Abstract
Introduction
In January 2025, this journal published the paper “Measurement and optimization of estimation method for moisture diffusivity of porous building materials with different salt content” (Xie et al., 2025). In the article, among others, capillary absorption in salt-free and salt-laden bricks is both measured and simulated, with their critical disparity as a crucial finding of the article. That leads the paper to contest the validity of the ruler-based diffusivity determination of (Evangelides et al., 2018). This discussion – considered a post-publication critique – however substantiates that the disagreement of measured and simulated capillary absorption in Xie et al. (2025) can in no way stem from the (ruler-based) diffusivity, and instead must be allocated to (unknown) flaws in Xie et al. (2025)’s simulation.
The main findings capturing Xie et al. (2025)’s contest of the ruler-based diffusivity determination are depicted in Xie et al. (2025)’s Figures 10, 13, and 16. Figure 10 shows the disagreement between measured and simulated capillary absorption when employing the original ruler-based diffusivity, while Figure 13 and 16 illustrate the improved agreement when that original diffusivity is modified. With both modifications, the high diffusivities at high moisture contents are reduced, firstly by applying an approximate exponential diffusivity instead, secondly by applying saturated instead of capillary moisture content for the ruler-based diffusivity determination. In Xie et al. (2025)’s conclusion, it is asserted that “the use of saturated moisture content in the ‘ruler method’ seems to give more accurate moisture diffusivity than that of capillary moisture content,” a conclusion that contradicts much of the established literature on this front.
Ruler-based diffusivity determination
The claimed problems with the ruler-based diffusivity determination are exemplified in Xie et al. (2025)’s Figure 10, which shows a deviation between measured and simulated capillary absorption. This critique only involves the salt-free brick, but similar results apply for the salt-laden variants. Quantitatively, the measured and simulated capillary absorption coefficients respectively are 0.230 kg/m2s0.5 and 0.755 kg/m2s0.5, which thus differ with a factor 3.3. Ensuingly, Xie et al. (2025) supposes that “the moisture diffusivity obtained from the ruler method in our experiment may be larger than the actual value,” and subsequently attributes the differences to “the value of boundary moisture content in the θ-λ profile.” This allocation of error to the ruler-based diffusivity determination does not hold though, as it is contradicted by analytical solutions as well as logical arguments.
In Xie et al. (2025)’s Figure 12, exponential linearization of the moisture diffusivity is implemented, yielding the enhanced agreement between measured and simulated capillary absorption in Xie et al. (2025)’s Figure 13. The simulated capillary absorption coefficient after this linearisation reduces to 0.174 kg/m2s0.5, now slightly below the measured 0.230 kg/m2s0.5. This simulation result can however not be correct, as it refutes the analytical solution for the capillary absorption coefficient of porous materials with exponential diffusivity (Lockington et al., 1999). The general expression for an exponential diffusivity is:
with Dℓ [m2/s] moisture diffusivity, θ [m3/m3] moisture content, θcap [m3/m3] capillary moisture content, D0 [m2/s] and n [-] fitting parameters. Fitting on the exponential diffusivity comprised in Xie et al. (2025)’s Figure 12a yields D0 6.2·10–10 m2/s and n 6.5 for the salt-free brick. For this exponential diffusivity, an analytical solution for the related capillary absorption coefficient is available (Lockington et al., 1999):
with Acap [kg/m2s0.5] capillary absorption coefficient, and ρwat [kg/m3] water density. For the salt-free brick considered, 0.094 kg/m2s0.5 is attained by equation (2), which is about half of Xie et al. (2025)’s simulated 0.174 kg/m2s0.5. A correct numerical simulation would however reproduce this analytical value aptly, implying that Xie et al. (2025)’s simulated result cannot be correct.
The same argument can be formulated with respect to Xie et al. (2025)’s simulation with the original ruler-based diffusivity from Evangelides et al. (2018). The development of that diffusivity determination method clearly states that their expression for the lambda profile:
brings about this analytical solution for the capillary absorption coefficient:
with a [m3/m3], b [s0.5/m], c [-] fitting factors. For the salt-free brick considered, the values in Xie et al. (2025)’s Table 1 yield 0.230 kg/m2s0.5 as analytical outcome, which is perfectly in line with the measured value it is based on. It does differ strongly though from Xie et al. (2025)’s simulated 0.755 kg/m2s0.5. A correct numerical simulation would however reproduce this analytical value aptly, implying that Xie et al. (2025)’s simulated result cannot be correct.
That invalidity of Xie et al. (2025)’s simulation can also be established on logical grounds. The inherent premise of diffusivity determination via the Boltzmann transformation is that subsequent application of the obtained diffusivity in analytical or numerical calculations should reproduce the lambda profile (and hence the capillary absorption coefficient, which is equivalent to its integral) that it was based on (or at least the approximation, see e.g. equation (3), that was applied in the Boltzmann transformation). This inherent premise is recognized in multiple sources (Carmeliet et al., 2004; Evangelides et al., 2018; Lockington et al., 1999; Nizovtsev et al., 2008; Pavlik and Cerny, 2012; Ren et al., 2019; among others), but is evidently not accepted in (Xie et al., 2025). Violation of this inherent premise would however bring about unsound findings. This argument can be elaborated based on Xie et al. (2025)’s measured and simulated lambda profiles. While the latter is not explicitly presented, it can be inferred easily. The simulated capillary absorption in Xie et al. (2025)’s Figure 10 shows that the simulation respects the capillary moisture content as upper limit. This infers that the high simulated capillary absorption coefficient 0.755 kg/m2s0.5 (relative to the low measured capillary absorption coefficient 0.230 kg/m2s0.5) can only stem from a faster penetration of the moisture front into the material. Such faster penetration in the simulation would then logically yield a simulated lambda profile that is “stretched” significantly to higher lambda values, relative to the measured lambda profile in Xie et al. (2025)’s Figure 9a. Concretely, presuming the same “vertical form” for the measured and simulated lambda profile, the simulated profile ends at 2.2 cm/min0.5 while the measured profile ends at 0.683 cm/min0.5. Only this growth of the lambda end point with a factor 3.3 complies with the increase with a factor 3.3 of the simulated versus the measured capillary absorption coefficient. If one were then to calculate the moisture diffusivity with the stretched simulated lambda profile, the resulting “simulated” diffusivity would be above the original “measured” diffusivity, implying a logical conflict between input and output of the simulation. Concretely, the integral and derivative in Xie et al. (2025)’s equation (8) would respectively increase and decrease with a factor 3.3, thus raising the resulting “simulated” diffusivity with about a factor 11 relative to the original “measured” diffusivity. Such deviation between the input “measured” diffusivity and the output “simulated” diffusivity is not acceptable, and again confirms that the simulation cannot be correct.
Doubtful moisture retention curve
While being unrelated to the primary message of this critique, one more flaw appears to occur in the moisture retention curve in Xie et al. (2025)’s Figure 5b, as it essentially deviates from the mercury intrusion porosimetry it is based on. Figure 1 in Xie et al. (2025) depicts the mercury intrusion results for the salt-free bricks. This graph illustrates that most of the brick’s pores have diameters between 40 and 4000 nm, with a concentrated share of the pores having diameters at around 1500 nm. The latter translates, via Kelvin’s law, to about 200 J/kg as chemical potential. This infers that the most strongly sloped part of the moisture retention curve should be centered on this chemical potential value. Regrettably, that is not the case in Xie et al. (2025)’s Figure 5: the most strongly sloped part of the curve (in the 0.10 m3/m3 < θ < 0.27 m3/m3 range) is located at a chemical potential of around 1000 J/kg instead of the expected 200 J/kg.
Conclusion
In January 2025, this journal published the paper “Measurement and optimization of estimation method for moisture diffusivity of porous building materials with different salt content” (Xie et al., 2025). Based on observed deviations between measured and simulated capillary absorption in salt-free and salt-laden bricks, the paper contests the validity of the ruler-based diffusivity determination of Evangelides et al. (2018), and proposes potential improvements to come to a “more accurate diffusivity.” The analytical solutions and logical arguments presented above establish however that the deviation between measured and simulated capillary absorption should not be allocated to the experimental (ruler-based) diffusivity determination, but instead to the invalidity of Xie et al. (2025)’s simulations. In addition, a concern on the disparity between moisture retention curve and mercury intrusion porosimetry has been formulated. In conclusion hence, this critique invites Xie et al. (2025)’s authors to reflect on and respond to these concerns in their reply.
