Centrifugal Differential Mobility Analysis—Validation and First Two-Dimensional Measurements
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe study introduces a Centrifugal Differential Mobility Analyzer (CDMA) capable of 2D particle characterization. This approach is novel for aerosols research, particularly for nanoscale systems. The paper presents flow simulations of the measuring device and detailed experimental investigations of the transfer functions.
There are some issues that could improve the paper such as:
Justify the use of specific models (like the k–ω SST turbulence model) and explore its sensitivity to assumptions. Would alternative models (e.g., LES or DNS) provide greater accuracy, especially in non-laminar regions like the inlet and outlet?
Discussion of the comparisons with other established measurement techniques will help contextualize the CDMA’s performance.
How do the assumptions (e.g., neglecting particle diffusion or inertial effects in some derivations) influence the accuracy of particle trajectory predictions? Have sensitivity analyses been conducted to quantify these impacts?
Were the silver nanoparticles used as test aerosols representative of broader particle systems? Would using different particle materials or shapes change the performance of the CDMA?
The integration of scanning voltage modes is proposed to reduce measurement time. Could this introduce new challenges, such as susceptibility to aerosol generation fluctuations?
Author Response
Justify the use of specific models (like the k–ω SST turbulence model) and explore its sensitivity to assumptions. Would alternative models (e.g., LES or DNS) provide greater accuracy, especially in non-laminar regions like the inlet and outlet?
The SST model was selected due to the relatively small gaps present throughout the apparatus, as it provides more accurate results in the viscous sublayer of wall-bounded flows and offers greater numerical stability compared to the model. While Large Eddy Simulation (LES) or even Direct Numerical Simulation (DNS) would yield significantly more detailed results – particularly in capturing small vortices that might be present but are currently averaged out – the present simulation serves as an initial assessment of the flow conditions in the CDMA and their influence on the transfer function. Additionally, LES or DNS could provide further insights into whether currently observed losses originate from small-scale vortices in the inlet or outlet regions. However, such flow simulations are currently out of scope of this research project due to their complexity.
The statement regarding the choice of turbulence model has been revised for improved clarity, and reference to the use of LES and DNS simulations has been incorporated the section on numerical flow simulations.
Discussion of the comparisons with other established measurement techniques will help contextualize the CDMA’s performance.
Yes, that is correct. To address this, we have added a concise section in the introduction summarizing relevant literature on various measurement techniques for two-dimensional characterization.
How do the assumptions (e.g., neglecting particle diffusion or inertial effects in some derivations) influence the accuracy of particle trajectory predictions? Have sensitivity analyses been conducted to quantify these impacts?
We have applied the commonly used assumptions, which are highly valid in this context. For instance, considering the stopping distance. The maximum feasible flow velocity within the CDMA is approximately 1 cm/s. For a particle with a diameter of 1 µm, the stopping distance – the distance a particle would travel if the fluid were to come to a complete stop – is only 0.3 nm. Even at ten times this velocity, the particle would travel merely 3 nm. For smaller particles, the stopping distance is even shorter, indicating that particles of this size closely adhere to the streamlines and inertia is negligible.
In contrast, diffusion effects cannot be neglected, particularly for smaller particles. However, these effects are inherently accounted for in the transfer function. A previous study on this topic has already been published or is currently under revision (Rüther, T.N.; Schmid, H.J. Prediction of the transfer function for a Centrifugal Differential Mobility Analyzer by Streamline functions. Submitted in Aerosol Science and Technology.). Based on these results, the transfer functions derived without considering diffusion are afterwards corrected for the diffusion effects. Therefore, diffusion effects in the classifying region are properly accounted for in the findal transfer function. Additional diffusion effects, like losses in inlet and outlet tubing are accounted for by experimentally determined parameters of the real transfer functions. This is now explained in more detail in Sections 6.3 and 6.4 so that we hope it becomes easier to understand.
Further sensitivity analyses have not yet been conducted, as the effects in question were assumed to be minimal or, in the case of diffusion (at least in the final step), well-understood. However, such an analysis could provide valuable insights into the actual behavior and should be considered for future investigations. A brief suggestion of this has been included in the conclusions.
Were the silver nanoparticles used as test aerosols representative of broader particle systems? Would using different particle materials or shapes change the performance of the CDMA?
From our perspective, these assumptions are valid. We also employed an FMAG( Flow Focusing Monodisperse Aerosol Generator – TSI 1520) to generate DEHS particles, which are spherical and possess a significantly lower density than silver, and the process worked quite effectively. These results are presented in (Rüther, T.N.; Rasche, D.B.; Schmid, H.J. The POCS Algorithm – An Effective Tool for Calculating 2D Particle Property Distributions via Data Inversion of Exemplary CDMA Measurement Data. Submitted to Aerosol Science, currently under revision). However, additional measurements could not be conducted at this stage due to the requirement for a highly stable aerosol generation process, which needs to remain constant for at least four hours—an outcome that is challenging to achieve. This problem will be significantly reduced when a voltage scanning approach will be implemented in the near future.
However, we are convinced that the distinct advantage of the CDMA is that is not only works for different materials and particle structures, but that it even allow to characterize these properties in detail.
We have included a statement in the conclusions suggesting the need to validate the process for a broader range of materials and particle sizes.
The integration of scanning voltage modes is proposed to reduce measurement time. Could this introduce new challenges, such as susceptibility to aerosol generation fluctuations?
Voltage scanning is well established in DMA measurements, i.e. Scanning Mobility Particle Sizing (SMPS). From these experiences we know that scanning works pretty efficient since idle times after increasing the voltage do not exist any more. However, if the scan time is reduced too extensively, the statistical data quality degrades since only small numbers of particles of a given mobility are assessed. Of course this error directly correlates with the inverse of the particle concentration in the aerosol. Long-time fluctuations of the particle source are even of less importance, since all fluctuations will deteriorate the measurement result. Therefore, the shorter the measuring time, the less influence of particle source fluctuations. Short-time fluctuations can be accounted for by using longer scan times. On the other hand, shorter measurement times due to scanning compared to the current stepwise voltage increase are mandatory for capturing more transient processes, which may only remain stable for short periods, such as half an hour.
Reviewer 2 Report
Comments and Suggestions for AuthorsI really like the work and the approach. The CDMA principle offers highly interesting new possibilities to characterize nanoparticles in the gas phase.
The manuscript is extremely difficult to read as the way the data is presented as too long though and needs a major revision. It needs to be better structured in detail. On the one hand, it contains too much information that is not essential; on the other hand, it lacks an easily understandable, brief but comprehensive description of the functional principle.
In the individual sub-chapters, things are too often taken for granted that are incomprehensible to someone who has not studied the other three papers.
=> Is all the information given really necessary? Can someone who did not study the other three papers understand, what this paper is about?
In "6.3. Determination of the transfer function parameters for τe = 0 and Ze = 0 at different β-values" I got lost: Why is β the best parameter to characterize the CPDMA, what is β by the way... Can be found in nomenclature...
I am sure that this will be a very nice paper.
Please see attached file with comments and some exemplary suggestions.
Comments for author File: 
Comments.pdf
I am not the best person to give advice on improvements of English Language, but the manuscript contains some German-sounding formulations. Even more important many sentences are hard to understand as they are by far too long.
Author Response
The manuscript is extremely difficult to read as the way the data is presented as too long though and needs a major revision. It needs to be better structured in detail. On the one hand, it contains too much information that is not essential; on the other hand, it lacks an easily understandable, brief but comprehensive description of the functional principle.
We have made a concerted effort to enhance the overall structure of the paper, aiming to improve its clarity, coherence, and readability. Particular attention has been given to organizing the content in a more logical and accessible manner to facilitate comprehension for a broad readership. Additionally, a concise description of the operating principle has been incorporated to provide readers with a fundamental understanding of the key concepts and mechanisms discussed in the study. These revisions are intended to ensure that the paper effectively communicates its findings while maintaining a high level of scientific rigor.
In the individual sub-chapters, things are too often taken for granted that are incomprehensible to someone who has not studied the other three papers. => Is all the information given really necessary? Can someone who did not study the other three papers understand, what this paper is about?
The authors have made a deliberate effort to explicitly identify and elaborate on fundamental concepts within the text, thereby reducing the amount of prior knowledge required for a comprehensive understanding of the paper. By clarifying key assumptions and underlying principles, we aim to make the content more accessible to a broader audience, particularly to those who had not read our previous papers and even including those who may not be experts in the field. However, given the complexity and depth of the subject matter, it is neither practical nor feasible to reiterate all relevant background information in every instance. To maintain the paper’s focus and conciseness, references to previous publications are provided where necessary, allowing readers to consult foundational studies for a more in-depth exploration of specific topics.
In "6.3. Determination of the transfer function parameters for τe = 0 and Ze = 0 at different β-values" I got lost: Why is β the best parameter to characterize the CPDMA, what is β by the way... Can be found in nomenclature...
The flow ratio $\beta$ directly influences the width of the transfer function, with smaller $\beta$-values resulting in a narrower transfer function. Consequently, a lower $\beta$ leads to an improved resolution, as it enhances the system’s ability to distinguish between closely spaced particle sizes. This relationship is crucial in optimizing measurement precision and ensuring accurate characterization of the aerosol properties.
So we inserted this into the text and also gave the definition of the beta value.
Further Comments:
The abstracts jumps right into very specific details. It would be helpful for readers who are not experts but might have research questions that are answered by the CDMA to get a bit more information what it does. What is meant with “complex shaped technical aerosols? , what parameters, what size range? “e.g. of aggregates at different sintering stages.”
Nice example for what CDMA is useful for.
“The inversion of the data is conducted using the projection onto convex sets approach.” Already lost as none expert.
We have revised the abstract completely to improve clarity and ensure that the key information is more accessible to non-experts. The revised version enhances readability while maintaining scientific precision, making complex concepts easier to understand. Additionally, we have adjusted the wording to provide a clearer presentation of the study’s objectives, methodology, and key findings.
“Naturally,…” German?
The original wording closely resembled German sentence structures and phrasing. To improve clarity and readability in English, we have carefully revised and restructured the entire section to better align with standard academic English conventions. This involved not only adapting individual sentences but also refining the overall flow and coherence of the text.
Confusing: …giving structural information at least by a 2D projection. … can measure 2D distributions.
We have also revised and refined the wording of the paragraph to improve clarity and ensure a more precise scientific expression. In particular, to prevent potential misunderstandings regarding the term "2D," we have replaced "2D projection" with "projection area." This adjustment more accurately reflects the information provided by scanning electron microscopy (SEM) images, as these images can offer insights beyond just two size parameters.
Requires the reader to exactly know, what it is about. Needs to be explained: “However, these methods are complex in terms of the equipment which makes it expensive and requires a high degree of expertise. Furthermore, in the case of two classifiers the resulting particle concentration at the exit is typically extremely low resulting in poor statistics of the resulting size distributions or very long measurement times.”
We have also reworded and clarified this paragraph to improve its readability and scientific precision. In particular, we have emphasized the issue of significant particle losses that arise due to the convolution of both transfer functions. When particles are required to pass through two classifiers in tandem, they experience compounded losses at each stage of classification, which leads to a substantial reduction in the overall particle concentration. This dual filtration effect exacerbates the challenges associated with accurately measuring particle size distributions, as it results in a smaller fraction of particles being detected and measured. Consequently, this convolution not only impacts the statistical reliability of the size distributions but also necessitates extended measurement times or the need for more sophisticated statistical methods to ensure robust data acquisition.
True in case of environmental aerosols. Incorrect in most cases of engineered Nanoparticles Line 39: Dynamic Differential Mobility Analyzer (DMA)
Here, the term "dynamic" was incorrectly used instead of "differential." We have since corrected this error by replacing "dynamic" with "differential" to align with the proper scientific terminology.
The Introduction should more clearly state, what the purpose of the CDMA is. Furthermore, how does this paper add to the three other papers that have been published on this topic. It would be helpful for the understanding if those papers would be mentioned in the Introduction already, with a short information, what they are about.
We are convinced that the extensive revisions made to the first section have significantly improved its clarity and comprehensiveness, offering a much more robust overview of the Centrifugal Differential Mobility Analyzer (CDMA). The changes aim to enhance the reader's understanding of the fundamental principles and functionality of the CDMA, ensuring it is presented in a more accessible and coherent manner. In addition, we have provided a concise classification of our related literature, contextualizing our other papers and their contributions to the CDMA. Through these revisions, we aim to provide a more seamless integration of previous findings, while clearly illustrating the unique contributions of this study.
(at least) A short explanation of the two principles that are applied are necessary.
The authors hope that the provided information now is sufficient for a clear understanding of the fundamental principles underlying both the Differential Mobility Analyzer (DMA) and the Aerodynamic Aerosol Classifier (AAC). To further clarify these concepts, additional explanations have been included in the text. This enhancement aims to ensure that the key operational principles of both instruments are explicitly articulated, allowing for a more thorough comprehension of their roles and interrelationships in aerosol characterization.
, ω denotes the rotational velocity of what?
It is the speed of both cylinders. We added this.
Equation 3: What is dv? Found in Nomenclature, explain for easier readability.
Sorry – the explanation was indeed missing. We added this information here.
Line 79: If the theory has been described in /8/, it would be helpful to refer to “For further information, see [8]” at the beginning of the section.
We added this context at the beginning of that chapter, too.
- Numerical… L97: the k − ω SST turbulence model Reference?
We added a reference.
L115: …were resolved with greater precision. It does not become clear what “greater precision” mean? Is it important?
It is a standard practice to use a higher resolution at the boundaries and in regions where flow disruptions occur to ensure more accurate representation of overall flow behavior while limiting numerical effort.
L116: … β = 0.2 (Qa = Qs = 0.3 l/min, 116 Qsh = Qex = 1.5 l/min) Why have theses values been chosen for the CDMA experiments?
These values were determined based on preliminary tests, the methodology and results of which are discussed in detail in the first paper. To ensure transparency and reproducibility, we have included the appropriate reference and provided a more comprehensive explanation of the rationale behind their selection.
Fig3: Why is there a solid red line at position x = 0.151m Being not familiar with the design, it is difficult to extract information.
This marks the location where the aerosol stream merges with the sheath air, effectively representing the endpoint of the inlet region. To enhance clarity, we have incorporated this information both in the figure caption and within the main text, ensuring a more precise description of the flow dynamics at this critical junction.
Fig. 5: Flow direction? An arrow would improve readability of sketch. What do the black arrows mean? Relative velocity to what?
We reworked that figure. Hopefully it is clearer now.
Fig. 6: x = 0.16m line, 475RPM: Why uneven?
We reworked the diagrams. Now the plots are even.
Figure 6. Plots of the axial velocities for 475RPM and 2000RPM. Left: at Ï• = 0 â—¦ with respect to radial coordinate r. Right: at the middle of the classification gap (r¯ = 72.6 mm, see also dashed line left).
Dashed line left: Which one of the 6?
We changed it to a dotted line, to make the difference visible.
Radius r and radial coordinate r is confusing.
However, the authors consider this distinction to be meaningful. While the radial coordinate inherently represents a range of values, refers to a single specific value, namely a radius. An alternative approach could be renaming ​ to . If the reviewer requests this modification, we will implement the change accordingly.
Fig. 7: sheathairinlet… three words… I do not understand the figure. What is the essential information? How are the two planes arranged within the CDMA? Top down view left side: Very “messy”.
Fig. 8. Consider optimised presentation. The important part, the area in which the flow stabilises, is shown too small. Zoom in on inlet region? T
We have revised this section and replaced Figures 7 and 8 with a new figure that provides a more comprehensive and intuitive overview. Additionally, we have thoroughly restructured and refined the paragraph to enhance readability, coherence, and logical flow. These improvements aim to make the discussion more accessible and ensure that the key points are conveyed more effectively. We hope that these modifications contribute to a clearer and more structured presentation of the content.
L139: Obviously, there is no cross mixing or back circulation, but the streamlines of the particle laden aerosol flow widen considerably which is due to two different reasons: This is not obvious…Problem: Many diagramm and sketches that are difficult to interpret
We have revised the text to enhance clarity and provide a more comprehensive explanation. In particular, we aimed to ensure that the underlying concepts are more accessible and better structured. Additionally, we have adjusted several figures to improve their interpretability, making it easier for the reader to grasp the key aspects of the analysis. We hope these modifications contribute to a clearer and more coherent presentation of the subject matter.
L151: At higher rotational speeds however, a larger flow length is required until a homogeneous distribution in circumferential direction is achieved. Where can I see that? Most likely the information is there, but it is not obvious.
We reworked the whole paragraph including the figures. Hopefully it’s much clearer now.
L167: It has not become clear what “the deflection bent” is
It should be the same as the sheath air arc. We changed the wording here. Hopefully it is clearer now.
Figure 8: Is “end of sheath air arc” the same as “deflection bent”? Does this figure really show what you want to explain? The individual arrows of the flow field are not visible, which probably is not a problem. As a reader I just wonder why it looks so messy. I recommend to “clean” this figure up and focus on the message. Is it really necessary to show the entire length or would it be sufficient to show only the section, where the flow stabilizes plus “a bit”. Flipped by 90 degree the same size of the figure would give a lo more space for details.
Thank you for your valuable comment. In response, we have revised the figures to provide a clearer and more comprehensive representation of the investigations conducted. We hope that these improvements significantly enhance both the readability and the contextual understanding of this chapter.
L181 Consequently, the boundary profiles are of primary interest, as the particles are traveling there first, but they they stabilize relatively quickly.
Who is “they”? Or what does is meant with “the particles” stabalize?
We intended to emphasize that the velocity profiles near the walls, particularly close to the inner wall, are of primary interest. Since the velocity profiles stabilize at the walls first, any initial distortion in the central flow region should have a minimal impact on particle trajectories. As the flow profile in the center stabilizes later – i.e. the flow profiles converges towards the fully developed flow – this effect is expected to diminish. We have revised this section to provide a clearer formulation of our argument and hope this now better conveys our intended message.
L184 When particles lag behind the rotational speed, they do not experience the full centrifugal force.
Why would particles “lag behind the rotational speed”?
Particle in principle follow the flow inertialess as discussed above. The problem is the development of the fluid flow profile: The rotational velocity of the fluid has to increase with the radius (particularly upstream of the classifying region). This increased rotational velocity has to be accomplished by shear forces induced at the walls. As a consequence, the airflow in the radial direction is accelerated, particularly in the central region of the flow. This leads to a delay in the rotational speed there. We hope that this explanation now provides a clearer understanding of the phenomenon.
L180 – L191: This paragraph is not clear to me. Is this a summary of reference /8/, which is not yet available?
We reworked that statement.
5.2 Ideal transfer function based on streamline approach
/9/ references paper that has not been published yet.
Yes, that’s right. It has been in the review process for a long time. Now it’s resubmitted and will hopefully be accepted in very due time, to insert the correct reference and the doi.
L 326: where the gap width is small, fovoring diffusion, favoring
We changed this.
Figure 19: Extremely busy and hard to read. Consider reduction and focus on most important parts. Would a top-view (instead of 3D plots) be easier to read?
We changed it to two-dimensional plots.
It is not clear to me, what additional information Figure A1 gives.
Our intention was simply to provide an additional schematic to improve the understanding of the sections and the specific components under investigation. However, if preferred, we are open to removing it.
Appendix B is interesting in a way, but is it necessary for this paper? It would be sufficient to state that transfer functions of three DMAs have been compared and the two that have been used for this 3 study agree with in xy%
Yes, that is correct. However, this specific approach to determining transfer functions has not been conducted in this manner before, particularly with a subsequent comparison of different DMAs. Given the crucial role of accurately determining the transfer function of the preclassifying DMA, the authors deemed it essential to provide a detailed description of this procedure. This ensures that readers have the necessary information to reproduce the method themselves and achieve comparable results, thereby enhancing the transparency and reproducibility of the findings.
However, if the reviewer and/or editor do not consider this worth taken into the appendix we would be open to include it as supplementary material only.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors have created a novel integration of two standardized measurement tools – DMA (Differential Mobility Analyzer) and AAC (Aerosol Apparatus for Characterization) – to directly assess the morphological characteristics of nanoparticles. This method is advantageous since it facilitates the concurrent examination of distinct particle characteristics.
Nonetheless, the difficulties in merging these two technologies are substantial, as the impact of the centrifugal force field on particle distribution and motion, and consequently on the symmetry of the flow field, is tremendous. Accurate modeling is essential for deriving dependable outcomes from the measurement data. Despite considerable diffusion losses in the experimental investigation of wellknown particle systems, the measurements that were conducted were feasible. However, they necessitated a sophisticated preparatory estimate of the transfer function. This transfer function is essential for accurately interpreting measurement findings and quantifying all of the losses. The authors' willingness to construct a prototype and thoroughly investigate the various elements affecting the measurement data is particularly commendable
Comments for author File: Comments.pdf
Author Response
We gratefully acknowledge the large effort the reviewers have taken to study our manuscript and to give very valuable comments and suggestions. We apologize that the paper did not meet the quality requirements of the reviewers as our owns.
We revised the manuscript very carefully in order to caerully take into account all comments of the reviewers. We believe, that the manuscript increased drastically in clarity and readability.
In the following, we will comment on each individual comment and we will briefly explain how we took the respective comment into account.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsDear author
The manuscript is excellent from my point of view and I recommend the publication and have only found a few typos. Otherwise, I think it can be published as is.
Please see the attached letter
Kind regards!
Comments for author File: Comments.pdf
Author Response
Many thanks again to the reviewer, for this very nice review with even well further suggestions!
1.) Excellent abstract and introduction.
Thank you very much!
2) Just an idea: Did you consider using the CDMA for measuring unipolar charging efficiency of (fractal like) agglomerates?
Indeed, the intention is to utilise this method to initially validate the charge distribution of spherical particles. However, the extension to a unipolar charge distribution has not yet been considered, and could become a really interesting task after this first step.
3.) Page 3 – Line 129: first dst must be dv
Yes, we changed it.
4.) Figure 1 + Description: Excellent. Maybe print A & B in bold or in another color (e.g. green?)
We printed it in bold letters.
5.) Page 5 line 169 ..
We deleted the double dot.
6.) 4. Numerical flow simulation: Excellent!
Thank you!
7.) Figure 2: Very good! It really helps to understand the geometry and the complexity of the simulation.
Thanks!
8.) Page 6 … it is a pleasure reading this…
Again thank you!
9.) Figure 4: No need to change, but having the axial flow velocity as x-axis in both cases would make it easier to follow... (I think the problem is, that I still struggle with the rotational coordinate…)
We changed this according to your advice.
10.) Figure 5: While thinking about it, I thought it might have been nice to have a scale bar. The information is in the paper, but it is tedious to find it. (No need to change, a nice to have).
Ideed.
11.) Page 8 line 262 … is based on the current simulation model … just for easier reading.
Done.
12.) Page 12 line 342-345: A) English. B) Vortices: This is an assumption. Simulation does not show that. => Likely…
A) We improved our wording.
B) Inserted “likely”.
13.) Page 12 line 351 … and higher mass (the but does not make sense to me).
Done.
14.) Page 13 line 368 … assumed ans as …
Done.
15.) Page 15 line 425 a Ruether…
Done.
16.) Page 17 line 514 … a smaller drag force than…
Done.
17.) Page 18 line 529 more irregularly , shaped
We deleted the comma.
18.) Page 18 line 539 (suggestion): for generating particles more efficiently
Indeed, that’s a much better formulation!
Reviewer 3 Report
Comments and Suggestions for AuthorsI appreciate your efforts in rewriting the manuscript and integrating my remarks. All of my recommendations have been comprehensively addressed. I consent to the publication of the manuscript.
Author Response
Once more, the author wishes to express their profound gratitude to the reviewer for their diligent efforts in meticulously reviewing and enhancing the quality of this article.
