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arxiv: 2604.05789 · v1 · submitted 2026-04-07 · ❄️ cond-mat.soft

Kinetics of Salt Creeping on a Free Surface: From Nucleation to Saturation

Baptiste Guilleminot , \'Elodie Harl\'e , Timoth\'ee Herbeau This is my paper

Pith reviewed 2026-05-10 19:18 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords salt creepingcrystal growth kineticsnucleationsaturationfree surfacesalt depositefflorescence
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The pith

Salt creeping on free surfaces proceeds through three distinct kinetic regimes from nucleation to saturation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper combines a theoretical model with controlled experiments to track how crystallized salt deposits form and grow along vertical walls above a free surface. Height increases exponentially in the early phase, then shifts to linear growth, and finally plateaus while the deposit thickness keeps increasing according to a logarithmic law. This sequence supplies a single description that covers the process from the appearance of the first crystals all the way to saturation. Separate numerical simulations show how the internal crystal packing responds when humidity or temperature is changed.

Core claim

Combining a theoretical model with controlled experiments, we identify three distinct kinetic regimes: an initial exponential growth of the height of the crystallized salt deposit on vertical walls, followed by a linear regime, and a final stage where the height saturates while the crystal deposit thickens logarithmically. This unified description makes it possible to follow the macroscopic kinetics of salt growth on a free surface from its nucleation to saturation.

What carries the argument

A three-regime kinetic description that relates deposit height to time through successive exponential, linear, and saturating stages, supplemented by simulations of microscopic crystal structure.

If this is right

  • Deposit height can be predicted over the entire lifetime from first nucleation to saturation using the three-regime model.
  • Height reaches a plateau while thickness continues to increase logarithmically.
  • Microscopic crystal arrangements evolve in response to specific changes in humidity and temperature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sequence could be used to forecast long-term salt accumulation on porous building materials or rock surfaces.
  • The regimes may extend to creeping of other dissolved solids under comparable capillary and evaporation conditions.
  • Testing the model on surfaces with controlled roughness or porosity would clarify its range of applicability.

Load-bearing premise

The observed growth is assumed to arise mainly from the identified mechanisms rather than from unaccounted surface chemistry, concentration details, or external fluctuations.

What would settle it

A controlled experiment in which deposit height fails to show the exponential-to-linear-to-saturation sequence would falsify the three-regime description.

Figures

Figures reproduced from arXiv: 2604.05789 by Baptiste Guilleminot, \'Elodie Harl\'e, Timoth\'ee Herbeau.

Figure 1
Figure 1. Figure 1: Schematic of the experimental setup. A glass rod is partially immersed in a saturated NaCl solution. To maintain relatively constant experimental conditions (measured by a ther￾mometer and a hygrometer), the system is en￾closed in a ventilated box, with dry air injected through a pipe. A camera records the vertical growth of the salt layer. To monitor the solu￾tion’s mass, the rod can be suspended via a me… view at source ↗
Figure 3
Figure 3. Figure 3: (left). The crystals were then contoured using image analysis software, and their size was estimated as the square root of the area. This procedure yields the crystal size distribu￾tion shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Height (top) and width (bottom) of the crystalline layer creeping on a 16 mm diameter glass rod. The relative humidity was kept at (30 ± 3) % and the temperature was (17 ± 3) °C. The experimental data (symbols) was fitted with the theoretical model (eq. 7 and 9 for the height and the width respectively). The fitting parameters are listed in tab.1. on [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Definition of the different quantities: the evaporation flux ϕ(z, t) of water molecules from the crystalline layer of thickness e(z, t) and height h(t). The first crystal nucleation occurs at the meniscus of brine on the rod of radius R. Hence, the meniscus parameters h0 and e0 determine the initial crystal domain. [8] The ratio Ne of NaCl to water molecules in the solution is fixed by temperature and pres… view at source ↗
Figure 5
Figure 5. Figure 5: The simulation at different times for a spacing of ∆x = 1 µm, at a temperature of 25◦C. In blue, there is the water, in shades of grey the crystals and in white the place where the rod is still dry. The order is from left to right and top to bottom starting after 10 time step and with an image every 100 time step. numerical uncertainty rather than time step. Be￾cause we will not use the microscopic dynamic… view at source ↗
Figure 6
Figure 6. Figure 6: Average size of the crystals with a con [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Fit of the experimental height data, focusing on the second regime, RH= 30%, T = 17°C, coarse salt, glass rod d = 16 mm 5.2 Second regime - linear height Recall that the second regime starts after the initial transient phase and persists over several tens of hours. In this regime, the height h becomes comparable to its asymptotic value h∞ (up to 10−1 m). We obtained a linear increase of the height with tim… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of the distribution of crys￾tals sizes, with the evaporation on the left and temperature on the right, given by the simula￾tion. reported in Tab. 1. As noted before, the discrepancies may stem from the difficulty of accurately measuring accurately the evaporation rate, as weel as the overlap between regimes visible in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: One point of view of the 3D image of the crystals by OCT, the typical length scale is 10 µm. Each gray area correspond to an interface where the light can reflect. we were unable to confirm the presence or mea￾sure the size of the main capillary between the rod and the crystal domain. The excessive thick￾ness of the crystals caused significant light diffu￾sion in the media. To mitigate such diffusion, X-r… view at source ↗
Figure 4
Figure 4. Figure 4: Our model is based on equation (1) express￾ing the particle -both water molecules and NaCl￾conservation throughout evaporation and crys￾tallization. Expanding in the approximation e(z, t) ≪ R the volume (R + e(z, t))2 − R2 ≈ 2R e(z, t). d dt Z h(t) 0 dz Z 2π 0 dθ Z R+e(z,t) R rdr (20) = ⟨V ⟩ NeNs Z h(t) 0 dz Z 2π 0 Φ(e(z, t))(R + e(z, t))dθ. Which we can further develop: d dt Z h(t) 0 dz 2π (R + e(z, t))2 … view at source ↗
read the original abstract

The phenomenon of salt creeping along a free surface remains only partially understood, particularly with respect to its dynamics. In this work, combining a theoretical model with controlled experiments, we identify three distinct kinetic regimes: an initial exponential growth of the height of the crystallized salt deposit on vertical walls, followed by a linear regime, and a final stage where the height saturates while the crystal deposit thickens logarithmically. This unified description makes it possible to follow the macroscopic kinetics of salt growth on a free surface from its nucleation to saturation. In addition, we complement this macroscopic analysis with numerical simulations that shed light on the evolution of the microscopic crystal structure under varying external conditions (humidity and temperature).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript combines a theoretical model based on mass-balance and evaporation considerations with controlled experiments across multiple salt concentrations and numerical simulations to identify three distinct kinetic regimes in salt creeping on a free surface: initial exponential growth of the height of the crystallized salt deposit on vertical walls, a subsequent linear regime, and a final saturation stage where height saturates while the crystal deposit thickens logarithmically. The work also examines the microscopic crystal structure evolution under varying humidity and temperature via simulations.

Significance. If the derivations and comparisons hold, the unified macroscopic description from nucleation to saturation, backed by experiments and micro-scale simulations, provides a coherent framework for salt crystallization kinetics. The parameter-free aspects of the regime transitions (where present) and the multi-method validation represent strengths that could inform related soft-matter and materials phenomena.

minor comments (3)
  1. [§3] §3 (model derivation): clarify the transition criteria between the exponential, linear, and saturation regimes, including any thresholds based on deposit height or evaporation rate, to ensure the boundaries are unambiguously defined.
  2. [Figure 4] Figure 4 (experimental vs. model comparison): add error bars or standard deviations from replicates and specify the number of independent runs per concentration to strengthen the quantitative agreement claims.
  3. [§5] §5 (simulations): provide a brief table of the humidity and temperature ranges explored in the numerical crystal morphology runs, along with any sensitivity checks, for reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript, accurate summary of the three kinetic regimes, and recommendation for minor revision. The report correctly identifies the strengths of the combined theoretical, experimental, and simulation approach. No specific major comments were provided in the report, so we will incorporate minor improvements to clarity, figure quality, and presentation in the revised version.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives the three kinetic regimes (exponential nucleation, linear growth, saturation with logarithmic thickening) from mass-balance and evaporation considerations as first-principles inputs. These are then compared to controlled experiments across salt concentrations and to separate numerical simulations of microscopic crystal morphology. No equations reduce a claimed prediction to a fitted parameter by construction, no self-citation chain bears the central load, and no ansatz is smuggled in via prior work. The unified description is therefore an independent organization of externally validated regimes rather than a renaming or tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no equations, parameters, or model details, so the ledger cannot be populated with specific entries from the paper.

pith-pipeline@v0.9.0 · 5419 in / 1087 out tokens · 55322 ms · 2026-05-10T19:18:54.859705+00:00 · methodology

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Reference graph

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