces between the water molecules are stronger compared to the cohesive forces between oil molecules, so water tends to form droplets and repel the oil.

When oil and water are mixed, the resulting viscosity depends on the proportion of oil and water in the mixture. In general, if a small amount of oil is added to water, the viscosity of the mixture will remain relatively close to that of water. However, as more oil is added, the viscosity of the mixture tends to increase due to the higher viscosity of oil.

Generally, exploring various physical properties can be beneficial to understand the passive mixer’s potential to create diverse flow patterns that enhance the interfacial area between two phases. An overview of key factors involving this study is illustrated in Fig. 3.

The comprehensive overview of key factors influencing the efficacy of the novel passive mixer.

When two liquid phases that cannot mix together come into contact within a narrow channel, various flow patterns may be created based on factors like geometry, operating conditions, and the physical properties of the fluids. The formation of these flow patterns is determined by the interactions between different forces, such as viscous shear, inertial force, and interfacial tension. Since the channel is small in size, the influence of gravity can be disregarded because the Bond number is extremely small (Bo < 1) (Yao et al.36). The Bond number quantifies the ratio of gravitational force to surface tension force in the liquid system. By assuming a characteristic length (Lc) of 0.8 mm (microchannel diameter) and using the system’s physical properties (Δρ = 67 kg/m³, γ = 1.38 mN/m), the Bond number is calculated as follows: Bo = \(\:\frac{{\Delta\:}{\uprho\:}.\text{g}.{{L}_{c}}^{2}.}{{\upgamma\:}}\)= 0.3. This value is below 1, indicating that surface tension force prevails over gravitational force in this system. To improve the detection and prediction of the dominant force in a specific flow pattern, several dimensionless numbers are employed. These numbers include the Reynolds number, Capillary number, and Weber number, which are useful in identifying the flow patterns. While various researchers have created numerous flow maps, Zhang et al. proposed a comprehensive approach to predicting the flow patterns. They introduced combined dimensionless groups, namely \(\:{Ca}_{C}{Re}_{C}^{0.5}\) and \(\:{Ca}_{d}^{0.7}{Re}_{d}^{0.5}\) for the continuous and dispersed phases, respectively (Zhang et al.37). The flow map contains four flow regime categories. The first category is characterized by the dominance of the interfacial tension and includes slug flow and sub-regimes. The second and third categories are associated with the dominance of interfacial or viscous forces, leading to droplet flow at high\(\:\:{Ca}_{C}{Re}_{C}^{0.5}\) and annular regime at high \(\:{Ca}_{d}^{0.7}{Re}_{d}^{0.5}\). Lastly, at high values of \(\:{Ca}_{C}{Re}_{C}^{0.5}\) and \(\:{Ca}_{d}^{0.7}{Re}_{d}^{0.5}\), the fourth area exhibits a serpentine or chaotic flow regime, characterized by well mixing as a prominent feature. It is worth mentioning that these flow patterns are not completely separate from each other, and various forces can work together at the same time, resulting in combined flow behaviors. The particular flow pattern witnessed in a microchannel is influenced by the relative intensities and interplay of the involved forces, as well as the shape and operating conditions of the channel.

When fluid flows through a microchannel, the interactions between the fluid molecules and the channel walls become more pronounced due to the smaller dimensions. This result in an increase in the viscous forces compared to the inertial forces, making viscosity a dominant factor in determining the flow behavior. In microchannel, the flow is often characterized by a phenomenon known as “viscous-dominated flow.” This means that the viscosity of the fluid rather than other factors like inertia primarily governs the flow behavior. The high surface-to-volume ratio in the microchannel amplifies the effects of viscous forces, causing the fluid to flow more slowly and in a more controlled manner. The presence of fluid with higher viscosity in a microchannel can lead to several effects. The most important impact is causing a higher pressure drop along the channel length, as viscous forces resist the flow. This pressure drop is proportional to the viscosity of the fluid and inversely proportional to the channel dimensions.

The surface tension also plays a significant role in the microchannel flow, particularly at the liquid-gas interface. In the microchannels, where the dimensions are small, leading to a greater influence of the surface tension compared to flows in the larger-scale contactors. Surface tension is the cohesive force that exists at the interface between a liquid and air. It is caused by the attractive forces between the molecules within the liquid. In the microchannels, the surface tension force becomes more prominent due to the relatively larger surface area.

Surface tension influences the wetting characteristics of the liquid on the channel walls. Depending on the fluid and the wall material, the liquid may either wet or non-wet the walls. The wetting behavior affects the contact angle and the flow patterns within the microchannel.

The contact angle of a fluid on the channel walls can have an effective influence on the observed flow patterns in microchannels. The contact angle represents the angle at which the fluid-air interface meets the solid surface of the microchannel. It is determined by the interplay between intermolecular forces, surface tension, and the nature of the fluid and channel wall materials. The contact angle affects the wetting behavior of the fluid on the channel walls, which, in turn, influences the flow patterns in the following ways:

Flow Resistance: The contact angle determines the degree of wetting or non-wetting behavior of the fluid on the channel walls. In the case of a fully wetting fluid (contact angle close to zero), the fluid spreads uniformly along the walls, resulting in a lower flow resistance. This promotes smoother and more predictable flow patterns. Conversely, for non-wetting fluids (contact angle close to 180 degrees), the fluid tends to bead up and create a higher flow resistance, leading to flow instabilities, pressure variations, and potential flow blockages.

Meniscus Formation: The contact angle affects the shape and stability of the fluid meniscus at the leading and trailing edges of the fluid flow. A small contact angle leads to a more curved meniscus, while a larger contact angle results in a flatter meniscus. These menisci can induce capillary-driven flow or affect the pressure distribution, causing flow disturbances, recirculation zones, or even flow reversal.

Surface Tension Effects: The contact angle influences the surface tension forces acting on the fluid. In the presence of a varying contact angle, surface tension gradients can generate Marangoni flow, where the fluid moves from regions of low surface tension to high surface tension. These surface tension-driven flows can significantly impact the flow patterns, creating localized velocity variations, secondary flows, or flow instabilities.

Contact Line Dynamics: The contact line is the interface between the fluid and the solid surface where the contact angle is formed. The motion and dynamics of the contact line depend on the balance between viscous forces, capillary forces, and surface tension forces. The contact line dynamics can lead to complex flow patterns, such as contact line instability or spreading behaviors, which directly affect the overall flow behavior in the microchannel.

It is important to consider the contact angle of the fluid when designing the microchannels and microfluidic systems. Understanding and controlling the wetting behavior and contact angle, results in optimization of the flow patterns, minimization of the flow disruptions, enhancement of the fluid transport, and improvement in the overall performance of microfluidic devices.

According to the importance of contact angle in determining the flow pattern, the wettability of applicable fluids in this research on the glass plate is evaluated, which can be seen in the Fig. 4, cooking oil and water exhibit partial wetness on glass, meaning they have a contact angle greater than zero degrees. However, it seems that the oil has greater wettability with glass against having a lower contact angle.

Contact angle of (A) water, (B) oil on the glass plate.

After introduction of the water and oil in the microchannel equipped with helical wire by using two syringe pumps in the same flow rates, a flow pattern like slug flow is generated in the system. As can be seen in Fig. 5, periodic slug-like trends are observed in the microchannel in which a slug rotates around the helical wire while moving along the channel. For instance, the slug illustrated in Fig. 5(A) forms again during a time span of 625 milliseconds, as evidenced by Fig. 5(E). The deformation of a slug in a microchannel is caused by the balancing of various forces, including pressure, inertia, interfacial tension, and adhesion force between dispersed phase and helical wire, resulting in a continuous alteration of its shape. It also appears that the twisting motion of a slug around a helical wire plays an important role in causing the slug to break up into droplets. Transforming the slug piece into a droplet by expansion and contraction results in an amplified interfacial area between the two phases, thereby greatly enhancing the rate of mass transfer. At first glance, it is assumed that rotating slugs can enhance the slug’s internal rotational movements, leading to an improvement in the mass transfer. In other words, boosting both the internal rotational movement and interfacial area are crucial factors that enhance the mixing and mass transfer rate.

Different shapes of one slug along the microchannel length at the same flow rate of oil/water (0.2 mL/min) at the middle of the microchannel.

The presence of a significant number of small droplets accompanying the slug is a characteristic that strongly distinguishes the physical properties of this system. The establishment of these droplets is extremely dependent on the physical properties of the two immiscible phases. This flow regime that is characterized by the slug dispersion has occurred when the fluid pairs have minimal interfacial tension (N. Kashid et al.17 ; Zhang et al.37). The existence of a bumpy interface within the T-mixer may be the underlying cause of this occurrence. It is important to mention that in each experimental run, the microchannel was filled with oil at first, which caused the dispersing of water in oil.

The influence of the passive mixer (i.e., helical wire) appears to be more pronounced in the process of breaking the slug into droplets in this immiscible system, possibly due to the significant disparity in the physical properties between the continuous and dispersed phases.

As previously stated, the adhesion force is an extra force created on the slug piece by placing a barrier in the microchannel. In order to elucidate the fragmentation mechanism within a helical wire-equipped microchannel, an investigation into the forces acting upon the dispersed phase slugs was conducted. At low flow rates, consecutive snapshots were taken to observe the first separation of the slug in the microchannel by presenting helical wire. At approximately 0.04 mL/min, the formation of the first droplet was monitored at nearly the middle of the microchannel (Fig. 6). The critical Weber number for the dispersed phase where the first detachment of droplets has occurred is 3.8 × 10−3.

The initial slug detachment in the nearly middle of the microchannel with the same flow rate of oil/water (0.04 mL/min).

When analyzing the separation point on the wire in depth, four specific forces act upon the slug, resulting in its detachment. These forces, which include inertia (\(\:{F}_{i}\)), pressure (\(\:{F}_{p})\), interfacial tension (\(\:{F}_{\sigma\:}\)), and shear forces (\(\:{F}_{\tau\:}\)), are involved at the separation point (Eq. 2). Understanding the interplay between these forces is essential for comprehending the slug’s behavior and the mechanism behind its detachment.

In commence, because of the laminar regime flow, the Hagen-Poiseuille equation (\(\:\varDelta\:p=\frac{8\mu\:LQ}{\pi\:{R}^{4}}\)) is employed to predict the pressure drop at the separation point for a single slug. By multiplying this pressure drop by the cross-sectional area (\(\:{A}_{c}\)=5.03 × 10−7 m2), the pressure force \(\:{F}_{p}\) (as attachment force) is determined (Eq. 3). In contrast to this force, the interfacial tension force \(\:{F}_{\sigma\:}\) exerted on the effective length of the helical wire is determined using the interfacial tension value (\(\:\gamma\:\)=1.38 mN/m) (Eq. 4). After these simplifications and computations, it was found that both \(\:{F}_{p}\) and \(\:{F}_{\sigma\:}\) are of similar magnitude and nearly equal in value (\(\:{F}_{p}\)=2.73 × 10−7 N and \(\:{F}_{\sigma\:}\)=2.7 × 10−7 N). Hereafter, the confrontation of two other forces is investigated. Considering the value of \(\:\rho\:\)=1000 kg/m3, \(\:V\)=0.014 m/s, and microchannel section area of \(\:{A}_{c}\)=5.03 × 10−7 m2, the inertia force is determined by using Eq. 2 with the value of 0.87 nN. The calculation of shear force in this novel geometry is complicated. Nevertheless, by making certain assumptions, it can be ascertained. Initially, by utilizing cylindrical coordinates, it is possible to assume that the velocity variations in the r and θ directions are negligible except the one that is related to the variation of rotational velocity (\(\:{V}_{\theta\:})\) along the microchannel (z-direction). In laminar flow and at very low velocities, and as well as high length-to-diameter ratio (\(\:\frac{L}{D}=\frac{200}{0.8}=250\)), this assumption closely approximates reality. Subsequently, taking into account these simplifications, it is demonstrated that the only effective shear force applied on slug piece in the contact location with helical wire is \(\:{\tau\:}_{\theta\:z}\). Equation 5, shows that the shear force at the separation point is divided into two terms as follows:

Where \(\:\mu\:\) represents the viscosity of continuous phase, while \(\:{V}_{\theta\:}\) and \(\:{V}_{z}\) denote the rotational and axial velocities, respectively

After performing these calculations with the assistance of image processing, it has been found that the magnitude of the shear force along the microchannel (\(\:\mu\:\frac{1}{r}\frac{\partial\:{V}_{z}}{\partial\:\theta\:}\)) is significantly greater than the force applied by rotational movement (\(\:\mu\:\frac{\partial\:{V}_{\theta\:}}{\partial\:z}\)). In other words, the term related to the variation of velocity in the z direction has much more effect in the formation of droplets by breaking the slug with helical wire. It appears that by increasing the flow rate, a large fragmentation of the dispersed phase would be established, which required a comprehensive investigation on flow rates. The calculated values for the shear force \(\:{F}_{\tau\:}\) and inertial force \(\:{F}_{i}\) are 1.02 nN and 0.87 nN, respectively, indicating the overcoming of detachment forces. To validate this analytical method, a lower flow rate of 0.025 mL/min was used where no detachment was observed. Upon this estimation, it was noted that the shear force was slightly less than the inertial force (\(\:{F}_{\tau\:}\)=0.37 nN.\(\:\:{F}_{i}\)=0.42 nN), showcasing the effectiveness of the helical wire in fragmenting slug pieces under truly laminar flow conditions.

In this part of the study, the hydraulic characteristic of the microchannel equipped with helical wire was explored to realize the impact of altering the flow rate. Initially, the immiscible system was examined by taking photographs in a microchannel without a passive mixer. Figure 7 illustrates how the flow regimes evolve in this distinct system with varying physical properties. Evidently, the slug flow regime was observed as the dominant flow characteristic within the flow rate range of 0.1–0.8 mL/min. Additionally, the consecutive images indicate that increasing the flow rate results in a reduction in the size of the slug, which means that the flow rate has a crucial impact on the flow regime. This reduction continues until the slug size reaches approximately 600 μm at a flow rate of 0.8 mL/min. This size reduction is also inferred from the previous section regarding analytical estimation.

Different flow patterns by changing the flow rates in the range of 0.1–0.8 mL/min for oil/water in the absence of passive mixer (helical wire) at the middle of the microchannel.

To obtain quantitative observations, image processing is employed on photographs to analyze the impact of the helical wire on the size of the slug. Evaluating the effectiveness of a passive mixer is essential since it can lead to improved mass transfer by enhancing the interfacial area between two phases and facilitating internal rotational movement of slugs. One approach is to estimate the periodic shape deforming of the slug along the length of the microchannel. The elongation and shrinkage of the rotating slug caused by the helical wire can be distinctly observed in Fig. 8 over a time period. This deformation on the interfacial area would be very useful in the enhancement of the mass transfer systems, such as the extraction process. One of the major factors that enhances the rate of mass transfer is the reproducing of the interface area between two phases. It is probable that the elongation and shrinkage of the slug while passing through the microchannel contribute to this enhancement. However, further analysis should be carried out to arrive at this conclusion. To achieve this objective, a section of a microchannel (in the middle of the microchannel) was chosen to capture photographs at various flow rates between 0.1 and 0.8 mL/min (Fig. 9). It should be noted that the presence of a minimal interfacial tension between the two phases can significantly contribute to the heightened fragmentation observed as the slug traverses the microchannel.

Changing of slug length along the microchannel at the same flow rate of oil/water (0.2 mL/min) at the middle of microchannel.

Adjusting the flow rates between 0.1–0.8 mL/min for the oil/water system results in various flow patterns.

By altering the flow, different flow patterns illustrate how the slug’s size reduces with an increase in the flow rate. In order to understand the establishment of these flow patterns, it is necessary to examine the effective forces within this system specifically for a single slug. Viscous, interfacial tension, and inertia forces are three common forces observed in different systems applicable to the microchannel. However, there is an additional force associated with the adhesion of the dispersed phase and helical wire in this context (Fig. 10).

Balance of forces on the slug piece in microchannel equipped with helical wire.

It appears that as this additional force resulting from the passive mixer increases, the impact of increasing the flow rate becomes more significant, leading to greater fragmentation of the slug along the microchannel. This fragmentation continues until a stable droplet size is achieved within the microchannel, indicating that no further breakage will occur in the microchannel. It is anticipated that as the slug size is reduced to a droplet, the interfacial area will increase. To demonstrate this concept, the average diameter of the slug or droplet is analyzed for each flow pattern, considering different values of the flow rate (Fig. 11). As the flow rate is increased from 0.3 to 0.4 mL/min, there is a steep decrease in the average size of the slug/droplet. This transition zone can represent the maximum interfacial area that is achieved in a microchannel equipped with a helical wire. In other terms, there is no further increase in the interfacial surface area as the droplet size has reached a stable state. It is important to mention that in order to obtain an accurate assessment; the average size of the slug or droplet is obtained over a period of 1 s for each experimental run.

Average diameter of slug/droplet against different flow rates for oil/water system.

Generally, the utilization of helical wire within the microchannel initiates the rotation of slugs, causing further size reduction, which is consistent with the observations in Figs. 7 and 9. For instance, at the flowrate of 0.5 mL/min, a substantial quantity of small droplets becomes apparent when the helical wire is present, in contrast to when it is absent. At a flow rate of 0.8 mL/min, the average size of the slug or droplet in the microchannel is 390 μm with the helical mixer and 600 μm without it, demonstrating the effect of incorporating a passive mixer.

Changing the flow regimes from slug-dispersed to chaotic flow has occurred (Fig. 9). The breaking of slugs in the oil/water system due to the presence of helical wire can be described as the transformation of slugs into smaller droplets, resembling a splintering process (Figs. 7 and 9). In simpler terms, the fragmentation of the slug occurs gradually as the flow increases, reaching a point where the dispersed slug has no longer been detectable. Additionally, when considering the impact of increasing flow rate, it can be inferred that the passive mixer is more effective in enhancing more interfacial area.

As previously mentioned, there are inherent advantages in utilizing a passive mixer within the microchannel. To witness this advantage, one can observe a reduction in the microchannel length when employing a passive mixer. This, in turn, leads to the generation of an effective surface area within a shorter distance. The breakage of slug pieces along the microchannel for the oil/water system is presented in Fig. 12.

Reducing the size of slug along the microchannel for oil/water system with the equal flowrate of 0.6 mL/min.

When comparing images captured over the different distances, it becomes apparent that the passive mixer demonstrates great effectiveness along the microchannel. This implies that the flow patterns and the extent of the passive mixer’s effect are significantly influenced by the physical properties such as interfacial tension, viscosity, and so on. For example, when considering a length of 12 cm, a significantly higher number of droplets can be observed in the oil/water system. This size reduction occurred in a way that, at a length of 18 cm, it becomes evident that nearly all droplets in the oil/water system have attained a stable size. The series of consecutive photos taken at different lengths for the oil/water system indicates that after the water slugs break within the microchannel by helical wire, the interfacial area of water and oil increases at the interface until the droplet size reaches a visually constant level, establishing a stable regime that persists until the end. This phenomenon may be attributed to the inherent capability of the passive mixer within the microchannel, which enhances the surface area and facilitates efficient mixing even in laminar flow conditions. In other words, increasing the slug fragmentation leads to more efficient contact of water and oil, resulting in complete changes to the flow pattern. The sequence of images used to examine the flow patterns along the microchannel provides significant insights into the crucial role of physical properties in establishing these flow patterns. In addition, the high fragmentation of water in oil can be seen clearly in the image captured at a distance of 18 cm from the entrance.

A flow map in a microchannel provides insights into how liquids move, mix, and interact within this miniature system. It may depict information such as fluid velocities, pressure gradients, and the distribution of phases. Understanding the flow dynamics in the microchannels is important where precise control and manipulation of small fluid volumes are essential. Flow maps help to have a general view of flow regime distribution and analyze the intricate flow patterns within the microchannels, aiding in the design and optimization of the microfluidic systems. The generated flow map for the oil/water system delineates that three distinct regions can be identified at a consistent flow rate of two fluids within the range of 0.1–0.8 mL/min, flow contains long slug, slug-droplet flow, and droplet flow are three regimes, which are certainly created in the flow map of Fig. 13. When the oil flow rate is set at 0.1 mL/min, there was no observed dispersion in the flow map, and only continuous, extended slug moved through the microchannel (flow contains long slug regime). Even with a higher water flow rate, no major breakage was observed; instead, the elongated slug merely became thinner. In the equal flowrate of 0.3 mL/min, there is a transition area called the slug-droplet flow regime that happens between two other regimes. In this region, the slugs are accompanied by several small droplets, and as the water flow rate increases, the slugs tend to grow slightly in size while the oil flow rate remains constant. As the oil flow rate continues to increase, the slugs completely disappear, leaving only droplets visible in the microchannel (droplet flow regime). For example, adjusting the oil flow rate from 0.5 to 0.6 mL/min leads to a complete restructuring of the flow regime so that the effectiveness of the passive mixer is more apparent. This implies that the shear force applied by the helical wire peaks with higher flow rates. To provide a thorough insight into the distribution of the flow regime within the 0.1–0.8 mL/min flowrate range for both phases, Fig. 14 depicts the two-phase flow map in terms of the flow rates. In general, the droplet regime is a major flow regime that covers nearly most of the flow map, which can be ascribed to the presence of helical wire.

A flow map created for an oil/water system equipped with helical wire.

A symbolic flow map for an oil/water system equipped with helical wire.

The application and advantages of the microchannel span across various industries. Nevertheless, there exists a considerable amount of ambiguity regarding the diverse flow patterns occurring within the microchannel, which can be attributed to factors like physical properties, operating conditions, geometry, and other similar variables. To achieve the desired behavior in the microchannel, researchers and engineers strive to optimize the channel geometry, fluid properties, and operational parameters. They carefully design and control these factors to balance the various forces involved, ensuring reliable and efficient fluid flow, mixing, separation, or other desired functionalities in the microfluidic systems. By understanding and manipulating the dominant forces in the microchannel, scientists and engineers can harness the unique characteristics of the microchannel to develop applications in various fields, such as lab-on-a-chip devices, biomedical diagnostics, chemical synthesis, environmental analysis, and so on.

In recent research, regardless of the operating conditions, by introducing a novel geometry, different flow patterns were observed in the existing research, which is attributed to the physical properties and certainly the new shape of the microchannel. In other words, the alterations in the flow pattern were primarily attributed to the interfacial tension, viscosity, and contact angle, three critical factors. Through the examination of a distinct system characterized by physical properties, it was determined that the implementation of a barrier in the microchannel makes additional force (i.e., the adhesion between dispersed phase and wire) enhance the interfacial area in the two-phase system, particularly in the immiscible case. This observation implies that the implementation of a helical wire as a passive mixer is efficient in systems where there is a significant disparity in the physical properties between the dispersed and continuous phases, specifically in terms of the interfacial tension and viscosity. This concept greatly enhances the potential for broadening the application of this microchannel in different processes, such as solvent extraction, where it is necessary to intensify the mass transfer. Indeed, there are two existing ways to intensify the mixing in the microchannel by modifying the geometry. The first method is related to using a unique body to provide folding, splitting, and stretching the flow. The second one pertains to utilizing a barrier within the microchannel, which could potentially offer more cost-effective advantages when considering scale up issues. After choosing a microchannel configuration, it is crucial to consider both the ease of fabrication and cost-effectiveness as important factors. These aspects should be taken into account alongside the development of the microchannel device.

Microfluidic systems are emerging technology with the capacity to intensify processes, particularly those related to mass transfer. Numerous microchannel designs in terms of material and geometry have been proposed and developed to develop this device. Employing both active and passive mixers within the microchannel is a strategy among various designs to enhance mixing rates and mass transfer. When comparing active and passive mixers, the preference often lies with passive ones due to their minimal energy consumption. The implementation of a helical wire as a passive mixer in the microchannel proved highly effective, resulting in enhanced interfacial area and consequently an increase in mass transfer. A comparative study between microchannels with and without the helical wire by oil/water system was conducted, revealing the efficacy of the innovative passive mixer in fractionating the dispersed phase and extending the interface area of two phases. Analyzing the equilibrium of forces reveals that as the velocity, represented by the flow rate, increases, the adhesion force between the dispersed phase and the wire intensifies, leading to more significant fragmentation of slug pieces. It seems that the presence of the helical wire induced internal rotational motion within the slug, especially in flow contains long slug and slug-droplet flow regimes led to the increased breakage within the slug at higher velocities, nearly transitioning the flow regime to the droplet formation. The proposed novel passive mixer can be applied to diverse systems, but it is important to optimize its geometrical dimensions based on the specific physical properties of each system.

It should be justified that “All data generated or analysed during this study are included in this published article”.

Cross-sectional area

Bond number

Microchannel diameter

Capillary number

Pressure force

Inertia force

Shear force

Interfacial force

Microchannel length

Characteristic length

Effective length

Flowrate

Microchannel radius

Reynolds number

Velocity

Velocity in θ direction

Velocity in θ direction

Weber number

Surface tension

Pressure drop

Viscosity

Density

Density difference between phases

Shear in Z direction

Continuous phase

Dispersed phase

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School of Chemical Engineering, Iran University of Science and Technology (IUST), P.O. Box 16765-163, Tehran, Iran

Sobhan Farahani, Salman Movahedirad & Mohammad Amin Sobati

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Sobhan Farahani: Methodology, Formal analysis, Software, Validation, Resources, Investigation, Writing – original draft. Salman Movahedirad: Conceptualization, Methodology, Writing – review & editing, Supervision, Project administration. Mohammad Amin Sobati: Conceptualization, Methodology, Writing – review & editing, Supervision, Project administration.

Correspondence to Salman Movahedirad.

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Farahani, S., Movahedirad, S. & Sobati, M.A. Characterization of the oil water two phase flow in a novel microchannel contactor equipped with helical wire static mixer. Sci Rep 14, 23369 (2024). https://doi.org/10.1038/s41598-024-75356-7

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Received: 08 June 2024

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Published: 08 October 2024

DOI: https://doi.org/10.1038/s41598-024-75356-7

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