the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Jul 2026
Determination of water diffusion coefficients in aerosols based on characteristic time analysis
Abstract. The water diffusion coefficient in atmospheric particles is a key parameter characterising particle-phase water transport and is essential for understanding aerosol phase state, phase transitions, and multiphase chemical processes. In this study, we develop a characteristic-time-based method for directly measuring the water diffusion coefficient in an individual droplet. The progress of water diffusion is represented by the relative abundance of H2O and D2O within the droplet, which is retrieved from Raman spectra and quantified here as the D2O fraction. The characteristic time is derived as the time at which the measured D2O fraction reaches the value predicted by the aqueous-phase diffusion model. Since the characteristic time derived from this model depends only on the water diffusion coefficient and droplet radius, the water diffusion coefficient can be calculated directly from the measured characteristic time and droplet radius. Using this method, water diffusion coefficients in sucrose droplets at 30–45 % RH were determined to be 1×10-16 to 1×10-14 m2s-1. The water diffusion coefficient showed a clear RH dependence, with lower coefficients observed at lower RH. These results are consistent with previous experimental measurements, supporting the reliability of our method. A key advantage of this method is that it does not require tracking the complete H2O/D2O exchange process, as measurements are only needed until the characteristic time, thereby shortening the experimental observation time and making the method particularly suitable for diffusion measurements in highly viscous aerosol particles. This method applies to both spherical droplets and non-spherical diffusion systems, which allows it to be adapted to different experimental platforms. It therefore provides a basis for understanding mass transport in aerosols and related atmospheric chemical processes.
- Preprint
(1753 KB) - Metadata XML
-
Supplement
(1045 KB) - BibTeX
- EndNote
Status: open (until 18 Aug 2026)
- RC1: 'Comment on egusphere-2026-3646', Anonymous Referee #1, 27 Jul 2026 reply
-
RC2: 'Comment on egusphere-2026-3646', Anonymous Referee #2, 31 Jul 2026
reply
This manuscript presents a characteristic-time-based method for determining water diffusion coefficients in individual sucrose droplets using Raman H2O/D2O isotope-exchange measurements. The approach is potentially useful because measurements of very slow diffusion processes can require long experimental observation periods. The theoretical framework appears internally consistent under the assumptions adopted, and the measured diffusion coefficients are broadly comparable with previous sucrose measurements.
However, several methodological assumptions have not been sufficiently validated. Please see my comments below.
1. The principal advantage claimed for the proposed method is that it can determine Dw without observing the complete isotope-exchange process. However, the manuscript does not compare the characteristic-time method with conventional full-curve fitting using the same experimental datasets. The authors should apply both methods to the available experiments and compare the resulting diffusion coefficients, uncertainties, and required observation times. Agreement with previous literature alone is not sufficient to validate the new retrieval method. Alternatively, the authors should explain well why such experiments on full-curve fitting has not been done, or why the current methodology is enough to support your statements.
2. Section 5.1 primarily describes similarities and differences between the present results and previous studies, but does not sufficiently explain what these comparisons imply for the reliability of the proposed method. The discussion should focus more directly on the authors’ results, methodological assumptions, and limitations. Claims regarding non-spherical systems, different experimental platforms, low temperatures, and RH conditions below the measured range should be moderated because these applications were not demonstrated in the present study.
3. Figure 4 includes a curve labelled “Fit,” but the fitting method and fitted parameters are not explained. It is also unclear whether the reported Dw was derived from this fit or from the characteristic-time method. The authors should define the fit and use it to compare the two retrieval approaches where possible. The reduction in observation time should also be quantified rather than described only qualitatively.
Minor comments:
1. Lines 30 to 34 move rapidly from hindered molecular diffusion to particle size distributions, gas-particle partitioning, chemical kinetics, ice nucleation, human health, air quality, and climate. The mechanistic links should be explained more clearly, or the broader claims should be narrowed.
2. Line 44, the sentence would read more naturally as “Price et al. (2014) subsequently developed...”.
3. RH is defined earlier in the Introduction. The use of “RH” and “relative humidity” should be made more consistent throughout the manuscript. The authors used "relative humidity" throughout the manuscript in many places.
4. The final paragraph of the Introduction should be revised to distinguish the study objective, the main finding, and potential future applications. The statement that the results are “consistent with previous studies” is too general.
5. Please standardise the use of “temperature – humidity,” “temperature-humidity,” “O – D,” “O–D,” “O – H,” and “O–H.” “Temperature and humidity probe” would be clearer.
6. Numerical and unit formatting should be standardised.
7. Please specify whether the upstream or downstream RH probe was used to determine the stabilisation time.
8. At Line 126, “Where” should be changed to “where.”
9. The explanation following the captions of Figs. 3 and 4 repeats information already provided in the captions. The paragraph should be shortened and focused on additional interpretation.
9. The Fig. 5 legend appears to use “Davis et al.” This should be corrected to “Davies and Wilson.” Similarly, “Davies et al.” is not appropriate for a publication with two authors.
10. There is a missing space before the citation at approximately Line 320, “concentration(Zobrist et al....”.
11. The statement that differences among previous studies may reflect “experimental platforms, instrumental performance, and environmental control” is too general. Specific mechanisms should be discussed.
12. The statement that the data are “well described” by the Vignes-type parameterization should be supported by quantitative fit statistics.
13. The figures resolution are somehow low, please increase the resolution (such as 600 dpi or 900 dpi).
Citation: https://doi.org/10.5194/egusphere-2026-3646-RC2 -
RC3: 'Comment on egusphere-2026-3646', Anonymous Referee #3, 10 Aug 2026
reply
Guo et al. present a characteristic time-based analytical framework to constrain water diffusion coefficients (Dw) in viscous droplets. By leveraging eigenfunction solutions to Fick’s second law, the authors demonstrate that the isotope fraction at characteristic time (τ) scales linearly with the initial spatial distribution. The method provides a promising route to shorten experimental runtimes in complex conditions. The theoretical derivation is generally sound and clearly presented. The manuscript is suitable for publication after addressing the following questions.
Major comments:
- Defining the precise onset of RH stabilization is critical, as it directly fixes the time origin for calculating τ and the derived Dw. Currently, the choice of five characteristic times (5ω) for RH stabilization appears empirical. The authors should provide a clear physical mechanism or appropriate literature references to justify this criterion, or adopt a more rigorous mathematical definition for the stabilization point. Moreover, using the term "characteristic time" for both the experimental RH response parameter (ω) and the isotope diffusion timescale (τ) introduces unnecessary confusion.
- The authors should include, for at least a subset of the measured droplets, a side-by-side comparison of Dw values obtained via the new characteristic-time method and conventional fitting of the entire D2O-fraction time series. Such comparison would provide a more direct and convincing validation of the proposed method, rather than relying solely on qualitative agreement with literature values obtained under different conditions and platforms.
- The Introduction and Discussion repeatedly emphasize that the method is particularly advantageous for slow-diffusion (low-RH, high-viscosity) systems where conventional isotope-tracer measurements become impractical. However, the RH range investigated here (30–45%) does not extend into this regime. I recommend that the authors extend the measurements to lower RH (or lower temperature) to directly demonstrate the method's capability under conditions where conventional approaches fail.
Minor suggestions:
- In Figure 3, the x-axis should be extended to show data prior to the D2O flow switch to illustrate the initial perturbation dynamics.
- In Figure 5, "Davis et al." should be corrected to "Davies and Wilson".
Citation: https://doi.org/10.5194/egusphere-2026-3646-RC3
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 135 | 34 | 16 | 185 | 22 | 10 | 9 |
- HTML: 135
- PDF: 34
- XML: 16
- Total: 185
- Supplement: 22
- BibTeX: 10
- EndNote: 9
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
This manuscript presents an innovative, time-saving methodology for directly measuring the water diffusion coefficient within single levitated aerosol droplets. Understanding internal mass transport limitations in highly viscous or semisolid atmospheric particles is an active area of atmospheric chemistry, and this study addresses a major bottleneck: the prohibitive experimental observation timescales required by traditional full-exchange Raman isotope tracer methods.
By framing the calculation around a mathematically derived characteristic diffusion time rather than a complete fit of the exchange curve, the authors demonstrate that can be successfully retrieved using only the initial segment of the diffusion profile. This offers a major technical advantage for probing highly viscous states at low relative humidity (RH) or low temperatures where diffusion is exceptionally slow. The manuscript is well-structured, mathematically rigorous, and the results for sucrose droplets correlate nicely with literature trends. I recommend this manuscript for publication after addressing the following specific points.
Specific Comments