the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The Centrifugal Differential Mobility Analyser – A new device for determination of two-dimensional property distributions
Abstract. Usually, for the characterisation of nanoparticles an equivalent property is measured, e.g. the mobility equivalent diameter. In the case of non-spherical, complex shaped nanoparticles, one equivalent particle size is not sufficient for a complete characterisation. Most of the methods utilised to gain deeper insight into the morphology of nanoparticles are very time consuming and costly or have bad statistics (such as tandem-setups or SEM/TEM images). To overcome these disadvantages, a prototype of a new compact device, the Centrifugal Differential Mobility Analyser, the CDMA, was built, which can measure the full two-dimensional distribution of mobility and stokes equivalent diameters by classification in a cylinder gap, through electrical and centrifugal forces. An evaluation method to determine the transfer probabilities is developed and used in this work to compare the measurement results with the theory for the pure rotational behaviour (like the Aerodynamic Aerosol Classifier) and the pure electrical behaviour (like the Dynamic Mobility Analyser). In addition, the ideal two-dimensional transfer function was derived using a particle trajectory approach. This two-dimensional transfer function is a prerequisite for obtaining the full two-dimensional particle size distribution from measurements by inversion.
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RC1: 'Comment on ar-2024-29', Anonymous Referee #1, 03 Nov 2024
The manuscript describes a very interesting novel aerosol classifier, the CDMA, that combines the concepts of the well-established differential mobility analyzer (DMA) and the still rather new aerodynamic aerosol classifier (AAC). With this combination, it will eventually be possible to carry out measurements of the number size distributions in terms of the electrical mobility as well as the aerodynamic diameter with one device. This would reduce both the experimental equipment effort and the time for such measurements. The instruments appears to be thoroughly designed and the experiments conducted for the first characterization are meaningful. The manuscript therefore merits publication, but will need to be revised, before it may be accepted.
Major concerns:
- The use of the different equivalent diameters is confusing. In the abstract, it is mentioned that the CDMA could measure size distributions based on the mobility and Stokes equivalent diameter. To the best of my knowledge, these two are the same. Apparently, this should be the mobility (or Stokes) and aerodynamic diameter. After reading Appendix A, I can follow the authors’ arguments for using the mobility diameter in the calculation of the Cunningham factor and thus the particle relaxation time. For a spherical particle, the mobility (or Stokes) diameter equals the geometric diameter, which describes the curvature of the sphere’s surface, which is responsible for the molecular slip. Nonetheless, the classification in the AAC mode is still density-dependent and consequently based on the aerodynamic and not the Stokes diameter.
- From the title of the manuscript, I would have expected a fully characterized device. However, the conclusion is that improvements are needed and shall be implemented in a second prototype, for which a more comprehensive evaluation will be conducted. I therefore suggest to make this clearer in the title by including terms like “concept” or “initial validation”.
- The manuscript uses many equations with a multitude of different symbols. I found it a bit cumbersome to search for the meaning of the different symbols, at places where they were not used for the first time. I therefore suggest to add a nomenclature in the beginning or in an appendix (depending on the publisher’s policy on that).
- It seems that all trajectory calculations assumed plug flow and no hyperbolic flow. Is this justified or a simplification? This should be discussed in the manuscript.
Line 13: The first sentence of the introduction does not really have any content. I suggest eliminating it.
Line 15: A DMA classifies particles based on the (electrical) mobility diameter. I only know the term “hydrodynamic diameter” from the characterization of particles in liquids.
Lines 18ff: The discussion on particle surface area appears completely out of the blue and is not picked up again in the manuscript. Either explain in more detail why this is important for this work or eliminate this discussion.
Line 29: What is described here as tandem setups does not necessarily contain two or more measurement systems, but usually just different classification systems.
Line 51: The flow is not applied to the inner cylinder, but introduced near the cylinder.
Line 56/equation 1: The force balance is typically written as q*E + Fdrag = m*a. Here the drag force will receive a negative sign due to the direction of the relative velocity between particle and flow. In the way that equation (1) is set up, the signs do not seem to fit.
Line 65: it should read inner r1 and outer r4 radius.
Lines 91ff: Please provide information on the flow rates of the CDMA.
Line 92: The density should be either 1 g/cm³ or 1000 kg/m³
Line 94: I don’t understand this. Ok, you need a suitable sealing for the device, but why “for both the mobility and the Stokes diameter” (again, Stokes should be aerodynamic diameter, but that is not the reason why I don’t understand the sentence).
Lines 98/99: It would be helpful if you could indicate the location of these seals in Figure 2.
Lines 99-109: 1) Which polarity do you apply, i.e. which particle polarity do you classify?; 2) A voltage is always applied between two electrodes by applying different potentials to the individual electrodes, 3) Why is the high potential applied to the outer cylinder and the low potential (ground) to the inner cylinder? What about precautions for user safety?
Line 154: “radii” should read “radius”
Line 155: What do you mean with “particles already have a larger radius”?
Line 169: Figure caption of Figure 5: Are these “streamlines” or particle trajectories?
Line 173: What is meant with “…the transfer function of the two transfer functions…”?
Line 177-182: Please describe your measurement setup and parameters in sufficient detail: e.g. what is the “previous” instrument? What DMA flow rates did you adjust? Which neutralizer was used (85-Kr or x-ray)? Which particle polarity did you classify?
Line 186: “silver precipitates as nanoparticle”: Do you mean that the silver vapor nucleates to form nanoparticles?
Line 190/191: The sentence, starting with “Because it takes approximately 30 minutes” doesn’t make sense. Isn’t it rather that the time it takes for a complete scan defines the requirement for the stability of the test aerosol?
Line 201/Figure 8: Every figure should generally -in conjunction with its caption- be self-explanatory. Figure 8b is far from this requirement. E.g. what are the “measurement data”? Axis caption (µ-1) and n2/n1 are also not described. Please modify the figure in a way that it is at least fundamentally (i.e. not in every detail) understandable without the need to read the text.
Line 272: The charge distribution of neutralized particles is more a convention rather than the ground truth. I would therefore always phrase that it is assumed to be known. Please add a reference for the charge distribution that you used (Wiedensohler approximation?)
Line 274: “simply” should read “singly”
Line 327 (Appendix B): dm and dSt doesn’t make much sense (see above), this should be dm and dae.
Citation: https://doi.org/10.5194/ar-2024-29-RC1 -
AC1: 'Reply on RC1', Torben Rüther, 06 Nov 2024
Thank you very much for the helpful comments!
We formulated a response letter which is attached in the supplements.
- AC2: 'Reply on AC1', Torben Rüther, 06 Nov 2024
-
RC3: 'Reply on AC1', Christof Asbach, 19 Nov 2024
I would like to thank the authors for a very thorough review of the manuscript and for adding the nomenclature. I agree with all the changes made and would recommend acceptance of the manuscript as-is, but I still struggle with the use of the use of the equivalent diameters (Stokes, mobility and aerodynamic). I revisited the definitions in both Hinds (2022) and Kulkarni, Baron and Willeke (2011) textbooks and agree (and learned) that Stokes and mobility diameter are not necessarily the same. For spherical particles, however, they are identical, as was also implicitly pointed out in the author response with the equation dSt2 = dv3/dm. It should also be noted that the Stokes-Einstein equation (D = kTB) is defined by the particle mobility and thus the mobility diameter. I can see the similarities between the definitions of the Stokes and aerodynamic diameters as pointed out in the author response, i.e. both are defined via the settling velocity. However, the crucial difference is that the Stokes diameter assumes the true particle density, whereas the aerodynamic diameter standardizes the particle density (and shape) and assumes a common density of 1000 kg/m³. Consequently, all particles with the same aerodynamic diameter will encounter the same settling velocity, whereas particles with the same Stokes diameter will migrate at different settling velocities, if they have different particle densities. Similarly, in any force balance between a particle mass-based driving force (such as gravity or the centrifugal force) and the counteracting drag force, all particles with the same mass to drag ratio (i.e. also for different combinations of size and density) will migrate at the same velocity. This is why the AAC and the CDMA in AAC-mode classify particles based on the aerodynamic diameter (irrespective of their geometric size, shape and density), whereas particles with equal Stokes diameter, but different densities would be differently classified. Mentioning that the instrument could differentiate between mobility and Stokes diameter therefore appears misleading to me.
That said and to avoid any confusion in the paper, I suggest to only use the terms mobility diameter and aerodynamic diameter, which are also the commonly used equivalent diameters for DMA and AAC, respectively, and to avoid the Stokes diameter. Since the classification in the CDMA is based on the (electrical) mobility and inertial (aerodynamic) properties, this would –in my opinion- be clear and straightforward.
Citation: https://doi.org/10.5194/ar-2024-29-RC3 -
AC4: 'Reply on RC3', Torben Rüther, 24 Nov 2024
We gratefully acknowledge the valuable comments of referee#1 on our revisions.
Based on these comments we agree that we missed to clearly clarify our intentions in the manuscript and that the claim that the CDMA can differentiate according to the Stokes diameter may appear misleading. We regret that we missed to discuss this important issue in detail before.
Therefore, we added a paragraph explaining the different approaches and the reason why we prefer to use the Stokes diameter for characterization (since we primarily aim for shape characterization). However, we clearly outline, that this requires knowledge of the (exact) particle material density. In this case, we still think, the Stokes diameter is the better choice for 2D particle characterization with the CDMA. However, an inversion for aerodynamic diameter would be possible as well, however for the sake of loosing direct information on particle shape.
We hope that the new paragraph helps the readers to better understand the suggested approach without being misleading any more.
-
AC4: 'Reply on RC3', Torben Rüther, 24 Nov 2024
-
RC2: 'Comment on ar-2024-29', Anonymous Referee #2, 15 Nov 2024
This is an excellent paper on a novel concept for obtaining a two-dimensional size distribution (mobility and Stokes-equivalent). This novel instrument is well described and thoroughly tested. The experimental approach and analysis is excellent. Enough ideas emerged for a second, more performant instrument. Nevertheless, these results need to be published.
Overall, I guess that the main drawback of this instrument will be the fact that in a certain selected mobility diameter interval there will be quite a number of particles having a multiple charge, and by consequence having a different mass range and therefore also different Stokes-equivalent size ranges. This will make a precise inversion algorithm quite complicated (but not impossible).
Most of the minor comments were already made by referee no.1.
Citation: https://doi.org/10.5194/ar-2024-29-RC2 -
AC3: 'Reply on RC2', Torben Rüther, 18 Nov 2024
We are very grateful to the reviewer for the positive feedback and for taking the time and effort to review the manuscript.
And regarding the problem of multiple charges, you are absolutely right. To solve this, we have chosen and implemented an iterative approach to data inversion (projection onto convex sets), which gives very promising first results. These results are currently being prepared for publication in a separate paper which will be submitted in due future.
Citation: https://doi.org/10.5194/ar-2024-29-AC3
-
AC3: 'Reply on RC2', Torben Rüther, 18 Nov 2024
Status: closed
-
RC1: 'Comment on ar-2024-29', Anonymous Referee #1, 03 Nov 2024
The manuscript describes a very interesting novel aerosol classifier, the CDMA, that combines the concepts of the well-established differential mobility analyzer (DMA) and the still rather new aerodynamic aerosol classifier (AAC). With this combination, it will eventually be possible to carry out measurements of the number size distributions in terms of the electrical mobility as well as the aerodynamic diameter with one device. This would reduce both the experimental equipment effort and the time for such measurements. The instruments appears to be thoroughly designed and the experiments conducted for the first characterization are meaningful. The manuscript therefore merits publication, but will need to be revised, before it may be accepted.
Major concerns:
- The use of the different equivalent diameters is confusing. In the abstract, it is mentioned that the CDMA could measure size distributions based on the mobility and Stokes equivalent diameter. To the best of my knowledge, these two are the same. Apparently, this should be the mobility (or Stokes) and aerodynamic diameter. After reading Appendix A, I can follow the authors’ arguments for using the mobility diameter in the calculation of the Cunningham factor and thus the particle relaxation time. For a spherical particle, the mobility (or Stokes) diameter equals the geometric diameter, which describes the curvature of the sphere’s surface, which is responsible for the molecular slip. Nonetheless, the classification in the AAC mode is still density-dependent and consequently based on the aerodynamic and not the Stokes diameter.
- From the title of the manuscript, I would have expected a fully characterized device. However, the conclusion is that improvements are needed and shall be implemented in a second prototype, for which a more comprehensive evaluation will be conducted. I therefore suggest to make this clearer in the title by including terms like “concept” or “initial validation”.
- The manuscript uses many equations with a multitude of different symbols. I found it a bit cumbersome to search for the meaning of the different symbols, at places where they were not used for the first time. I therefore suggest to add a nomenclature in the beginning or in an appendix (depending on the publisher’s policy on that).
- It seems that all trajectory calculations assumed plug flow and no hyperbolic flow. Is this justified or a simplification? This should be discussed in the manuscript.
Line 13: The first sentence of the introduction does not really have any content. I suggest eliminating it.
Line 15: A DMA classifies particles based on the (electrical) mobility diameter. I only know the term “hydrodynamic diameter” from the characterization of particles in liquids.
Lines 18ff: The discussion on particle surface area appears completely out of the blue and is not picked up again in the manuscript. Either explain in more detail why this is important for this work or eliminate this discussion.
Line 29: What is described here as tandem setups does not necessarily contain two or more measurement systems, but usually just different classification systems.
Line 51: The flow is not applied to the inner cylinder, but introduced near the cylinder.
Line 56/equation 1: The force balance is typically written as q*E + Fdrag = m*a. Here the drag force will receive a negative sign due to the direction of the relative velocity between particle and flow. In the way that equation (1) is set up, the signs do not seem to fit.
Line 65: it should read inner r1 and outer r4 radius.
Lines 91ff: Please provide information on the flow rates of the CDMA.
Line 92: The density should be either 1 g/cm³ or 1000 kg/m³
Line 94: I don’t understand this. Ok, you need a suitable sealing for the device, but why “for both the mobility and the Stokes diameter” (again, Stokes should be aerodynamic diameter, but that is not the reason why I don’t understand the sentence).
Lines 98/99: It would be helpful if you could indicate the location of these seals in Figure 2.
Lines 99-109: 1) Which polarity do you apply, i.e. which particle polarity do you classify?; 2) A voltage is always applied between two electrodes by applying different potentials to the individual electrodes, 3) Why is the high potential applied to the outer cylinder and the low potential (ground) to the inner cylinder? What about precautions for user safety?
Line 154: “radii” should read “radius”
Line 155: What do you mean with “particles already have a larger radius”?
Line 169: Figure caption of Figure 5: Are these “streamlines” or particle trajectories?
Line 173: What is meant with “…the transfer function of the two transfer functions…”?
Line 177-182: Please describe your measurement setup and parameters in sufficient detail: e.g. what is the “previous” instrument? What DMA flow rates did you adjust? Which neutralizer was used (85-Kr or x-ray)? Which particle polarity did you classify?
Line 186: “silver precipitates as nanoparticle”: Do you mean that the silver vapor nucleates to form nanoparticles?
Line 190/191: The sentence, starting with “Because it takes approximately 30 minutes” doesn’t make sense. Isn’t it rather that the time it takes for a complete scan defines the requirement for the stability of the test aerosol?
Line 201/Figure 8: Every figure should generally -in conjunction with its caption- be self-explanatory. Figure 8b is far from this requirement. E.g. what are the “measurement data”? Axis caption (µ-1) and n2/n1 are also not described. Please modify the figure in a way that it is at least fundamentally (i.e. not in every detail) understandable without the need to read the text.
Line 272: The charge distribution of neutralized particles is more a convention rather than the ground truth. I would therefore always phrase that it is assumed to be known. Please add a reference for the charge distribution that you used (Wiedensohler approximation?)
Line 274: “simply” should read “singly”
Line 327 (Appendix B): dm and dSt doesn’t make much sense (see above), this should be dm and dae.
Citation: https://doi.org/10.5194/ar-2024-29-RC1 -
AC1: 'Reply on RC1', Torben Rüther, 06 Nov 2024
Thank you very much for the helpful comments!
We formulated a response letter which is attached in the supplements.
- AC2: 'Reply on AC1', Torben Rüther, 06 Nov 2024
-
RC3: 'Reply on AC1', Christof Asbach, 19 Nov 2024
I would like to thank the authors for a very thorough review of the manuscript and for adding the nomenclature. I agree with all the changes made and would recommend acceptance of the manuscript as-is, but I still struggle with the use of the use of the equivalent diameters (Stokes, mobility and aerodynamic). I revisited the definitions in both Hinds (2022) and Kulkarni, Baron and Willeke (2011) textbooks and agree (and learned) that Stokes and mobility diameter are not necessarily the same. For spherical particles, however, they are identical, as was also implicitly pointed out in the author response with the equation dSt2 = dv3/dm. It should also be noted that the Stokes-Einstein equation (D = kTB) is defined by the particle mobility and thus the mobility diameter. I can see the similarities between the definitions of the Stokes and aerodynamic diameters as pointed out in the author response, i.e. both are defined via the settling velocity. However, the crucial difference is that the Stokes diameter assumes the true particle density, whereas the aerodynamic diameter standardizes the particle density (and shape) and assumes a common density of 1000 kg/m³. Consequently, all particles with the same aerodynamic diameter will encounter the same settling velocity, whereas particles with the same Stokes diameter will migrate at different settling velocities, if they have different particle densities. Similarly, in any force balance between a particle mass-based driving force (such as gravity or the centrifugal force) and the counteracting drag force, all particles with the same mass to drag ratio (i.e. also for different combinations of size and density) will migrate at the same velocity. This is why the AAC and the CDMA in AAC-mode classify particles based on the aerodynamic diameter (irrespective of their geometric size, shape and density), whereas particles with equal Stokes diameter, but different densities would be differently classified. Mentioning that the instrument could differentiate between mobility and Stokes diameter therefore appears misleading to me.
That said and to avoid any confusion in the paper, I suggest to only use the terms mobility diameter and aerodynamic diameter, which are also the commonly used equivalent diameters for DMA and AAC, respectively, and to avoid the Stokes diameter. Since the classification in the CDMA is based on the (electrical) mobility and inertial (aerodynamic) properties, this would –in my opinion- be clear and straightforward.
Citation: https://doi.org/10.5194/ar-2024-29-RC3 -
AC4: 'Reply on RC3', Torben Rüther, 24 Nov 2024
We gratefully acknowledge the valuable comments of referee#1 on our revisions.
Based on these comments we agree that we missed to clearly clarify our intentions in the manuscript and that the claim that the CDMA can differentiate according to the Stokes diameter may appear misleading. We regret that we missed to discuss this important issue in detail before.
Therefore, we added a paragraph explaining the different approaches and the reason why we prefer to use the Stokes diameter for characterization (since we primarily aim for shape characterization). However, we clearly outline, that this requires knowledge of the (exact) particle material density. In this case, we still think, the Stokes diameter is the better choice for 2D particle characterization with the CDMA. However, an inversion for aerodynamic diameter would be possible as well, however for the sake of loosing direct information on particle shape.
We hope that the new paragraph helps the readers to better understand the suggested approach without being misleading any more.
-
AC4: 'Reply on RC3', Torben Rüther, 24 Nov 2024
-
RC2: 'Comment on ar-2024-29', Anonymous Referee #2, 15 Nov 2024
This is an excellent paper on a novel concept for obtaining a two-dimensional size distribution (mobility and Stokes-equivalent). This novel instrument is well described and thoroughly tested. The experimental approach and analysis is excellent. Enough ideas emerged for a second, more performant instrument. Nevertheless, these results need to be published.
Overall, I guess that the main drawback of this instrument will be the fact that in a certain selected mobility diameter interval there will be quite a number of particles having a multiple charge, and by consequence having a different mass range and therefore also different Stokes-equivalent size ranges. This will make a precise inversion algorithm quite complicated (but not impossible).
Most of the minor comments were already made by referee no.1.
Citation: https://doi.org/10.5194/ar-2024-29-RC2 -
AC3: 'Reply on RC2', Torben Rüther, 18 Nov 2024
We are very grateful to the reviewer for the positive feedback and for taking the time and effort to review the manuscript.
And regarding the problem of multiple charges, you are absolutely right. To solve this, we have chosen and implemented an iterative approach to data inversion (projection onto convex sets), which gives very promising first results. These results are currently being prepared for publication in a separate paper which will be submitted in due future.
Citation: https://doi.org/10.5194/ar-2024-29-AC3
-
AC3: 'Reply on RC2', Torben Rüther, 18 Nov 2024
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