the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Aug 2024
Technical note: An assessment of the relative contribution of the Soret effect to open water evaporation
Abstract. It is standard practice to assume that evaporation depends on the gradient in water vapor concentration as per Fick’s law. However, Fick’s law is only true in an isothermal system. In general, we anticipate an additional mass flux due to the temperature gradient (in a non-isothermal system) and this is known as Soret diffusion or the Soret effect. Here we evaluate the relative magnitude of the Soret effect and find that under typical environmental conditions it is at least two orders of magnitude smaller than classical concentration-dependent mass (‘Fickian’) diffusion. This result justifies the standard practice of ignoring the effect of the temperature gradient by assuming evaporation follows the gradient in water vapor concentration.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(580 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2023', Andrew Kowalski, 03 Sep 2024
The manuscript by Roderick and Shakespeare purports to characterise the influence of the Soret effect, whereby temperature gradients influence mass diffusion, versus the classical concentration-dependent mass (‘Fickian’) diffusion. But in order to do this requires first correctly characterising Fickian diffusion, and this I believe the authors have not yet done. In brief, the authors have specified Fick's law based on gradients in the molar fraction, whereas Newtonian analyses demonstrate that it must be specified in terms of the mass fraction, and the difference between the two is hardly trivial for fluids of varying molecular mass. Respectfully, I therefore believe that the manuscript should be rejected. My arguments for why their specification of Fick’s 1st Law is incorrect are laid out in an open-access paper (Kowalski et al., 2021) that can be accessed here (https://link.springer.com/article/10.1007/s10546-021-00605-5; see sections 3.2 and 4 in particular), but are reinforced in the attached PDF file.
Independent of this, I point out that the authors' Eq. (1) is dimensionally inhomogeneous unless the diffusive flux density (J) is specified in molar terms, with units as in Table 1 rather than the mass-based units that they indicate at line 62. Also, the axis labels should be larger in order to be legible, particularly for Figure 2.
Reference
Kowalski, A. S., Serrano-Ortiz, P., Miranda-García, G., and Fratini, G., 2021. "Disentangling turbulent gas diffusion from non-diffusive transport in the boundary layer." Boundary-Layer Meteorology, 179 (3), 347-367.
- AC6: 'Reply on RC1', Michael Roderick, 29 Oct 2024
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RC2: 'Comment on egusphere-2024-2023', Anonymous Referee #2, 06 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-RC2-supplement.pdf
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AC1: 'Reply on RC2', Michael Roderick, 19 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC1-supplement.pdf
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AC1: 'Reply on RC2', Michael Roderick, 19 Sep 2024
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RC3: 'Comment on egusphere-2024-2023', Anonymous Referee #3, 18 Sep 2024
This manuscript gives a detailed discussion on the relative contributions of Fickian’s diffusion and Soret effect on open water evaporation, and justifies the popular practice of estimating open water evaporation through the water vapor concentration gradients. The authors prove that the Soret effect is two orders of magnitude smaller than that by concentration-dependent diffusion. I consider such kind of work is just quite rare because of limited laboratary experiments and it is valuable for us to understand the processes behind it. In figure1, the thermal diffusion factor is 0.05 for N2-N2O and N2-CO2, but 0.33 for H2-CO2. It seems that even though the thermal diffusion factor of 0.33 is used for Soret effect estimation, its contribution is still much smaller compared to the concentration gradients. In abstract, the authors mentioned that “under typical environmental conditions it is at least two orders of magnitude smaller than classical concentration-dependent mass (‘Fickian’) diffusion. ”. From Figure1 and Figure 2, we could find that the Soret effect can be neglected in open water estimation. I ‘m just wandering under what conditions in open water evaporation estimation (fresh water and saline water) the Soret effect can not be ignored? If no, please add some examples in the discussion of the manuscript. Further, the figure quality is not good, please make figures with good quality. Generally, I consider the manuscript is a good materials that can help us to understand clear the water-atmosphere interaction processes.
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC3 -
AC2: 'Reply on RC3', Michael Roderick, 19 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC2-supplement.pdf
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AC2: 'Reply on RC3', Michael Roderick, 19 Sep 2024
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RC4: 'Comment on egusphere-2024-2023', Anonymous Referee #4, 23 Sep 2024
This study quantifies the magnitude of the Soret effect on open water evaporation and demonstrate that it is typically two orders of magnitude smaller than the mass diffusion component (Fickian diffusion). This finding justifies the common practice of ignoring the Soret effect when describing evaporation in hydrological sciences.
I believe this is an important study that should be accepted after minor corrections and clarifications. The manuscript is well-written and exhibits excellent readability. However, it may benefit from clarifications regarding the following points.
Comments:
C1: Multiple times throughout the manuscript, the sentences give an impression that evaporation is entirely a Fick’s diffusion process (Line 26,212). However, estimation of evaporation also requires an explicit consideration of an energy term. Over open-water surfaces the gradient in the water-vapor is further strongly controlled by changes in temperature and incoming energy as reflected in the classical equilibrium energy partitioning approach (Slatyer and McIlroy, 1961).
C2: In Line 123, it may be useful to provide a sensitivity estimate of α_T with respect to temperature using the equation from Youssef et al. (1965). This would demonstrate that variations in α_T with temperature are not substantial enough to cause significant changes in the Soret effect.
C3: In Line 135, Check the equation. Should x_a be written as a dependence on T_a as well. (x_s(T_s) + x_a(T_a))/2.
C4: Line 147: The authors quantified the relative contribution of the Soret effect for standard conditions with data described in Table 3. Later they talk about describing the condition where mole fraction gradient would become zero and Soret effect would then be 100% of the total flux. They mention that this leads to total flux being vanishingly small “as described below (line 147)”. However, the results for this condition are not described unless they are referring to the next section of the manuscript.
C5: Line 171: It may be helpful to add a brief discussion for why the boundary layer thickness declines with wind-speed for a wider audience.
C6: One key difference between Griffani et al. (2024) and this study is the magnitude of the thermal diffusion factor, which is one order of magnitude higher in the former. While the authors provide a thoughtful justification for their use of 0.05 for the magnitude of diffusion coefficient, there is no experimental data for H2O-dry air mixtures. It would be important to validate these estimates with new experiments; perhaps the authors could include this as an outlook for future research.
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC4 -
AC3: 'Reply on RC4', Michael Roderick, 25 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC3-supplement.pdf
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AC3: 'Reply on RC4', Michael Roderick, 25 Sep 2024
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RC5: 'Review of egusphere-2024-2023', Anonymous Referee #5, 23 Sep 2024
Please find my review of the manuscript as the attached file.
Best regards.-
AC4: 'Reply on RC5', Michael Roderick, 25 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC4-supplement.pdf
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AC4: 'Reply on RC5', Michael Roderick, 25 Sep 2024
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RC6: 'Comment on egusphere-2024-2023', Demetris Koutsoyiannis, 26 Sep 2024
My review is contained in the attached file.
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RC7: 'Reply on RC6', Andrew Kowalski, 27 Sep 2024
My reply to this comment is contained in the attached PDF file.
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RC8: 'Reply on RC7', Demetris Koutsoyiannis, 27 Sep 2024
Reply to Andrew Kowalski
I am pleased that we agree with Professor Kowalski on important issues of academic ethics and the duty of scientists to seek the truth.
I accept his criticism that I used undocumented assumptions in my “homework” and I modify my phrase “precisely equivalent” to “practically equivalent”. For I think he is right that there is gradient in the molar mass and the density of the gas mixture. However, my intuition says that these gradients are negligible in the narrow layer determining the evaporation (though they become important for large altitude ranges). As an engineer, I never considered these gradients in my evaporation calculations. Hopefully, this discussion will show, in a quantified manner, if my intuition is correct or not.
Demetris Koutsoyiannis
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC8 - AC5: 'Combined Reply to RC6, RC7, RC8', Michael Roderick, 10 Oct 2024
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RC8: 'Reply on RC7', Demetris Koutsoyiannis, 27 Sep 2024
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RC7: 'Reply on RC6', Andrew Kowalski, 27 Sep 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2023', Andrew Kowalski, 03 Sep 2024
The manuscript by Roderick and Shakespeare purports to characterise the influence of the Soret effect, whereby temperature gradients influence mass diffusion, versus the classical concentration-dependent mass (‘Fickian’) diffusion. But in order to do this requires first correctly characterising Fickian diffusion, and this I believe the authors have not yet done. In brief, the authors have specified Fick's law based on gradients in the molar fraction, whereas Newtonian analyses demonstrate that it must be specified in terms of the mass fraction, and the difference between the two is hardly trivial for fluids of varying molecular mass. Respectfully, I therefore believe that the manuscript should be rejected. My arguments for why their specification of Fick’s 1st Law is incorrect are laid out in an open-access paper (Kowalski et al., 2021) that can be accessed here (https://link.springer.com/article/10.1007/s10546-021-00605-5; see sections 3.2 and 4 in particular), but are reinforced in the attached PDF file.
Independent of this, I point out that the authors' Eq. (1) is dimensionally inhomogeneous unless the diffusive flux density (J) is specified in molar terms, with units as in Table 1 rather than the mass-based units that they indicate at line 62. Also, the axis labels should be larger in order to be legible, particularly for Figure 2.
Reference
Kowalski, A. S., Serrano-Ortiz, P., Miranda-García, G., and Fratini, G., 2021. "Disentangling turbulent gas diffusion from non-diffusive transport in the boundary layer." Boundary-Layer Meteorology, 179 (3), 347-367.
- AC6: 'Reply on RC1', Michael Roderick, 29 Oct 2024
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RC2: 'Comment on egusphere-2024-2023', Anonymous Referee #2, 06 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-RC2-supplement.pdf
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AC1: 'Reply on RC2', Michael Roderick, 19 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC1-supplement.pdf
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AC1: 'Reply on RC2', Michael Roderick, 19 Sep 2024
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RC3: 'Comment on egusphere-2024-2023', Anonymous Referee #3, 18 Sep 2024
This manuscript gives a detailed discussion on the relative contributions of Fickian’s diffusion and Soret effect on open water evaporation, and justifies the popular practice of estimating open water evaporation through the water vapor concentration gradients. The authors prove that the Soret effect is two orders of magnitude smaller than that by concentration-dependent diffusion. I consider such kind of work is just quite rare because of limited laboratary experiments and it is valuable for us to understand the processes behind it. In figure1, the thermal diffusion factor is 0.05 for N2-N2O and N2-CO2, but 0.33 for H2-CO2. It seems that even though the thermal diffusion factor of 0.33 is used for Soret effect estimation, its contribution is still much smaller compared to the concentration gradients. In abstract, the authors mentioned that “under typical environmental conditions it is at least two orders of magnitude smaller than classical concentration-dependent mass (‘Fickian’) diffusion. ”. From Figure1 and Figure 2, we could find that the Soret effect can be neglected in open water estimation. I ‘m just wandering under what conditions in open water evaporation estimation (fresh water and saline water) the Soret effect can not be ignored? If no, please add some examples in the discussion of the manuscript. Further, the figure quality is not good, please make figures with good quality. Generally, I consider the manuscript is a good materials that can help us to understand clear the water-atmosphere interaction processes.
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC3 -
AC2: 'Reply on RC3', Michael Roderick, 19 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC2-supplement.pdf
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AC2: 'Reply on RC3', Michael Roderick, 19 Sep 2024
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RC4: 'Comment on egusphere-2024-2023', Anonymous Referee #4, 23 Sep 2024
This study quantifies the magnitude of the Soret effect on open water evaporation and demonstrate that it is typically two orders of magnitude smaller than the mass diffusion component (Fickian diffusion). This finding justifies the common practice of ignoring the Soret effect when describing evaporation in hydrological sciences.
I believe this is an important study that should be accepted after minor corrections and clarifications. The manuscript is well-written and exhibits excellent readability. However, it may benefit from clarifications regarding the following points.
Comments:
C1: Multiple times throughout the manuscript, the sentences give an impression that evaporation is entirely a Fick’s diffusion process (Line 26,212). However, estimation of evaporation also requires an explicit consideration of an energy term. Over open-water surfaces the gradient in the water-vapor is further strongly controlled by changes in temperature and incoming energy as reflected in the classical equilibrium energy partitioning approach (Slatyer and McIlroy, 1961).
C2: In Line 123, it may be useful to provide a sensitivity estimate of α_T with respect to temperature using the equation from Youssef et al. (1965). This would demonstrate that variations in α_T with temperature are not substantial enough to cause significant changes in the Soret effect.
C3: In Line 135, Check the equation. Should x_a be written as a dependence on T_a as well. (x_s(T_s) + x_a(T_a))/2.
C4: Line 147: The authors quantified the relative contribution of the Soret effect for standard conditions with data described in Table 3. Later they talk about describing the condition where mole fraction gradient would become zero and Soret effect would then be 100% of the total flux. They mention that this leads to total flux being vanishingly small “as described below (line 147)”. However, the results for this condition are not described unless they are referring to the next section of the manuscript.
C5: Line 171: It may be helpful to add a brief discussion for why the boundary layer thickness declines with wind-speed for a wider audience.
C6: One key difference between Griffani et al. (2024) and this study is the magnitude of the thermal diffusion factor, which is one order of magnitude higher in the former. While the authors provide a thoughtful justification for their use of 0.05 for the magnitude of diffusion coefficient, there is no experimental data for H2O-dry air mixtures. It would be important to validate these estimates with new experiments; perhaps the authors could include this as an outlook for future research.
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC4 -
AC3: 'Reply on RC4', Michael Roderick, 25 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC3-supplement.pdf
-
AC3: 'Reply on RC4', Michael Roderick, 25 Sep 2024
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RC5: 'Review of egusphere-2024-2023', Anonymous Referee #5, 23 Sep 2024
Please find my review of the manuscript as the attached file.
Best regards.-
AC4: 'Reply on RC5', Michael Roderick, 25 Sep 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-AC4-supplement.pdf
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AC4: 'Reply on RC5', Michael Roderick, 25 Sep 2024
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RC6: 'Comment on egusphere-2024-2023', Demetris Koutsoyiannis, 26 Sep 2024
My review is contained in the attached file.
-
RC7: 'Reply on RC6', Andrew Kowalski, 27 Sep 2024
My reply to this comment is contained in the attached PDF file.
-
RC8: 'Reply on RC7', Demetris Koutsoyiannis, 27 Sep 2024
Reply to Andrew Kowalski
I am pleased that we agree with Professor Kowalski on important issues of academic ethics and the duty of scientists to seek the truth.
I accept his criticism that I used undocumented assumptions in my “homework” and I modify my phrase “precisely equivalent” to “practically equivalent”. For I think he is right that there is gradient in the molar mass and the density of the gas mixture. However, my intuition says that these gradients are negligible in the narrow layer determining the evaporation (though they become important for large altitude ranges). As an engineer, I never considered these gradients in my evaporation calculations. Hopefully, this discussion will show, in a quantified manner, if my intuition is correct or not.
Demetris Koutsoyiannis
Citation: https://doi.org/10.5194/egusphere-2024-2023-RC8 - AC5: 'Combined Reply to RC6, RC7, RC8', Michael Roderick, 10 Oct 2024
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RC8: 'Reply on RC7', Demetris Koutsoyiannis, 27 Sep 2024
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RC7: 'Reply on RC6', Andrew Kowalski, 27 Sep 2024
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Michael L. Roderick
Callum J. Shakespeare
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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