3D-Printed Microfluidic Chip System with Integrated Fluidic Breakers and Phaseguide Fluid Structures for Optimal Passive Mixing

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1) In the abstract, there is no need to have subsections. Just the text.

2) There is a lot of scope for improving the introduction of the manuscript.

For eg, a) It is good to include a wide range of applications of LOC microfluidic technologies, ranging from single cell analysis  (https://doi.org/10.1002/advs.202500975 ) (https://doi.org/10.1038/s41587-023-01685-z ), Bacterial diagnostics ( https://doi.org/10.1038/s41467-025-59736-9 ) ( 10.1126/sciadv.adv4558 ), assisted reproductive technologies (10.1039/D1LC01144H ), etc

b) Please explain how this technology would be useful in single-phase microfluidics, droplet microfluidics (https://doi.org/10.1038/s41592-023-01995-9), or even non-Newtonian phases in microfluidics (https://doi.org/10.1063/5.0255319).

2) Is it possible to have the results in terms of a non-dimensional number instead of flow rate?

3) I am not sure if I missed this in the manuscript, but at what location of the microfluidic channel are the results compared at exit? or a certain location?

 

Author Response

For better overview the comments of reviewer are underlined.

Reviewer 1

 

Comments and Suggestions for Authors

• In the abstract, there is no need to have subsections. Just the text.

Re: done

• There is a lot of scope for improving the introduction of the manuscript.

For eg,

10. a) It is good to include a wide range of applications of LOC microfluidic technologies, ranging from single cell analysis  (https://doi.org/10.1002/advs.202500975 ) (https://doi.org/10.1038/s41587-023-01685-z ), Bacterial diagnostics ( https://doi.org/10.1038/s41467-025-59736-9 ) ( 10.1126/sciadv.adv4558 ), assisted reproductive technologies (10.1039/D1LC01144H ), etc
11. b) Please explain how this technology would be useful in single-phase microfluidics, droplet microfluidics (https://doi.org/10.1038/s41592-023-01995-9), or even non-Newtonian phases in microfluidics (https://doi.org/10.1063/5.0255319).

Re: Since we felt it was hard to include the additional literature provided by the reviewer into the introduction we have now included it into the outlook in the conclusion in lines 795-800

“Future work should focus on optimizing printing processes to minimize these artifacts and further explore the application of SHM- and Tesla-structures in a wide range of applications of LOC microfluidic technologies in the context of biomedical and chemical analysis e.g. in single cell analysis or bacterial diagnostics. Especially the non-newton fluid blood for (single) analysis would be very interesting to be tested here.”

• Is it possible to have the results in terms of a non-dimensional number instead of flow rate?

Re: We transferred the given flow rates into Reynolds number and will add it into the material and method part for orientation. The calculated data show that all Re numbers are below 2300. All of them would be defined as laminar. However, we decided against the implementation of Reynolds numbers into the different figures of this publication, as this would not reflect the reality in this 3D-printed passive mixing structures. In order to get an impression nonetheless, we have implemented the corresponding Re numbers and their calculation in lines 224–232.

 

• I am not sure if I missed this in the manuscript, but at what location of the microfluidic channel are the results compared at exit? or a certain location?

Re: We described for the measurements the different locations in the supplementary part in Figure S3 and the associated description. We now transferred it into the M & M part 2.4 Determination of mixing efficiency using image analysis and data processing so that it is less likely to be overlooked (lines 239-276)

 

“Three regions of interest (ROI), marked as A, B, and C (Figure 1), were defined to indicate areas important for analysis and evaluation. Since the microfluidic polymer chip would have its own grey scale values, different areas (ROIs) in the 3D-printed devices were defined for determination of the initial status I₀ (ROI A), the investigation of pure diffusion after the stop structure (ROI B) and after the mixing structure (ROI C) (Figure 1). For the initial state (I₀), the rectangle was placed before the T stop-structure to exclude any mixing that might arise from the meeting of the fluids and the T stop-structure. The unknown mixed state (Iₓ) and the fully mixed state (Iₘₐₓ) were examined in ROI C (Figure 1) before the reservoir and behind the mixed structure, respectively. To determine Iₘₐₓ, both fluids were completely mixed by vortexing (30 sec) before they passed through the mixing structure. To compare the mixing efficiency of the different mixing structures, each was analyzed against the fully mixed state (Iₘₐₓ) in the channel”

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a 3D-printed microfluidic chip integrating phaseguide fluid structures, fluidic breakers, and multiple passive mixing geometries (SHM, TESLA, and SAR). The topic is relevant, and the experimental data appear potentially valuable. However, the current presentation suffers from substantial structural, conceptual, and interpretational issues that must be addressed before the manuscript can be considered for publication.

The abstract is informative but not suitable for a journal publication in its current form. It contains explicit section headings (Methods, Results, Conclusion), detailed experimental parameters, and specific quantitative results, which are inappropriate for a concise journal abstract.

The introduction is excessively detailed and reads more like a thesis chapter than a journal-style contextualization. It must be improved. The last paragraph should clearly state why this work is necessary and what it contributes. The focus should be on objectives, novelty, and significance, avoiding experimental or material details (these belong in the Methods section).

The Discussion section currently reads largely as a literature review rather than a critical analysis of the authors’ own data. While referencing previous work is important, the focus should be on interpreting the study’s results in the context of existing literature rather than summarizing other studies at length.

Several key figures are currently placed in the Supplementary Information, which significantly reduces the readability and clarity of the manuscript. The authors should consider moving some figures (e.g., Figures S3, S4, S5) back into the main manuscript.

The calculation of mixing efficiency should be clearly presented in the manuscript, including the formula, assumptions, and any relevant parameters.

Providing an example of the image-processing workflow used for efficiency evaluation would improve transparency and reproducibility.

Sections 3.1, 3.2, and 3.4 are presented as Results but are more similar to Methods or procedural descriptions.

Line 475–480 discusses fabrication but does not provide adequate context or reference to previous literature.

Lines 500–503 claim comparisons with other fabrication methods without presenting supporting evidence.

Repeated references to “data not shown” are unacceptable and must be replaced with actual figures or quantitative data.

The discussion of mixing efficiency is confusing, as parameters such as structure, flow rate, retention time, and fabrication technique are mixed together without clear separation.

Author Response

For better overview the comments of reviewer are underlined.

Reviewer 2

 

Comments and Suggestions for Authors

The manuscript presents a 3D-printed microfluidic chip integrating phaseguide fluid structures, fluidic breakers, and multiple passive mixing geometries (SHM, TESLA, and SAR). The topic is relevant, and the experimental data appear potentially valuable. However, the current presentation suffers from substantial structural, conceptual, and interpretational issues that must be addressed before the manuscript can be considered for publication.

The abstract is informative but not suitable for a journal publication in its current form. It contains explicit section headings (Methods, Results, Conclusion), detailed experimental parameters, and specific quantitative results, which are inappropriate for a concise journal abstract.

Re: We now provide a shorter and more concise introduction and have been more clear about the aims of the study in the final paragraph. The abstract has been amended in line with the suggestion.

The Discussion section currently reads largely as a literature review rather than a critical analysis of the authors’ own data. While referencing previous work is important, the focus should be on

            Re: The discussion has also been edited and rephrased and hopefully there is a better narrative flow from Introduction through Results to the Discussion.

Several key figures are currently placed in the Supplementary Information, which significantly reduces the readability and clarity of the manuscript. The authors should consider moving some figures (e.g., Figures S3, S4, S5) back into the main manuscript.

Re: Thanks a lot for the note. We moved the figure S3 and S4 and their description plus the calculation part from the supplementary part into the material and method part 2.4 Determination of mixing efficiency using image analysis and data processing. They are now Fig. 1 and Fig. 2. (lines 242-288).

We also moved figure S5 (now figure 5) and the explanatory section into the main text to explain in more detail the homogenous and non-homogenous mixing as a representative of an incomplete mixing in the uniform designs in the different mixing structures to have a more close associated and interpretation of the data in Figure 3 and 6. This figure demonstrate the ideal mixing state I_max which show clearly an homogenous distribution as a representative for an ideal complete mixing (lines 408-454 as shown below).

 

“A closer examination of the measured grayscale values revealed localized maxima that indicated regions of incomplete mixing. While the applied metric generally captured the transition from unmixed to mixed states across flow rates and structures, certain visual discrepancies between the observed and calculated values remained, particularly at higher flow rates. These inconsistencies were not fully resolved by the grayscale-based analysis method. Figure 5 presents selected frames from video recordings (full videos available in supplementary video section), corresponding to the ROI A, B, and C areas—defined as I₀ (completely unmixed), Iₓ (intermediate mixed state), and I_max (completely mixed via vortexing), respectively. To illustrate these unresolved differences, especially at flow rates ≥80 µL/min, representative snapshots have been included in Figure 5.

The analysis of Iₓ largely supports the trends observed in Figure 6, yet it highlights a challenge requiring further investigation. As expected, at the lowest flow rate of 1 µL/min, a diffusion-driven mixing process occurs, resulting in a visual mixing state indistinguishable from the completely vortexed reference, which is also confirmed by the data visualization in Figure 5.

At 40 µL/min, the SAR-structure and the reference channel (without mixing structures) exhibit a noticeable separation of the two differently colored fluids, with a diffuse interfacial boundary. However, at 100 µL/min, this diffuse region disappears entirely for both the SAR structure and the reference channel.

In contrast, the Tesla-structure demonstrates a relatively homogeneous mixing distribution at 80 µL/min, achieving an mixing efficiency of approximately 90% (Figure 3). However, at 100 µL/min, the mixing performance decreases further to 50%, with the reappearance of fluid separation and a diffuse interfacial boundary, similar to what was observed in the SAR-structure at 40 µL/min.

A more detailed visual analysis of the SHM-structure suggests discrepancies with previously published data, particularly at higher flow rates (80 µL/min and 200 µL/min). In both cases, a central channel of Coomassie-stained fluid remains visibly unmixed, indicating that complete mixing is not achieved under these conditions.

A visualized analysis of this chosen SHM mixing structure from 1 µL/min to 2 µL/min shows only a homogeneous distribution. Even at a flow rate of 4 µL/min, a blue region can be observed in the center of the channel in ROI C, which becomes increasingly clearer as the flow rate increases.

In Figure 5 for SHM-structure (second row) for flow rate of 80 µL/min and 200 µL/min in both sections, a central channel of Coomassie fluid appears suggesting incomplete mixing.“

The calculation of mixing efficiency should be clearly presented in the manuscript, including the formula, assumptions, and any relevant parameters.

Re: We moved the calculation of the mixing efficiency plus formula plus assumptions from supplementary section into the M&M (lines 290-316)

“Calculations for the mixing efficiency and theoretical considerations: As demonstrated in other publications [50] the use of the standard deviation provides a way to estimate the dispersion of grayscale values within the area under consideration. This means that the more varied the grayscale values are, the higher the standard deviation, and the lower the mixing of the two fluids.

In the initial state (I₀), the grayscale profiles show two clearly separated plateaus corresponding to the two fluids, resulting in a maximal difference in grayscale values between them. In the fully mixed state (I_max), the grayscale values are nearly identical, and the differences between pixels approach zero.

Before analysis, the first and last ten pixels of the analysis rectangle (ROI A) were taken as representatives for the fluids in their unmixed states. The grayscale values determined along the pixel distance were exported to an R script for further processing.

To compare the mixing efficiency of the different mixing structures, each was analysed against the fully mixed state (I_max) in the channel. The standard deviation was determined for the three states: modified initial state (I₀), unknown state (Iₓ), and fully mixed state (I_max). The standard deviation provides a quantitative measure of mixing efficiency: standard deviation is high in the initial state, low in the fully mixed state, and the intermediate state Iₓ falls accordingly in between.

The mixing efficiency (ME) was calculated as:

 = standard deviation of grayscale values in the intermediate state (I_x),

 = standard deviation in the unmixed state (I₀),

 = standard deviation in the fully mixed state (Iₘₐₓ).

In this formulation, ME = 0% corresponds to the unmixed state, and ME = 100% corresponds to the fully mixed reference. This metric reliably captured the transition from unmixed to mixed states across flow rates and structures, while compensating for pixel-level artifacts and background noise introduced during the printing process.”

 

Providing an example of the image-processing workflow used for efficiency evaluation would improve transparency and reproducibility.

Re: Thank you for this suggestion. The procedure is described in detail in the M&M. However, due to the large number of figures (12), we would prefer not to add another figure here.

 

Sections 3.1, 3.2, and 3.4 are presented as Results but are more similar to Methods or procedural descriptions.

Re: These paragraphs were edited with an emphasis on active result presentation. However, we would like to point out that design and implantation are results which need to be presented in this section.

Line 475–480 discusses fabrication but does not provide adequate context or reference to previous literature. (In our first version it is line 484 -492))

Lines 500–503 claim comparisons with other fabrication methods without presenting supporting evidence. (In our first version it is line 493 -497)

Repeated references to “data not shown” are unacceptable and must be replaced with actual figures or quantitative data.

Re: We have shortened the introductory paragraph of the discussion omitting the comparison and have additionally cited reference 18,19,20,32,46,53 which deal with the issues of different 3D fabrication. We`d like to point out that in line 579 – 588 and 611- 615 we discuss surface roughness introduced through printing as shown by Macdonald et a. (19) and Zeratkaar et al (20). (also see M&M section 2.1 Manufacturing 3D-printed Micromixers lines 180-195 and in the introduction, lines 67–81 we provide the context for this argumentation)

The discussion of mixing efficiency is confusing, as parameters such as structure, flow rate, retention time, and fabrication technique are mixed together without clear separation.

Re: We have also restructured and rephrased paragraph 4.4 of the discussion. We discuss this sudden drop at 16µL/min from line 660 to 679 in reference to other reports which observed the same feature. It appears that this is a feature of serpentine-like passive mixed structures all show the mixing efficiency drop feature which is probably due to an imbalance in flow rate and residence time at low flow rates.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This study develops a 3D-printed microfluidic chip with phaseguides and mixing structures (SHM, TESLA, SAR). Results show SHM achieves high efficiency, enhanced by fluid breakers for flow-rate-independent mixing. This work can be considered after addressing the following issues:

1. In the introduction, it is suggested that the author address the following issues：

1) The author emphasized the significance of micro-mixing and introduced the research progress. The author has devoted a considerable amount of space to reviewing the current research status of microfluidic passive mixers (such as TESLA, SAR, and SHM structures) and the application of 3D printing technology, but has failed to clearly and systematically establish the logical relationship between these current situations and the work of this paper. In particular, the limitations or unsolved problems of existing research have not been explicitly pointed out, thereby weakening the innovation and necessity of the work of this paper.

2) The introduction lists various mixers but does not summarize common problems

3) The introduction provides a comprehensive background on microfluidic mixers, but recent literature citations can be added to reflect their cutting-edge nature. Literatures, for example, 10.1016/j.chaos.2025.116373、10.1016/j.colsurfa.2024.135969、doi.org/10.1016/j.aca.2023.341685、doi.org/10.1016/j.chaos.2021.111048 and doi.org/10.1016/j.icheatmasstransfer.2024.108191. It is suggested that the authors supplement the above content.

2. In the experimental section, the authors applied a wide range of flow rates (1-200μL/min), but it is recommended to convert them to the Re range, which is helpful for understanding whether the mixing mechanism is dominated by molecular diffusion or chaotic convection.
3. In the experimental section, the authors merely briefly described the extraction process of concentration. How was the mixed mass calculated? Please supplement the relevant calculation formulas.
4. In Figure 2, the authors conducted a quantitative analysis. So, why does the Tesla mixer experience a sudden drop in mixing quality when the flow rate is 16μL/min? After that, the mixed quality first rose and then declined. What is the reason for this? Why does the SHM mixer rise first and then fall in the second half of the flow rate? The author provides explanations in lines 582 to 596, but the reasons are too vague and lack relevant evidence. In addition, the flow rate range described in the experimental design did not mention the working condition of 16μL/min.
5. Figure 5, as a key intuitive evidence demonstrating the uniformity of mixing, has a very superficial interpretation, merely describing "homogeneous" or "non-homogeneous", without being closely associated and interpreted with the quantitative data (Figure 6).
6. The naming of the full-text mixer should be consistent. For example, TESLA and Tesla.

Author Response

For better overview the comments of reviewer are underlined.

Reviewer 3

 

Comments and Suggestions for Authors

This study develops a 3D-printed microfluidic chip with phaseguides and mixing structures (SHM, TESLA, SAR). Results show SHM achieves high efficiency, enhanced by fluid breakers for flow-rate-independent mixing. This work can be considered after addressing the following issues:

In the introduction, it is suggested that the author address the following issues：

• The author emphasized the significance of micro-mixing and introduced the research progress. The author has devoted a considerable amount of space to reviewing the current research status of microfluidic passive mixers (such as TESLA, SAR, and SHM structures) and the application of 3D printing technology, but has failed to clearly and systematically establish the logical relationship between these current situations and the work of this paper. In particular, the limitations or unsolved problems of existing research have not been explicitly pointed out, thereby weakening the innovation and necessity of the work of this paper.

Re: To clarify we have edited the introduction and added following sentences and paragraphs:

Line 157-159 “We were able to demonstrate advantages in the implementation of microfluidic structures but also show possible drawbacks of the use of 3D-printing in the used mixing structures.”

Line 166 – 174 “While simple designs are easy, highly efficient 3D structures (e.g. helical mixers) can be difficult and costly to fabricate and complex designs that enhance mixing (e.g. obstacle arrays) can significantly increase pressure drop, requiring more pumping power.

We designed novel geometries with optimized obstacle arrays to induce better chaotic flow with shorter lengths for low pumping power and simple manufacturing setup facing the key challenges of microfluidics.

We implemented 3D printed SAR-, Tesla-, SHM-structures along with a basic unperturbed channel into one chip and performed comparative mixing efficiency experiments”

• The introduction lists various mixers but does not summarize common problems

Re: We added the following sentence in lines 52 – 59 adding two recent reviews including one suggested by the reviewer:

“Common problems in passive micromixers include the need for long channels/high residence times for good mixing, challenges withclogging by particulates, poor performance with highly viscous fluids, complex fabrication for intricate designs, and achieving the right balance between high mixing efficiency and low pressure drop. While low-cost, they struggle with slow diffusion, requiring elaborate channel structures (serpentine, obstacles, etc.) to induce chaotic advection, which adds to manufacturing complexity and potential blockages, especially in biomedical uses.“

• The introduction provides a comprehensive background on microfluidic mixers, but recent literature citations can be added to reflect their cutting-edge nature. Literatures, for example, 10.1016/j.chaos.2025.116373、1016/j.colsurfa.2024.135969、doi.org/10.1016/j.aca.2023.341685、doi.org/10.1016/j.chaos.2021.111048 and doi.org/10.1016/j.icheatmasstransfer.2024.108191. It is suggested that the authors supplement the above content.

Re: We added DOI: 10.1016/j.aca.2023.341685 as reference 13 (line 59)

2. In the experimental section, the authors applied a wide range of flow rates (1-200μL/min), but it is recommended to convert them to the Re range, which is helpful for understanding whether the mixing mechanism is dominated by molecular diffusion or chaotic convection.

 

Re: We transferred the given flow rates into Reynolds number and added the results it into the supplementary material for orientation. The calculated data show that all Re numbers are below 2300. All of them would be defined as laminar. In order to get an impression nonetheless, we have implemented the corresponding Re numbers and their calculation in lines 224–232. However, we decided against the implementation of Reynolds numbers into the different figures of this publication, as this would not reflect the reality in this 3D-printed passive mixing structures.

To explain: Most groups use expensive mask, complex photolithographic setups etc. to generate exact copies of their CAD designs. Before a 3D-printed chip is realised, a CAD drawing (represented in Figure 3D) shows the design and planned dimensions. The transformation into the print file (Figure 7 left panel) generates a clearly pixelated map creating other structural elements, which when printed can influence the flow of the liquid. Experts of 3D-printing know that a round whole in a CAD drawing will be a slit in a resin-based system, so you have to design an oval whole to round it. Also due to the viscosity of the various resins printing results may differ.

 

3. In the experimental section, the authors merely briefly described the extraction process of concentration. How was the mixed mass calculated? Please supplement the relevant calculation formulas.

 

Re: In M&M lines 217-219 we detail the concentration used, we did not use an extraction process. The relevant bases for calculation of the mixing efficiency using the gray scale of both dyes unmixed and totally mixed are described in line .

 

4. In Figure 2, the authors conducted a quantitative analysis. So, why does the Tesla mixer experience a sudden drop in mixing quality when the flow rate is 16μL/min? After that, the mixed quality first rose and then declined. What is the reason for this? Why does the SHM mixer rise first and then fall in the second half of the flow rate? The author provides explanations in lines 582 to 596, but the reasons are too vague and lack relevant evidence. In addition, the flow rate range described in the experimental design did not mention the working condition of 16μL/min.

 

Re: In lines 467-472 we now provide the requested detail:

“An exception is the measurement of the Tesla-structure at a flow rate of around 16 µL/min, where a distinct decrease in mixing efficiency to 75% was noted. To exclude potential artifacts from 3D-printing irregularities, the experiment was repeated using a different mixing chip, incorporating additional measurements at 15 and 17 µL/min. This confirmed the observed "negative peak" in mixing efficiency (data not shown).”

 

We have also restructured and rephrased paragraph 4.4 of the discussion.

We discuss this sudden drop at 16µL/min from line 657 to 703 in reference to other reports which observed the same feature. It appears that this is a feature of serpentine-like passive mixed structures all show the mixing efficiency drop feature which is probably due to an imbalance in flow rate and residence time at low flow rates.

 

“A combination of two potential explanations for the reduction in mixing efficiency at 16 µL/min in the Tesla-structure can be proposed. First, the mixing efficiency drop might be due to an imbalance in flow rate and residence time at low flow rates. Second, due to potential 3D-printing artifacts, certain features of the structure might exhibit reduced functionalities.

Hossain et al. [58,59] who specifically investigated Tesla-structures, report a similar mixing efficiency drop. This mixing efficiency drop is also evident in other works on SAR and Tesla-structures [6,7,25,60]. All of these studies describe the following pattern: initially higher mixing efficiency at very low flow rates or low Reynolds numbers, followed by a decrease in efficiency as flow rates increase, and then an increase in mixing efficiency at specific flow rates and Reynolds numbers, depending on the investigated system. The explanation for this behavior is that low Reynolds numbers result in a higher residence time, allowing sufficient time for mixing via diffusion. As Reynolds numbers increase, residence time decreases, causing a drastic drop in mixing efficiency. However, if Reynolds numbers reach high enough values, turbulent flows enhance mixing, which leads to a rise in efficiency. The specific characteristics and corresponding Reynolds numbers can vary between systems and indeed may be subject to the structural features of the systems [7]. Only, Enders et al. did not observe the drop in mixing efficiency however having begun their measurements at flow rates ≥ 50 µL/min, they did not observe this effect of low flow rates. [32].

Numerous analyses of Tesla-structures were conducted, working with positive imprints of PDMS from SU8 materials. In our 3D printed structures, the mixing efficiency decreases significantly at higher flow rates (from 80 µL/min, Figure 6) and low residence times (less than 10 sec, Figure 10). Whereas Enders et al. documented a consistent enhancement in mixing efficiency with increasing flow rate we observed a decline of the mixing efficiency exhibited from 100 μL/min. In our experiments we used resin Next Dent Orange not tested in the Multijet 3D-printing system trials by Enders et al. [32]. Thus, the possibility of a resin-specific influence cannot be excluded. Indeed, the flow rate dependent performance of the Tesla-structure might be negatively influenced by voxelization artifacts, as well as the lamellar structures in the sidewalls resulting from the 3D-printing DLP process and potential resin-related issues (artifacts). Detailed analysis of the print file reveals possible weaknesses in the printing process, including noticeable pixelation, particularly in the wing structure, which could be replicated in the 3D-printed device (Figure 11).

Variations in the wing feature design can significantly impact the overall performance of mixing structure [60, 61]. Therefore, it can be hypothesized that the angular features of the wing structures may influence the performance of the Tesla-structure, particularly at higher flow rates. It appears that the “Coanda effect” no longer occurs in this 3D-printed version at a certain flow rate

 

5. Figure 5, as a key intuitive evidence demonstrating the uniformity of mixing, has a very superficial interpretation, merely describing "homogeneous" or "non-homogeneous", without being closely associated and interpreted with the quantitative data (Figure 6).

 

Re: The terms homogeneous and non-homogeneous are used to describe the distribution of fluids in the channel leaning on the ideal mixing state I_max. We observed different non-homogeneous distributions in the various mixing structures of the two liquids. We found three different types of incomplete mixing. The easiest to interpret exhibit a noticeable separation of the two differently coloured fluids. Another is an obviously homogeneous-looking distribution, but not yet totally (100%) mixed. The third, more complex distribution is specifically caused by the SHM-structures showing an unmixed areal in the middle of the channel.

We re-introduced figure S5 into the main text to explain in more detail the homogenous and non-homogenous mixing in the different mixing structures. This figure shows the ideal mixing state I_max with a homogenous distribution as a representative for an ideal complete mixing in the last column. This should help to facilitate interpretation of Figures 4 and 8.

 

An additional results section now details (lines 408- 417):

“A closer examination of the measured grayscale values revealed localized maxima that indicated regions of incomplete mixing. While the applied metric generally captured the transition from unmixed to mixed states across flow rates and structures, certain visual discrepancies between the observed and calculated values remained, particularly at higher flow rates. These inconsistencies were not fully resolved by the grayscale-based analysis method. Figure 5 presents selected frames from video recordings (full videos available in supplementary video section), corresponding to the ROI A, B, and C areas—defined as I₀ (completely unmixed), Iₓ (intermediate mixed state), and Imax (completely mixed via vortexing), respectively. To illustrate these unresolved differences, especially at flow rates ≥80 µL/min, representative snapshots have been included in Figure 5.”

 

6. The naming of the full-text mixer should be consistent. For example, TESLA and Tesla.

 

Re: We unified the designation as Tesla, throughout the manuscript

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I still think the Introduction is excessively long and reads more like a general textbook-style review of passive micromixers and 3D-printing rather than a focused, journal-style problem framing. Although laminar-flow diffusion limitations are mentioned briefly, the Introduction never clearly states which application domain actually needs improved mixing. Many previous works are listed (Macdonald, Hong, Tran-Minh, Stroock, Kwak, etc.), but the manuscript does not clearly articulate what specific gap in existing Tesla/SAR/SHM mixer designs remains unresolved. The actual aim only appears in the paragraph “Our work”, where it is buried after long descriptive text and still does not define a clear hypothesis or design question.

Sections 1.1 and 1.2 appear in reversed numerical order (Tesla labeled as 1.2 precedes SAR labeled as 1.1).

I recommend that the authors substantially shorten the literature survey and instead:
• Begin with a concise problem statement explaining why enhanced passive mixing is needed for the intended application.
• Clearly identify the gap in existing Tesla/SAR/SHM mixer performance or fabrication limitations that remains unresolved.
• Explicitly state the study objective and hypothesis at the end of the Introduction.

The Results and Discussion sections focus on the comparative performance of SAR, Tesla, and SHM mixers and, most importantly, on the improvement achieved by introducing fluidic breakers into SHM structures. The Conclusion briefly mentions measurement limitations but ends with a general outlook on 3D-printing, which is not the key point of this paper and does not reflect the actual main outcome.

The Data Availability Statement is not written correctly and appears to be copied from the journal instructions rather than formulated as a proper data availability declaration.

Author Response

Reviewer 2

 

Comments and Suggestions for Authors

I still think the Introduction is excessively long and reads more like a general textbook-style review of passive micromixers and 3D-printing rather than a focused, journal-style problem framing. Although laminar-flow diffusion limitations are mentioned briefly, the Introduction never clearly states which application domain actually needs improved mixing. Many previous works are listed (Macdonald, Hong, Tran-Minh, Stroock, Kwak, etc.), but the manuscript does not clearly articulate what specific gap in existing Tesla/SAR/SHM mixer designs remains unresolved. The actual aim only appears in the paragraph “Our work”, where it is buried after long descriptive text and still does not define a clear hypothesis or design question

Sections 1.1 and 1.2 appear in reversed numerical order (Tesla labeled as 1.2 precedes SAR labeled as 1.1).

Re: is changed into the right order

 

I recommend that the authors substantially shorten the literature survey and instead:
• Begin with a concise problem statement explaining why enhanced passive mixing is needed for the intended application.
• Clearly identify the gap in existing Tesla/SAR/SHM mixer performance or fabrication limitations that remains unresolved.
• Explicitly state the study objective and hypothesis at the end of the Introduction.

The Results and Discussion sections focus on the comparative performance of SAR, Tesla, and SHM mixers and, most importantly, on the improvement achieved by introducing fluidic breakers into SHM structures. The Conclusion briefly mentions measurement limitations but ends with a general outlook on 3D-printing, which is not the key point of this paper and does not reflect the actual main outcome.

Re: To address the concerns, we edited the introduction. We also essentially rephrased the final paragraph of the introduction which now explicitly details the challenges and aims of the study (lines 142-187):

“The study addressed a first challenge to develop a not too complex microfluidic passive mixing structure with few structural elements which would be easy to 3D-print. This short length mixing structure should show highest mixing efficiency independent from any differences in flow rate or residence time of the fluids in the mixing area. Another challenge is to find a solution to filling microfluidic systems without bubbles.

Unlike conventional meandric/serpentine passive mixing structures, SAR-; Tesla-, and SHM mixing structures choose various approaches to increase the residence time of the liquid either by extending the length of the channels or by significantly reducing the flow rates.

 

• In Meander-/serpentine channels and modified Tesla- and SAR-structures, mixing efficiency first fluctuates depending on the flow velocity and increasing Reynolds numbers.
• Depending on flow velocity asymmetrical SHM-structures can form a poorly mixable zone in the middle of the channel, regardless of the number of mixing structures used.
• Highly efficient 3D structures (e.g. helical mixers) can be difficult and costly to fabricate and complex designs that enhance mixing (e.g. obstacle arrays) can significantly increase pressure drop, requiring more pumping power.
• It is a challenge to achieve bubble-free parallel filling of two fluids into a passive mixing structure

 

To test if implementation of passive structures can be done by 3D-printing with biocompatible polymer resin “Next Dent Surgical Guide" (NDSG) [46], we implemented 3D-printed SAR-, Tesla-, SHM-structures along with a basic unperturbed channel into one chip and through comparative mixing efficiency experiments studied the performance of all three mixing structures.

For precise characterization of the mixing process, two water-soluble dyes with low diffusion coefficients, Congo red and Coomassie Blue, were chosen. This allowed for more accurate measurement of mixing efficiencies, isolating the effects of the mixing structures.

Studying the influence of printing artefacts on the mixing efficiency we showed a possible influence of 3-D artefacts on laminar flow in the unperturbed channel without any mixing structures, but only marginal effects on the performance of the chosen passive mixing structures.

The 3D-printed Tesla structures, demonstrate a loss of mixing efficiencies at higher flow velocities. For the uniform designed SAR-structure were not able to demonstrate high mixing efficiencies. The best mixing efficiencies were shown with the uniform asymmetrical SHM-structures, which however formed a poorly mixable zone in the middle of the channel.

To circumvent this specific problem we designed novel geometries with optimized central interrupting arrays to induce better chaotic flow with shorter lengths for low pumping power. Independent of the type of fluidic breaker implemented we are able to achieve a 100% mixing efficiency at flow velocities commonly used in microfluidic systems. For bubble-free and parallel filling we introduced a phaseguide-based T-shaped stop structure at the Y-shaped inlet of the mixing channel which clearly enhanced mixing consistency.”

Likewise, the conclusion paragraph was rephrased (lines 778-816):

.      “This study highlights the potential of 3D-printing technologies, specifically SLA-and DLP-based systems, in the design and optimization of microfluidic mixing structures. Among the various printing methods, DLP-based systems, particularly those from Way2Production (W2P), demonstrated superior performance in the fabrication of microfluidic mixing structures, surpassing SLA-based printers like the Form 3 in terms of resolution and structural integrity.

However, challenges related to resin residue and printing artifacts, such as the formation of voxel-like structures and layer-specific roughness, were identified. These factors could introduce artifacts, affecting the accuracy of mixing efficiency measurements, particularly when working with intricate designs. Despite these challenges, the Tesla- and SHM-structures showed considerable promise, with the Tesla-structure achieving impressive mixing efficiencies of over 90% at lower flow rates, albeit with a noticeable decline in efficiency at higher flow rates.

Mixing efficiency was evaluated by image analysis techniques, assessing the standard deviation of grayscale values, in conjunction with residence time analysis. This approach yielded detailed insights into the fluid dynamics within the tested devices and proved robust for quantifying mixing efficiencies, capturing both diffusive and advective contributions, while minimizing potential artifacts introduced during the 3D-printing process.

The findings suggest that the performance of 3D-printed mixers is influenced by several factors, including channel resolution, material properties, and the specific design of the mixing structure. Notably, the SHM-structure, with its asymmetric uniform design, exhibited the highest mixing efficiency across all tested flow rates, further underscoring the importance of geometry in microfluidic mixing. Additionally, the study supports the notion that the effectiveness of these mixing structures varies with flow rates, with lower flow rates leading to higher mixing efficiencies due to increased residence times.

Testing central breaker structures to disrupt a central volume column non mixing zone observed in the SHM structure successfully yielded highly efficient mixing independent of the breaker structure chosen. This new insight should help to improve to design shorter passive mixing structures in the future. Introducing a phaseguide at the Y-inlet provides a solution for bubble free filling of fluids at the inlet.

In conclusion, this study reinforces the significant potential of 3D-printing of passive mixing structures while highlighting the need for careful consideration of printing artifacts and material properties. Future work should focus on optimizing printing processes to minimize these artifacts and further explore the application of SHM- and Tesla-structures in a wide range of applications of LOC microfluidic technologies in the context of biomedical and chemical analysis e.g. in single cell analysis or bacterial diagnostics. Especially the non-newton fluid blood for (single) analysis would be very interesting to be tested here. “

 

The Data Availability Statement is not written correctly and appears to be copied from the journal instructions rather than formulated as a proper data availability declaration.

Re: The data availability declaration was updated as follows:

“The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author”

Reviewer 3 Report

Comments and Suggestions for Authors

I have no more questions.

Author Response

Thx alot for your reviewing.