the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Comment on "Technical note: An assessment of the relative contribution of the Soret effect to open water evaporation" by Roderick and Shakespeare (2025)
Abstract. This comment addresses the definition of Fick’s 1st law employed in the paper “Technical note: An assessment of the relative contribution of the Soret effect to open water evaporation" by Roderick and Shakespeare (2025), and defended by the authors during the on-line discussion phase of their manuscript’s peer review process. Based on precedence in chemical engineering literature, the authors argue "the complete equivalence of mass- and molar-based frameworks for describing diffusion". On the contrary, here a very simple example shows that the authors’ preferred molar-based framework neglects the key role of inertia in momentum conservation, violates Newton’s laws of motion, and leads to different conclusions with regard to isotopic discrimination. It therefore ought not be considered equivalent to the inertial framework that is consistent with the laws of physics.
Status: final response (author comments only)
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CC1: 'Comment on egusphere-2025-2814', Michael Roderick, 15 Jul 2025
- AC1: 'Reply on CC1', Andrew Kowalski, 16 Jul 2025
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CC2: 'Comment on egusphere-2025-2814', Timo Vesala, 23 Feb 2026
- AC2: 'Reply on CC2', Andrew Kowalski, 26 Feb 2026
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EC1: 'Editorial comment on egusphere-2025-2814', Thom Bogaard, 04 Jun 2026
This comment is a continuation of the open-review discussion on the paper of Roderick and Shakespeare (2025). https://hess.copernicus.org/articles/29/2097/2025/
Both Kowalski and Roderick agree in the discussion on this comment that for the application in the analysis of the role of the Soret effect by Roderick and Shakespeare the use of molar-based or mass-based has no consequences (only with different humidity values.
Secondly, the dispute continues on the fundamental if a molar-based analysis violates Newton's law. The contribution of dr. Vesala shows however that in multicomponent systems ternary effects play a role as described by Stefan-Maxwell equations (with mathematical derivation by Curtiss and Hirschfelder 1949) counterbalances the seemingly emerged diffusive transport by the ternary effect. The answer does not disprove the point made by dr Vesala.
In that respect, the comment to the paper has not added new insight to the previous open-access discussion and also does not brought to light a flaw in the conclusions of the Roderick and Shakespeare 2025). For a continuation of the fundamental discussion if Newton's law is violated, I think a much more in-depth research is needed, starting with inclusion of the ternary effect and reanalysis of Curtiss and Hirschfelder 1949 which I consider out of scope of this commentary. I thanks all for their contribution to this scientific debate.
Thom Bogaard
EE Hess
Citation: https://doi.org/10.5194/egusphere-2025-2814-EC1 - AC3: 'Reply on EC1', Andrew Kowalski, 11 Jun 2026
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RC1: 'Comment on egusphere-2025-2814', Thom Bogaard, 04 Jun 2026
See the community comment by dr Vesala .
Citation: https://doi.org/10.5194/egusphere-2025-2814-RC1 -
AC4: 'Reply on RC1', Andrew Kowalski, 14 Jun 2026
At the behest of the editor, I will paste a copy of my reply to the comment by Dr. Vesala below. However, first I would like to point directly to the flaw in the derivation of the Maxwell-Stefan equations by Curtiss and Hirschfelder (J. Chem. Phys. 17, 550-555, 1949). Those authors treated the mass-average velocity of the fluid (i.e., "motion" as defined by Newton) as independent of the reordering of molecules by Brownian motion. Rather, however, when species of different molar masses are reordered, fluid motion occurs in the direction of the movement of the heavier molecules. Brownian reordering shifts the location of the fluid’s centre of mass, implying Newtonian motion.
This was made explicit with contrasting examples in my original comment during the discussion phase of the paper by Roderick and Shakespeare (2025; https://hess.copernicus.org/articles/29/2097/2025/), which contrasts Newtonian and Fickian transport, and can be found here:
https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2023/egusphere-2024-2023-RC1-supplement.pdf
Original reply to Dr. VesalaAt Dr. Vesala’s request, I have reread Sections 17.7 – 17.9 of Transport Phenomena by Bird, Steward and Lightfoot (2002). If I am not mistaken, these authors motivate the use of a mole-based framework to facilitate the quantification of chemical reactions, but note that a mass-based framework is “preferable” when the diffusion equations are solved together with the equation of motion. In my view, the mass-based framework is not merely preferable but actually essential to respect the key role played by inertia in Newton’s laws. My reply to the comment by Dr. Roderick shows that the differences between the two frameworks are not negligible over a range of water temperatures that is relevant to the Earth’s hydrological system.
Vilà-Guerau de Arellano et al. (2025) define the mole-average velocity of the mixture (u) in their Eq. (5), and then in their Appendix C refer to “the governing equations for u (Navier-Stokes equation)”. However, I do not believe that the Navier-Stokes equations govern mole-average velocities. To my mind, defining a mechanical velocity as the mole-average velocity seems incorrect in general. In this sense—for my example involving no net argon transport—it seems to me that both the “diffusive transport” due to a mole-fraction gradient and the “Stefan flow (ternary effect)” required to counterbalance it are artefacts of an invalid basis for quantifying motion.
Maybe it is overly optimistic on my part, but I hope that “shooting off” might mean: defending the centuries-old principles of classical mechanics established by Sir Isaac Newton.References
Bird, R. B., Stewart, W. E., and Lightfoot, E. N.: Transport Phenomena, John Wiley & Sons, Cambridge, 2002.
Vilà-Guerau de Arellano, J., Dewar, D., Faassen, K. A.P., Hölttä, T, de Kok, R., Luijkx, I.T. and Vesala, T., Technical note: New insights into stomatal oxygen transport viewed as a multicomponent diffusion process, Biogeosciences, 22, 6327–6341, https://doi.org/10.5194/bg-22-6327-2025, 2025.Citation: https://doi.org/10.5194/egusphere-2025-2814-AC4
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AC4: 'Reply on RC1', Andrew Kowalski, 14 Jun 2026
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