Branch-convergence structure based on double-layer chip: a universal method for enhancing microfluidic mixing†

Saijie Wang , Zhihan Zhang , Quanchen Xu , Yao Chen , Qian Wang , Boxi Lu , Xueqing Luo , Dou Wang * and Xingyu Jiang *
Guangdong Provincial Key Laboratory of Advanced Biomaterials, Department of Biomedical Engineering, Southern University of Science and Technology, No. 1088 Xueyuan Rd, Nanshan District, Shenzhen, Guangdong 518055, China. E-mail: wangd9@sustech.edu.cn; jiang@sustech.edu.cn

First published on 22nd August 2024

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Tribute to George Whitesides George was the greatest mentor a professional researcher could have hoped for, and his approaches to science have had a profound impact on how science is done today.

Introduction

Microfluidics-based mixing methods play a critical role in many fields, such as drug development,¹ clinical diagnosis,² nanomaterial synthesis³ and modification,⁴ and so forth. Compared with traditional devices, micromixers have the advantages of simple operation, strong controllability, and high mixing efficiency.⁵ However, due to the laminar flow characteristics of microfluidics, liquid mixing in microfluidic channels is inherently difficult, especially for rapid mixing, which has always been a challenging problem. Over the past two decades, researchers have developed numerous microfluidic chip-based mixing methods.⁶ According to the different principles of force application during the mixing process, these methods can be categorized into two groups: active mixing and passive mixing.

Active mixing refers to the method of mixing using external force fields, and the mixing mode is primarily convection induced by external forces. The commonly used external force fields mainly include electric,^7,8 magnetic,^9,10 sound,^11,12 and thermal fields.^13,14 The mixing method based on electric fields mainly utilizes the electroosmotic flow caused by induced charges. Electroosmotic flow can induce vortices on conductive surfaces and facilitate fluid mixing.¹⁵ This type of device is generally named the induced-charge electroosmotic micromixer. It has the advantages of simple device fabrication and low voltage requirements. But the electric field may cause liquid electrolysis, and electric field mixing typically necessitates specific electrode layouts and microchannel structures to achieve the desired mixing effect, which limits its flexibility and scalability in certain applications. The magnetic field-based mixing method mainly utilizes an external magnetic field to drive the movement of magnets in the channel, producing a stirring effect. Stirring magnets can be divided into fixed and non-fixed types. Fixed stirring magnets mainly refer to magnetic cilia,^16,17 while non-fixed stirring magnets include magnetic fluid,^18,19 magnetic beads,¹⁰ and magnetic rods.²⁰ Magnetic mixing has the advantages of highly controllable mixing effects and high mixing efficiency. But, it requires the cooperation of an external magnetic field, and the requirements for the frequency and direction of the magnetic field increase the operational complexity of the system. The mixing method based on the sound field primarily utilizes the sound pressure generated by sound waves to disrupt laminar flow and promote mixing.²¹ In addition, ultrasonic waves can induce rapidly expanding microbubbles, further increasing fluid turbulence.^22,23 However, for viscous liquids, it is difficult for sound waves to penetrate and cause disturbance. Additionally, the requirement for specialized equipment, such as sonic generators, limits its application. Thermal field-based mixing methods mainly utilize temperature gradients to induce thermal convection to promote fluid mixing.²⁴ Thermal mixing is suitable for a variety of liquids, including those with higher viscosity. But the mixing speed is relatively slow and may lead to the degradation of heat-sensitive materials.

Compared to active mixing, passive mixing does not require any additional equipment aside from pumps.²⁵ The passive method achieves mixing by generating vortex and chaotic flow through the specially designed microchannel structure. Specifically, it can be divided into channel bending-based,^26,27 channel barrier-based,^28,29 and lamination-based designs.^30,31 Channel bending is the most representative design among passive mixing methods. Symmetrical or asymmetric serpentine or spiral and their deformation structures can make fluid repeatedly stretched, folded, and expanded to achieve fluid mixing.³² This method is simple, but the mixing efficiency is limited, so it is often combined with methods based on channel barriers. Channel obstacles can induce the generation of Karman vortices.³³ Karman vortices can greatly improve mixing efficiency, but obstacles can easily promote sedimentation and channel clogging. The principle of lamination-based mixing involves rotating the fluids that have met and merged by 90°, then cutting them into multiple separate streams, rotating these streams by 90° again, and finally merging them.³⁰ Each cycle segment of lamination mixing can double the number of interfaces between fluids. Repeating this process can continuously increase the interfacial area between different fluids, thereby achieving mixing. Intuitively, these different fluids are arranged in the channels in an interdigitated and layered manner. In a channel with a fixed width, the greater the number of interfaces, that is, the greater the number of pairs of interdigitated and layered fluid, the smaller the width of each fluid layer, which further means that the smaller the displacement required to achieve complete mixing of the fluids. Lamination-based mixing methods have higher mixing efficiencies compared to other passive methods. Although the initial stage of lamination mixing has relatively weak mixing capability, a lamination mixer can be quite compact and achieve significant mixing in a small space. In addition, lamination mixing involves liquid rotation and requires three-dimensional channels, so the fabrication of lamination mixing chips generally requires high-precision micro-milling equipment. The development and promotion of 3D printing technology have made high-precision micro-milling equipment no longer necessary. Importantly, since 3D printing is simpler to produce than traditional photolithography, many traditional microfluidic mixing devices have also begun to be produced using 3D printing, the double-layer chip structure we proposed can also be realized by 3D printing.³⁰ We summarize the relatively common and advanced mixing techniques as shown in the following Table 1.

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In this work, we propose increasing the number of interfaces between fluids as a general strategy for enhancing mixing, which can be combined with other microfluidic mixing methods. We branch the fluid directly based on planar channels instead of employing the lamination mixing method to avoid mixing inefficiency in the initial stage of lamination. The planar channels only need to be fabricated using soft photolithography technology, eliminating the need for high-precision micro-milling equipment. Additionally, the double-layer chip can reduce the number of inlets, requiring only one inlet for each liquid. We demonstrated that the branch-convergence structure can significantly enhance microfluidic mixing. As a proof of concept, we synthesized lactic-co-glycolic acid (PLGA) nanoparticles using a branch-convergence structure chip, demonstrating that the synthesized PLGA nanoparticles have higher particle size uniformity compared to traditional chips.

Theoretical analysis

Mixing means that the components of different liquids are evenly distributed together in space. Each liquid needs to migrate anywhere within the channel. Assuming that only two liquids are to be mixed in a microchannel with a width of 100 μm (as shown in Fig. 1A, left), and each occupies half of the microchannel, then each liquid must migrate at least 50 μm to achieve mixing. We call this distance the mixing displacement. If two liquids are introduced in an interdigitated shape (as shown in Fig. 1A, right), in this fixed-width microchannel, the greater the number of intersecting layers, the smaller the mixing displacement (as shown in Fig. S1†). In traditional mixing methods, the mixing displacement is half the channel width (as shown in Fig. 1B, left). To reduce the mixing displacement, multiple channels can be used to bring the two liquids to the mixing segment (as shown in Fig. 1B, middle). But, multi-channel structures necessitate multiple inlets, which also means multiple external pipelines and even multiple syringe pumps. This will increase users' difficulty and decrease their willingness to use it.

To save the inlets, the main channel-branch channel form can be adopted (as shown in Fig. 1B, right). But, in a 2D chip, if one of the liquids adopts this form, the other liquid cannot do the same because the microchannels cannot intersect. To further save the inlet, we developed a double-layer PDMS chip (as shown in Fig. 1C), which can transform the 2D chip into a 3D chip to enable the intersection between fluidic channels. This design ultimately allows for the use of only one inlet for each liquid. In other words, the purpose of the double-layer chip is to branch the liquid from inlet 2. Specifically, the function of the double-layer chip is to branch the liquid from inlet 2 within the layer formed by the two layers of PDMS. Subsequently, the branched liquid descends into the layer formed by the substrate and the second layer of PDMS to meet the liquid from inlet 1. Finally, the two liquids enter the mixing segment alternately and parallelly in the interdigitated formation.

We emphasize that it is not difficult to make a double-layer PDMS chip. The microchannels are visible to the naked eye (as shown in Fig. 1D) and require only manual alignment to complete the bonding. This simple alignment is achieved by designing the upper-layer PDMS slab (as shown in Fig. 1D middle). That is, each branch in the upper PDMS slab is aligned with the punching hole in the lower-layer PDMS slab through a line of alignment circles with diameters of 4 mm (as shown in Fig. 1D). The large sizes of these alignment circles can be easily spotted by the naked eye, hence allowing straightforward alignment of two slabs of PDMS with microfluidic structures.

The flow rate of each branch should be as close to each other as possible. Due to the friction of the channel wall, the longer the channel, the greater the resistance to the fluid, resulting in a smaller flow rate. Thus, it is necessary to keep the channel length of each branch consistent. The symmetrical and tortuous channel arrangement shown in Fig. 1B right and C can ensure that the length of each branch for each liquid is as close to each other as possible. In addition, the number of bends is also the same.

The simulation of the traditional mixing chip and the branch-convergence structure chip are shown in Fig. 2. The flow rates of the fluorescent solution and ultrapure water were set to 5 mL h⁻¹, and the concentration of the fluorescent solution was set to 0.03 mM. The mixing segments (omitted, details can be found in the COMSOL simulation model in the ESI†) were composed of 5 serpentine cycles. According to the simulation results, the performance of the traditional mixing chip (as shown in Fig. 2A) is obviously inferior to that of the branch-convergence structure chip (as shown in Fig. 2B) under the same conditions. The liquid had almost no concentration change near the channel wall in the traditional mixing chip. Even in the central area of the channel, where there was some mixing effect, the mixing performance was not satisfactory enough. Conversely, satisfactory mixing was achieved with the branch-convergence structure chip, even for liquids near the channel walls.

It should be noted that the numerical simulation results are affected by conditions such as the model and meshing method. We open-sourced the geometric and simulation models, which can be found in ESI.†

Materials and methods

Fabrication of microfluidic chip

The structure of the microfluidic channel was drawn using AutoCAD software (Autodesk, Inc.), and the structural light-transmitting photomask plate corresponding to the drawing was customized (JiXian Optoelectronics Co., Ltd.). Based on the photomask plate and photomask exposure system (Mask Aligner, MA/BA6, SUSS MicroTec), SU-83050 negative photoresist (MicroChem, Inc.) was used to create channel positive molds on the silicon substrate (4 inches, Hangzhou Danguang Optoelectronics Technology Co., Ltd.). The steps include spin coating (step 1: spin at 500 rpm s⁻¹ for 15 s, acceleration is 100 rpm s⁻², step 2: spin at 3000 rpm s⁻¹ for 30 s, acceleration is 300 rpm s⁻²), soft baking (20 min at 95 °C), exposure (170 mJ cm⁻²), post-exposure baking (1 min at 65 °C and then 4 min at 95 °C), development (about 8 min), and hard baking (15 min at 150 °C). Finally, a microchannel mold with a height of 50 μm was fabricated.

Microfluidic chips were fabricated using SU-8 mold. Polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning) and curing agent were mixed in a mass ratio of 10:1. After thorough mixing and defoaming, the PDMS prepolymer was poured onto the SU-8 mold surface. Then, the entire SU-8 mold was vacuum defoamed once more to ensure the removal of air bubbles from the PDMS. It was placed on a horizontal shelf in an oven at 80 °C for 1 h to solidify the PDMS. The cured PDMS was carefully peeled off the mold. After cutting and drilling, the PDMS and glass substrate were subjected to plasma treatment at the power of 45 W for 1 minute. Subsequently, the two components were bonded together to complete the entire bonding process. The fabrication of double-layer chips only requires repeating the above bonding process. In addition, to increase the bonding strength between PDMS and the glass substrate, the bonded chip was heated in an 80 °C oven for 4 h.

Preparation of materials

The fluorescent dye solution with a concentration of 0.03 mM was prepared by diluting sulfo-cyanine5 (Cy5) fluorescent dye (146368-11-8, GlpBio Technology) with ultrapure water. In addition, other concentrations can also be used for experiments, but concentrations that are too high or too low may affect the visual effect.

PLGA nanoparticles were synthesized by mixing PLGA solution and ultrapure water.³⁶ The PLGA solution was prepared by dissolving 10 mg PLGA (Jinan Daigang Biomaterial Co., Ltd.) in 0.3 mL tetrafluoroethylene (TFE, Sigma-Aldrich) and 0.7 mL dimethylformamide (DMF, Sigma-Aldrich).³⁷

Data acquisition and processing method

The mixing performance was observed and recorded by an inverted fluorescence microscope (ECLIPSE Ts2-FL, Nikon Instruments) equipped with a CCD camera. The Cy5 reactive dye is excited by monochromatic light with the wavelength of 633 nm. Then the snapshots are captured using the software provided with the microscope. Since the collected snapshots were in grayscale, they were directly imported into MATLAB (MathWorks, Inc.) software to extract the grayscale values. The Origin (OriginLab, Inc.) software was utilized to calculate the standard deviation of grayscale values.

Hybrid performance was quantified by the mixing index (MI).^6,38,39 The calculation formula is as follows:

where σ_in and σ_out represent the standard deviation of grayscale values before and after the two solutions passed through the serpentine micromixer.

The data of PLGA nanoparticles size were acquired utilizing nanoparticle size and zeta potential analyzers (ZEN3700, Malvern Panalytical Ltd). The images of PLGA nanoparticles were taken using a transmission electron microscope (Tecnai G2 F30, Thermo Fisher Scientific).

Results

The effect of branch number

The number of branches significantly affects the final mixing performance. The greater the number of branches, the better the mixing performance. To study the effect of the number of branches on mixing, the flow rates of fluorescent solution and ultrapure water were controlled to 5 mL h⁻¹, and the circulation section of the serpentine mixing structure was 5 cycles. In addition, the 0-branch structure is actually the traditional mixing chip.

In the 0-branch mixing chip (as shown in Fig. 3A), there is almost no mixing between the two liquids after passing through five serpentine circulation sections. This is expected. In traditional mixing chips, dozens of cycle segments are often needed to achieve satisfactory mixing. Even with only 2 branches (as shown in Fig. 3B), the improvement in mixing is obvious compared to the 0-branch structure. Delamination can still be observed on the 2-branch chip, but it gradually diminishes as the number of branches increases. Delamination can still be observed in the 4-branch chip (as shown in Fig. 3C), but in the 8 branches chip (as shown in Fig. 3D), the delamination boundary no longer be found. Based on the images, the improvement in the mixing effect is evident from 0 branches to 2 branches, but the improvement diminishes from 2 branches to 4 branches. This trend can also be observed by calculating the mixing index (as shown in Fig. 3E). This is because the width of the serpentine channel is 100 μm, and in the case of 0 branches, the mixing displacement of each liquid is 50 μm. With 2 branches, the mixing displacement of each liquid was reduced to 25 μm. With 4 branches, it reduced to 12.5 μm. With 8 branches, it reduced to 6.25 μm. Thus, increasing from 0 branches to 2 branches reduces the mixing displacement by 25 μm (50–25 μm); increasing from 2 branches to 4 branches reduces it by 12.5 μm (25–12.5 μm); and increasing from 4 branches to 8 branches reduces it by 6.25 μm (12.5–6.25 μm). In other words, the greater the number of branches, the smaller the benefit (reduction in mixing displacement) gained from increasing the number of branches.

For the serpentine mixing structure, the streamlines near the center of the channel are shorter than those near the channel wall, and the stretching effect on the fluid caused by the deformation of the channel structure is also smaller. Thus, liquids closer to the center of the channel are more difficult to mix than liquids closer to the channel walls (as shown in Fig. 3B–D).

The effect of cycle number

The number of cycle sections significantly affects the mixing performance in serpentine mixing chips. The greater the number of cycles, the better the mixing performance. To study the effect of the number of cycles on mixing, the flow rates of fluorescent solution and ultrapure water were controlled to 5 mL h⁻¹, and number of branches was 8.

When there are only 3 cycles, alternating light and dark stripes can be clearly observed in the middle of the image (as shown in Fig. 4A). This is consistent with the conclusion analyzed in the previous subsection that liquids near the center of the channel are more challenging to mix than those near the channel walls. Under the condition of 5 cycles (as shown in Fig. 4B), the alternating light and dark stripes are no longer observed, and the width of the incompletely mixed range in the middle is reduced. As the number of cycles increases to 10 (as shown in Fig. 4C), the width of the incompletely mixed range is further reduced. It is not until the number of cycles is increased to 25 that the middle region achieves almost complete mixing (as shown in Fig. 4D). The emphasis here is on achieving basically mixing, rather than complete mixing, as the brightness changes can still be vaguely seen in the image at this point. This is also confirmed by the mixing index (as shown in Fig. 4E). Under the condition of 25 cycles, the mixing index is approximately 91%. In addition, the data corresponding to the complete mixing was obtained by mixing the fluorescent solution and ultrapure water at a 1:1 ratio using a vortex instrument and then directly injecting it into the chip. The mixing index of complete mixing is 96.1% instead of 100% due to the interference caused by the ambient experimental light.

When the number of cycles is less than 10, the mixing index decreases linearly with an increase in the number of cycles (as shown in Fig. 4E). But, the linear relationship terminates when the number of cycles exceeds 10. This is also because increasing the number of cycles can significantly affect the liquid near the channel wall, while the effect on the liquid near the center of the channel is relatively weak. When the liquid near the channel wall is completely mixed, increasing the number of cycles can only have a weak mixing effect on the liquid in the center of the channel. This can be mutually confirmed with grayscale images. From 10 cycles (as shown in Fig. 4C) to 25 cycles (as shown in Fig. 4D), the range of poor mixing areas in the middle was almost unchanged.

The effect of flow rate

The flow rate is an important factor affecting the fluid mixing mode and significantly impacts the final mixing performance. To study the effect of flow rate on mixing, the number of branches was set to 8, and the circulation section of the serpentine mixing structure was set to 25 cycles.

The primary mixing mechanisms are different at different flow rates. At lower flow rates, the mixing mode is mainly diffusion, while at higher flow rates, the mixing mode turns to chaotic advection dominated by Dean flow. When the flow rate is as low as 0.5 mL h⁻¹ (as shown in Fig. 5A), the liquid takes the longest time from the first cycle to the last cycle. The two liquids have sufficient time to diffuse and mix during this period. Thus, the mixing performance is satisfactory. When the flow rate is as high as 10 mL h⁻¹ (as shown in Fig. 5D), the liquid quickly passes through the entire serpentine mixing section, with the diffusion time being only 1/20 of that at 0.5 mL h⁻¹. At the high flow rate, the fluid is subjected to the combined effects of friction and centrifugal force, and the mixing mechanism is mainly chaotic advection (mainly based on Dean flow). Chaotic advection has a better mixing effect than diffusion. The mixing index is approximately 95% in the chaotic advection mode (10 mL h⁻¹) (as shown in Fig. 5E). And in diffusion mixing mode, it's about 91.4%. We preliminarily believe, between the low flow rate (0.5 mL h⁻¹) and the high flow rate (10 mL h⁻¹), the diffusion mode and chaotic advection mode are in a tug-of-war state, resulting in a decrease in mixing performance between 5 mL h⁻¹ and 8 mL h⁻¹.

Additionally, it is easy to misunderstand that even at 10 mL h⁻¹, the fluid is still laminar flow rather than turbulent flow. To achieve turbulent flow in the channel structure (the channel width is 100 μm and the height is 50 μm) of this study, the flow rate needs to be at least approximately 300 mL h⁻¹. It is difficult for traditional PDMS chips to withstand the high pressure corresponding to ultra-high flow rates.

Comparison of branch-convergence chip and traditional chip in the synthesis of PLGA nanoparticles

We synthesized PLGA nanoparticles using both the branch-convergence mixing chip (as shown in Fig. 6A) and the traditional mixing chip (as shown in Fig. 6B) and made strictly controlled comparisons to demonstrate the advancement and practicality of the branch-convergence structure (as shown in Fig. 6). The flow rate of the PLGA solution was 0.5 mL h⁻¹, and the flow rate of water was 8 mL h⁻¹. Each type of chip contained 25 serpentine mixing segments.

The test results showed that the average particle size of PLGA nanoparticles synthesized using the traditional mixing chip was 136.3 nm. Under the same conditions, using the branch-convergence mixing chip corresponded to a smaller average particle size of 43.8 nm. Importantly, the branch-convergence structure corresponded to a more slender particle size and number distribution curve (as shown in Fig. 6C), indicating that the PLGA nanoparticles synthesized using the branch-convergence mixing chip had better uniformity than those synthesized by the traditional mixing chips. Furthermore, this mixing method can not only be well-used for the synthesis of nanoparticles but is also capable of promoting the cross-linking of DNA molecules with silica microspheres for DNA storage⁴⁰ and facilitating the capture of target cells by magnetic beads in cell sorting.⁴¹

Conclusions

This work proposes a universal strategy to enhance the mixing efficiency of microfluidic chips through the branch-convergence structure. This strategy to enhance mixing is essentially achieved by increasing the number of interfaces between fluids. Based on the double-layer chip, the number of inlets can be reduced, requiring only one inlet for each liquid. We conducted methodological studies on branch-convergence structure chips using fluorescent solutions and ultrapure water. The results show that even with only 2 branches, there is a significant improvement compared to traditional mixing chips. In the case of 8 branches, the performance was improved by about 10 times. We used the serpentine channel as the mixing section. The more serpentine cycles there were, the better the mixing performance. Flow rate has a significant impact on mixing performance. At lower flow rates (0.5 mL h⁻¹), the mixing mode is primarily diffusion, while at higher flow rates (10 mL h⁻¹), the mixing is primarily chaotic advection. In addition, we synthesized PLGA nanoparticles as a proof of concept for the application. Compared with traditional mixing chips, branch-convergence structure chips can synthesize PLGA nanoparticles with better uniformity in continuous mixing.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Saijie Wang: conceptualization and design of the study, performing the experiment, interpretation of data, writing – original draft. Zhihan Zhang, Quanchen Xu, Yao Chen, Qian Wang, Boxi Lu and Xueqing Luo: performing the experiment. Dou Wang and Xingyu Jiang: conceptualization and supervision of the project, funding acquisition, writing – reviewing & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank the National Key R&D Program of China (2018YFA0902600), the National Natural Science Foundation of China (52203243, 22234004, 21761142006, 21535001, 22204068 and 81730051), Guangdong Provincial Key Laboratory of Advanced Biomaterials (2022B1212010003), Guangdong Innovative and Entrepreneurial Research Team Program (2019ZT08Y191), the Shenzhen Science and Technology Program (GJHZ20220913142610019, KQTD20190929172743294, SGDX20230116091642001, JCYJ20220818101407017), the Chinese Academy of Sciences (QYZDJ-SSW-SLH039), Guangdong Major Talent Introduction Project (2019CX01Y196). The authors acknowledge the assistance of SUSTech Core Research Facilities and the Cryo-EM facility of Southern University of Science and Technology for providing the facility support. Saijie Wang would like to thank associate professor Zhijian Liu (College of Marine Engineering, Dalian Maritime University) for helping with the basic operation and understanding of Microfluidics.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4lc00405a

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