Microfluidic systems are of growing importance for applications in the field of, for example, nanomedicine, biomedicine, rapid diagnostics and single cell investigations [1
]. The production of microdevices developed rapidly over the last decade and commonly used methods are standard photolithography, micromachining and polymer molding. The advances in 3D printing techniques offer new possibilities for the manufacturing of microdevices such as the use of liquid metals as fugitive inks for the manufacturing of channels [5
], the production of leak free seals [6
] or the use of fused filament to produce devices with circular channels. For further reading, see for example Ho et al. [7
The mixing of fluids in microfluidic devices is an important application and has received considerable attention recently. A key challenge in mixing is to utilize solute diffusion as well as possible, and at the same time optimize convective contributions to fluid mixing. This is a design challenge because diffusion occurs best in very narrow channels that imply, on the other hand, low Reynolds numbers (<<2000) that force the physics of flow towards the laminar regime and suppress turbulence. Important additional design considerations include simplicity of design, reproducibility and availability of rapid prototyping methods. Micromixers can be classified into passive and active mixers. In a passive micromixer, solutions inside a microchannel are mixed by enhancing the diffusion mixing component by suitably equipping a microchannel with additional features to exploit inertial forces, chaotic effects and flow folding. In contrast, in active mixers, an external force is applied to the fluid for mixing, such as an acoustic force [8
] or magnetic force [9
]. An advantage of active mixing is that channel length can be reduced in comparison to a passive mixer; however a disadvantage might be the need of additional external instruments. In this work, recent advances in rapid prototyping for true 3D channel geometries in polymeric microfluidic systems are utilized to improve passive mixing. Examples of mixing geometries are discussed below and presented in Figure 1
Liu et al. [12
] investigated mixing by using a serpentine shaped microchannel for Reynolds numbers 6–70 and found that such geometries are able to disturb the laminar flow at these Reynold numbers, similar to the events found in chaotic advection at higher Reynolds numbers and in larger channels.
Chen and Meiners [13
] presented topologic mixing by using helical channels that repeatedly fold the flow resulting in an exponential increase of the concentration gradients and with this, they obtained fast and efficient mixing by diffusion at Reynolds numbers between 0.1–2. Kumar et al. [14
] studied curved channels and concluded that for higher Schmidt number fluids, the mixing is improved at Re
~ 10, however is not affected at Re
~ 0.1. The Schmidt number (Sc
) is a dimensionless number defined as the ratio of viscosity and mass diffusivity. Additionally, it is shown that at low values of curvature ratio, the mixing is higher as compared to a higher curvature ratio. Lee et al. [15
] developed a split and recombination micromixer (also called a “splitting and recombination” (SAR) mixer). Here, structured units in a microchannel were used to increase the number of interfaces, which enhances mixing. They showed that mixing could be completed for 90% after 7 units and at a Reynolds number of 0.6. The experimental results used for quantifying the mixing efficiency are in agreement with numerical analysis.
A novel generation of this 3D SAR micromixer (called chain micromixer) was developed by Viktorov and Nimafar [16
] where the mixing performance of using microstructures on both the top and bottom floors of the microchannels were compared with other micromixers (e.g., T mixers). It was shown by both experimental as well as computational fluid dynamics that these chain mixers in particular have an efficacy of up to 98% that can be achieved at Reynolds numbers from 0.083 ≤ Re
≤ 4.166. Another study showed that mixing is also obtained by unbalanced splits and collisions of fluid streams and Dean vortices [17
] at Re
numbers from 10–80. Here the highest mixing performance was obtained by Re
> 40. The structures used could be described as a main channel, which is split into two sub-channels that are unequal in width and recombine after a certain distance. The repetition of such units would enhance mixing. Lim et al. [18
] designed a 3D crossing manifold micromixer, for which it was estimated by numerical simulation that a mixing ratio of 90% could be obtained for a channel length that is five times shorter than the channel width (Re
~ 1; Péclet ~ 1000). The Péclet number is a dimensionless number defined to be the ratio of the rate of advection of a physical quantity by the flow, to the rate of diffusion.
The fabrication of 3D microchannel systems in polydimethylsiloxane (PDMS) is in most cases a multilayer process as for example presented by Wu et al. [19
]. They developed a method that uses planar structures or pseudo 3D structures to generate real 3D geometry in a microfluidic system. The pseudo 3D structures are planar sheets of channels, which are bent into 3D geometries and subsequently embedded in PDMS to freeze the geometries. The manufacturing of 3D circular channel networks remains a challenge but progresses rapidly due to advances in 3D template casting methods that allow design of complex, connected 3D geometries with programmable flow exhibiting various channel geometries [20
]. The progress in 3D printing techniques are shown by the work of Hwang et al. [21
] who used a 3D printed mold to produce cylindrical microfluidic channels ranging from 200–1000 μm and compared these results with four different 3D printers. Parker et al. used a 3D printer with 16 μm layer resolution to manufacture a device capable of creating 200 μm hydrogel droplets [22
]. Other manufacturing methods are presented by, for example, Song et al. [23
] who used a metal wire (solder) process to produce helical channels into PDMS. By heating up the polymerized PDMS to 190 °C, the solder could be removed. Verma et al. [24
] showed that nylon thread could be formed into 2D or 3D structures and used as templates to generate helical channels.
Complex connectivity and geometries are relevant for various biomedical, chemical and pharmacological applications. Here, circular channel networks remain, due to their geometry, of interest for biomedical applications such as for the study of the rheological behavior of blood cells in microcirculatory blood flows. Still, a major part of these investigations is done by modeling. Further development of the models will require validation where the availability of circular microfluidic structures or networks might serve as an alternative to in vivo experiments (e.g., [26
]). A final and important example is the generation of nanoparticles based on polymers with these microsystems, which are attractive due to their flexibility in design, synthesis and functionalization. Such nanoparticles are an enabling technology for drug delivery and receptor-targeting required in the personalized medicine of the future. Our reports on the biomedical usage of such intelligent nanomaterials were a key trigger to develop improved assembly methods [27
]. Here, one of the key advantages is the ability, in principle, to tune the size and shape of the nanoparticles, which can critically influence behavior (e.g., stability, delivery, elimination time) in vivo. Micelles for example, consist of hydrophilic shells and hydrophobic cores, that are well suited for the encapsulation of hydrophobic molecules, such as drugs, diagnostic agents, or functional materials, and poly(2-methyl-2-oxazoline)–polydimethylsiloxane (PMOXA–PDMS) nanosystems in particular are known for biocompatibility, stealth properties and low permeability.
In this study, we further extended the recently published method of complex thread template casting [20
] to develop a new type of true 3D circular helical micromixers. The potential of such micromixers is explored by hydraulic analysis and fluid dynamics modeling and is experimentally tested by using the systems for multicomponent chemical reaction and nanomaterial assembly of advanced nanomaterial-forming polymers [29
3. Results and Discussion
Mixing was first studied in a simple 2-channel design containing two 200 μm channels and having a helix length of 28 mm with a pitch length of 2.24 mm (Figure 6
) using the color change of a pH dye as marker of mixing. Mixing is visible as a color change of the pH indicator and in this design is evident already after the first pitch. This is in strong contrast to the T-shaped device shown in Figure 9, where full mixing is not observed at the end of the channel.
Next, a triple helix design was constructed and tested and is shown in Figure 7
. Here, a differential diameter of the threads was chosen, giving additional flexibility to the design in situations where this might be desirable: for example, the flow resistance changes strongly with the channel diameter (Poiseuille law) and allows to tailor flow characteristics over a large range by simply changing the filament diameter. Three-component mixing was tested using hydrochloric acid, sodium hydroxide, and a pH indicator dye. Changing the relative flow between the channels led to consistently good mixing between the channels, but also along the channel, implying that the mixing process occurs continuously in time, rather than being a process with random fluctuations at the microscopic scale, suggesting that at this examined scale, mixing is not a chaotic process. This finding is also supported by the steady state flow and mixing that is found in the fluid dynamics simulation below.
As a next step in design complexity, a multi-phase mixing device was constructed by having a double helix design in a first segment, followed by an additional side channel after a given distance as shown in Figure 8
. This will allow to perform reactions sequentially in a channel without need for change of connectivity. In a first step, a pH indicator is mixed with hydroxide, showing rapid mixing as above. In a second step, the side channel adds acid to the mix, here in exact molar equilibrium with the base (thus creating a very fragile system sensitive to confounding factors). This now shows that over 7 mm, mixing is not complete in the final triple helix. Reasons for this finding might include the fact that the Dean number is very low in this system, in particular if such low flows are used; it might also be caused by a suboptimal conformal contact between the channels, although Figure 3
showing the cross section of the channels documents clearly that this was not the problem in this case. Mixing might be sped up by increasing the Dean number of the design, which is a function of the Reynold number (including velocity), the helix radius and helix curvature. Thus, increasing flow velocity and decreasing pitch length will increase mixing. Although increasing channel diameter would also increase the Dean number, which is not desirable here because of its strong negative effect on the diffusive component of mixing.
As a next step, the T-shaped, rectangular cross section microfluidic device reported in [29
] for nanoparticle assembly, was used as a comparator device and is shown in Figure 9
. The length of the channel was 15 mm, the width 200 μm, the height 45 μm and flow rates of 1 mL/h Phenol red (inlet 1, 3) and 0.5 mL/h NaOH (inlet 2) are used. The flow in this device was also laminar in the experiment as expected from the similarly low Reynolds number regime as above and as predicted by fluid dynamics simulation (not shown). Mixing was very slow in comparison with the helix devices. Note that the diffusion regime used here is the best that can be achieved practically, because the diffusion coefficient of protons that drives the color change is at least an order of magnitude larger than for most other reactants; in other chemical reactions, mixing would thus proceed even slower.
In these rectangular channels, one dimension is similar to the larger threads used above, while the other dimension is smaller, with a smaller overall cross section of the T-channel compared to the other geometries. Similar overall flows in a channel with narrower cross section will result in shorter transit time. Although it is generally difficult or impossible to achieve full dynamic similarity in the fluid dynamics sense in such dissimilar geometries, in particular when Navier–Stokes is coupled with convection–diffusion, the comparison done here is nevertheless instructive: The smaller dimension of the T device used for comparison favors mixing performance even with shorter transit time, because, since the seminal work of Albert Einstein in 1905 [34
], it has been known that diffusion is inversely proportional to the square of distance but proportional to linear time; for a given (laminar) flow, a smaller cross section will thus favor mixing despite faster transit. Also, as driving pressure scales with the fourth power of diameter (Hagen–Poiseuille), good mixing in larger diameter channels may be of considerable interest for real-world applications because of the strongly relaxed requirements for driving pressure and mechanical device stability. From a practical viewpoint, a user would like to mix a given volume per time of fluid with a given maximum permissible driving pressure. Thus, the findings support the benefit of the new helix mixer design.
shows the Reynolds and Péclet, Dean numbers and the pressure drop Δp
encountered in the experiments. Table 2
, presents characteristics of the helical channels as the calculated radius, radius of curvature, pitch length (one helical period where a full turn is made), and the calculated time to fully mix when only the molecular diffusion is present (tmix
). The molecular diffusion coefficient D is assumed to be 10−9
/s. The calculated pitch length of the double helix A (design I) is larger when compared to the double helix C (design II). The pitch length can be influenced during fabrication of the thread helices just by twisting the threads in the desired number. By doing so, one is also capable of control the packing of the helices and subsequently the mixing capacity. A tighter thread helix will increase the final touching surface in between the threads. The radii were calculated by using the dimensions of at least three images of cross sections of devices (in duplicate or triplicate). The radii used in all calculations were 1.79 × 10−4
± 1 × 10−7
m for the double helix (design I/A), 2.41 × 10−4
± 4.9 × 10−6
m for the triple helix (design I/B), 1.77 × 10−4
± 2.4 × 10−6
m for double helix (design II/C) and 1.97× 10−4
± 8.5 × 10−6
m for triple helix (design III/D).
The radius of curvature of individual channels is larger than the radius of the helix. This can lead to a secondary Dean flow due to the differential flow in channel locations near the center and peripherally, a phenomenon that is quantified by the Dean number.
The curvature ratio λ was the highest at the double helix (I/A) and the lowest for the double helix (I/B). In this work, with consistently low Reynolds numbers as Dean numbers, successful mixing was obtained at small length scales of less than 15 mm despite the fact that the Dean numbers were also quite low. This is supported also by the findings of Nguyen et al. [35
] who reported that at low Reynolds numbers of 1 < Re
< 10, as is the case with our experiments, Dean numbers in this low range are still capable of convective mixing.
Our computer simulations were performed to explore fluid flow geometry and patterns in such helices with the given design parameters. Simulation results are shown in Figure 11
. Our results are also supported by results from Kumar et al. who used computational fluid dynamics to investigate the mixing efficiency of curved tubes and reported that mixing efficiency is a rather complicated function—e.g., the curvature ratio, the pitch and the Reynolds number [14
]—and are critically dependent on the curvature ratio, a parameter that can be nicely controlled in our approach.
3.2. Assembly of Nanoparticles
In order to test the capability to generate nanomaterials by polymer self-assembly (as reported previously [29
]) using helical channels, we studied the self-assembly of an amphiphilic triblock (ABA) copolymer with a double helix system (200 μm inlets; design II in Figure 1
). Since microfluidic assembly and nanoprecipitation with these materials mainly depends on the initial concentration of copolymer in the organic solvent, organic phase fraction and flow, two sets (run 1 and 2) with different QT
and FRR were tested (see Table 1
) in a similar way to that done previously [29
]. The flow profile inside the device is presented in Figure 12
. DLS results are presented in Figure 13
, which shows nanoparticles of 29 nm for FRR 6.8 and 24.5 nm for FRR 33.3, with good reproducibility in repeated runs. The output of the device consists almost exclusively of nanoparticles with a narrowly defined size range. Nanoparticle size variation, measured as half-width of the particle size distribution curve in DLS, was 15 nm at FRR = 6.8 and 16 nm at FRR = 33.3. In comparison, using the T-shape device (reported in detail in [29
]), self-assembly of the same polymer at FRR = 7 yielded a size of 32.9 nm with a half-width of 26 nm, and at FRR = 30 yielded a size of 24.5 nm with a half-width of 28 nm. Thus, the helical device resulted in comparable nanoparticle size but lower size variation, supporting the benefit of rapid mixing in the new device.
From these results, we conclude that helical microfluidic channels are thus suitable for the in-line, continuous and reproducible assembly of polymer nanoparticles with narrow size variation.
3.3. Comparison with Other 3D Mixers
One key differentiating feature of this novel approach to 3D mixing is its rapid prototyping character. True 3D microchannel geometry with good reproducibility and effective control of flow is achieved without the need of cleanroom infrastructure, photolithographic techniques and silicon masters.
In comparison with other microchannels rapid prototyping methods that have been used by our lab, we observe the following:
Compared to 3D printing, we see much higher fidelity and reproducibility of channel geometry with the option of achieving smooth channel surfaces. In addition, the new manufacturing approach leads to much more stable designs that are able to withstand higher driving pressures.
In comparison to laminated PDMS microfluidics, this new approach eliminates a weak point in the microfluidic system structure that required significant attention to avoid leakage or delamination.
In contrast to micromilling, we could achieve significantly smaller features size, much better surface smoothness, and a significantly reduced work effort per device constructed. Also, we found that microdrilling was vulnerable to drill abrasion and required very accurate surface alignment to the machine to achieve reproducible results.
In terms of flow characteristics, we note that this new design impacts flow directionality at all fluid–wall interfaces, in contrast to 2.5D approaches such as herringbone structures that only impact flow direction on one wall. In the latter, in particular at very low Reynolds numbers, two different flow regimes may be encountered with an almost stagnant flow in the recesses of the herringbone, and a near-straight flow above the herringbone, with little curl. Effectively injecting momentum in the direction perpendicular to the main flow axis is of particular importance in this otherwise heavily viscosity-driven flow regime. In comparison to experimental asymmetric, multistage herringbone architectures [36
], mixing length is competitive in our design, but we suspect that further design optimizations are conceivable, which is a topic of our ongoing research.
In comparison with some other design/manufacture methods that require multiple manufacturing steps, e.g., manufacture of several layers/parts followed by assembly needing perfect alignment, this new approach allows single-step construction without the need for alignment and assembly.