the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Jun 2025
Technical note: New insights into stomatal oxygen transport viewed as a multicomponent diffusion process
Abstract. We investigate oxygen (O2) transport through stomata, focusing on its interaction with water vapour (H2O) flux. The dominant H2O flux exerts a drag force on other gases, a well-studied effect in the ternary air–water vapour–carbon dioxide (CO2) system but unexplored for O2 transport. This study aims to: (1) apply the Stefan–Maxwell equations to a quaternary system of H2O, O2, CO2, and N2; (2) identify conditions where O2 transport from stomata to the atmosphere occurs against its mole fraction gradient ('uphill'); and (3) derive an expression linking the O2 mole fraction in sub-stomatal air spaces (xₒᵢ) to that in the atmosphere (xₒₐ) based on atmospheric relative humidity.
Our theoretical results, constrained by typical flux observations of the quaternary system, reveal distinct transport regimes defined by the mole flux ratio of H2O and O2 (Fw/Fo). Uphill O2 diffusion occurs in the common regime where Fw/Fo»1, and the internal O₂ mole fraction increases toward its atmospheric value as relative humidity approaches 100 %. These theoretical results offer a framework for interpreting laboratory and field experiments on stomatal O2 exchange under stagnant atmospheric or low Reynolds number conditions and can support the development of more physically accurate models of leaf–atmosphere oxygen exchange.
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RC1: 'Comment on egusphere-2025-2705', Andrew Kowalski, 15 Jul 2025
- AC1: 'Reply on Dr. Andy Kowalski', Jordi Vila-Guerau de Arellano, 21 Aug 2025
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RC2: 'Mathematically sound, but please consider elaborating on real-world applicability', Anonymous Referee #2, 18 Jul 2025
The technical note by Vilà-Guerau de Arellano et al. explores to what extent oxygen transport through stomata is regulated by water fluxes in the context of multicomponent mass transfer. The central thesis is that, under low Reynolds number conditions dominated by molecular diffusion, as water fluxes from the evaporating substomatal cavity are typically much higher than oxygen fluxes, the gradient of oxygen across stomata is proportional to water fluxes according to the Stefan–Maxwell equations, leading to uphill diffusion of oxygen that counterbalances the Stefan flow. As the authors put it, this phenomenon “can strongly affect the interpretation of O2 exchange on stomatal level”, which I agree on the premise that mass transfer is dominated by multicomponent molecular diffusion and the Stefan flow induced by evaporation. But empirically, it is this premise that I have certain doubts about.
A leaf receiving an intermediate to high level of radiation is typically warmer than the ambient air, because it needs to dissipate heat through diffusion (what meteorologists call sensible heat transfer), in addition to outgoing thermal radiation and latent heat transfer through transpiration. As oxygen and water molecules have different molecular weights, this leaf-to-air temperature gradient may create conditions for thermophoresis in which oxygen molecules move down the temperature gradient (from the substomatal cavity to the air) as opposed to the direction of water vapor thermodiffusion. How thermodiffusion compares to the Stefan flow and molecular diffusion in stomatal oxygen transport seems unknown to me, and it bears consequences for how we interpret leaf-level oxygen exchange measurements.
Regarding the interpretation of Stefan–Maxwell diffusion as “the drag forces exerted by all other species,” I concur with my fellow reviewer that the underlying physical picture seems murky. It is clear that the authors are alluding to the kinetic theory of gases. But if Stefan–Maxwell diffusion originates from drag forces at the molecular level, in what sense does it differ from viscosity? It seems that this physical picture (lines 36–54) needs to be clarified to build a robust intuition.
I consider the nondimensional treatment in Appendix C a helpful framework for assessing under which conditions Stefan flow and multicomponent molecular diffusion matter. But it seems that the wind speed range quoted in line 425 is the condition in a greenhouse. Wind experienced by top-canopy leaves in a forest can be quite different. It would help to give a threshold of wind speed at which turbulent diffusion becomes more important than multicomponent molecular diffusion.
Lastly, Table 1 presents calculations of molar fluxes of water vapor, O2, and CO2 and their partition into Stefan flow and diffusive flux components. The calculations assume a water vapor mole fraction of 0.01, but in reality, it is the most variable component in the canopy air. In a desert, this value could be much smaller, whereas in a tropical rainforest at 35°C, the air could hold 5.5% water vapor (in mole fractions) at saturation. It would be helpful to expand this table (maybe into a figure) to show calculations under a range of realistic water vapor mole fractions.
Citation: https://doi.org/10.5194/egusphere-2025-2705-RC2 - AC2: 'Reply on referee 2', Jordi Vila-Guerau de Arellano, 21 Aug 2025
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