# Experimental Investigation and Modeling: Considerations of Simultaneous Surface Steel Droplets’ Evaporation and Corrosion

^{1}

^{2}

^{3}

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^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{st}), which, as a convention, is given in μm. The experimentally determinable constants A and n take into account the influence of the factors mentioned above on the dynamics A as well as the superficial formation of the rust layer, which reduces the intensity of corrosion n.

^{−}ions in the corrosion environment [7]. We show that most countries in the world have participated, since 1980, in a program to monitor the atmospheric corrosion of steels, so that data on the parameters of this model are available [8]. Now, the problem of atmospheric corrosion of steels is treated much more complexly, starting mainly from the fact that water reaches the steel structures through rain and through condensation in drops (dew), which determines two main cases of corrosion, namely film corrosion and corrosion drops. Both cases of atmospheric corrosion can be characterized by approaches which consider them to be cases of simultaneous transfer of momentum and mass [9,10], respectively, and of simultaneous transfer of heat and mass [11,12] which are associated with the electrochemical process that takes place at the corrosion surface. In the case of droplet corrosion, their appearance on the condensation surface is a relatively fast process, under 10–15 min [13], if the condensation conditions are met [14], as is shown by Equation (2), where p

_{s}is the water saturation pressure, t

_{s}and t

_{g}represent the surface and air temperature, respectively, U

_{r}gives the air relative humidity and t

_{dew}is the dew point temperature.

^{2}·grd). A coalescence of the small droplets on the steel surface, which is also fast, leads to a droplet size distribution estimated to follow a normal distribution, between 0.2 mm and 6 mm. Evaporation of a droplet from a surface is a simultaneous mass and heat transfer process with its duration depending on droplet size, on temperature difference t

_{s}-t

_{g}and on the fact that, here, the heat transfer coefficient is low (below 100 w/m

^{2}·grd), corresponding to weak natural convection or laminar gas flow along the evaporation surface. In other words, considering its duration in relation to the surface corrosion process, droplet evaporation is much more important than deposition.

^{−}for example). Given the repeatability of surface dew deposition, it must be shown whether repeated formation of the droplet on a rust trace accelerates or decelerates corrosion. The current paper focuses on these issues or, more correctly, on some aspects of these issues. Specifically, a new approach was used to experimentally investigate the simultaneous process of droplet evaporation and sub-droplet corrosion on the steel surface, the purpose of which was to validate the models developed to describe this phenomenon. The droplet evaporation model and the sub-droplet corrosion model are coupled by having the same transfer surface, which decreases with time. A new solution was thus proposed to express the dynamics of the transfer surface for evaporation, and for oxygen supply in the droplet as a function of the momentary droplet mass, respectively, while several new elements were considered for the two coupled models, the most significant being the decreasing circulation due to the Marangoni phenomenon.

## 2. Materials and Methods

#### 2.1. Experimental Setup and Procedures

^{+2}to Fe

^{+3}oxidation and with metal oxide precipitation, is expressed [8,9,10] by Equation (3):

_{p}represents the average droplet corrosion surface and using M

_{i}(I = Fe, Fe

_{2}O

_{3}·zH

_{2}O) gives the molecular mass of species i.

- Determining the mass of the steel plate;
- Loading the plate with droplets in the preset positions;
- Starting the recording the momentary mass of the plate with droplets and the state of the moist air parameters near the surface (at ~8 cm from it);
- Taking digital photographs of the plate with droplets at test starting, during the test and at the end of each test experiment;
- Ascertaining the drying of the droplets and saving the recordings in order to process them.

#### 2.2. Mathematical Modeling

_{τ}shows the distance from the center of the droplet to its boundary.

_{2}inside the droplet, and its consumption through the reaction on the surface, resulting in the generation of rust. We mention that inside the droplet there is an internal flow determined by the association of the Marangoni phenomenon with its evaporation [25,26,27]. Figure 5 schematically represents this flow. When falling outside, over the boundary layer, the experimental conditions characterize an environment, at most, in natural convection. Under these conditions, the vapors leaving the surface of the drop pass by diffusion over the inert (air) through the boundary layer of thickness δ. On any direction, z, normal to the surface of the drop, the specific flow rate is given by the differential expression in Equation (9), where c is the total molar concentration and D

_{v}represents the air vapor diffusion coefficient.

_{v}, δ and even y

_{Bm}in (10) depend on t

_{g}and t

_{s}

_{,}or more correctly on those differences, it was considered, for k

_{g}

_{,}as dependent on the heat transfer driving force t

_{g}− t

_{s}. So,

_{p}) as follows from the coupling of Equations (6)–(8), where we put V

_{τ0y}= m

_{pτ}/ρ

_{a}. With this consideration, Equation (13) can be written as Equation (14).

_{p}), then the momentary mass of the droplet becomes analytically expressible. Table 3 shows the calculation of the transfer surface, for the droplet masses of interest in the present work, so that α and f(m) from Equation (14) can be identified. In more detail from Equation (8) it is expressed as x = φ(y) and since R is fixed and m

_{p}is chosen, in the range of interest of our droplet mass, then solving the equation ${m}_{p}={\rho}_{w}{V}_{\tau oy}=\pi {\rho}_{v}{{\displaystyle \int}}_{0}^{{h}_{\tau}}{\left(\phi \left(y\right)\right)}^{2}dy$ (Equation (6)) gives the ${h}_{\tau}$, value, which then immediately leads to S or S(τ), as is shown in Equation (7), where it is correlated by regression polynomial after the momentary particle.

_{s}results from the fact that the specific heat flow brought by convection to the droplet (Equation (15)) is equal to the specific heat flow due to vaporization (Equation (16)). It is identified in Equation (15) that the value of the heat transfer coefficient is a function of the air temperature difference and the surface drop. So α

_{g}= α

_{g}(t

_{g}− t

_{s}). In Equation (16) the latent heat of vaporization of water was denoted by r

_{v}.

_{g}and q

_{v}, coupled with N

_{v}relationship, occurs for t

_{s}in Equation (17).

_{g}(t

_{g}− t

_{s}) using α

_{g}(t

_{g}− t

_{s}). This is given by Equation (18), where ρ

_{g}is the air density and c

_{pg}represents its specific heat coefficient. Coupling Equation (18) with Equation (19) leads to the expression of the droplet surface temperature by the conditional Equation (19). For y

_{v}(t

_{s}) Equation (20) is used, where p is the air pressure and A, B, C are the Antoine constants for expressing the water saturation vapor pressure.

_{vδ}depends on the relative air humidity (φ) and the saturation pressure of water vapor at its temperature t

_{g}. It should also be said that, after t

_{s}, this relationship is a transcendent equation so to analytically or graphically raise the dependence t

_{s}= t

_{s}(φ,t

_{g}), a calculation program is required.

_{c}have the specifications shown in Table 4.

_{O2d}to the concentration of c

_{O2s}, corresponding to the surface reaction, is considered the most important. Relation (22) expresses the specific flow rate of oxygen. This becomes (23) by expressing c

_{O2s}from the equality of oxygen transferred with oxygen consumed by the reaction surface.

_{O2d}can be considered as the equilibrium of concentration of oxygen and the droplet surface temperature. The mass transfer coefficient k

_{l}, given by adapting the literature [32,33], takes into account the fact that the driving force for the Marangoni flow inside the droplet is represented by the surface tension difference between the water at the droplet surface, σ(t

_{s}), and at the solid surface, (σ(t

_{p}) ≈ σ(t

_{g}), as shown by Equation (24). For the apparent reaction constant, k

_{rsa}, Equation (25) [10] was considered. Here the value of 2.3 × 10

^{−5}m/s [10] was assumed for k

_{rs}(oxygen surface reaction constant when the steel surface is not rusted (i.e., new, this is a novelty regarding the model from [10] previously)). In regard to the surface reaction rate constant, we show that it has a rather complex meaning. Thus, seeing the corrosion process as a process with a chemical kinetic in which the solid reacts with the limiting reactant (oxygen in water in the case of pure corrosion) and then it is influenced by local surface structure issues (local crystallinity, intra-granular inclusions). As these structural irregularities are distributed, the surface is seen to have average properties. As a result, the reaction rate constant of the surface corrosion process refers to a surface seen with average unevenness. The rust thickness, δ

_{r}

_{,}is linearly dependent on the mass of rust deposited at the solid interface of the droplet (Equation (26)). For the oxygen diffusion coefficient through the rust layer, the range of values is 0.2 × 10

^{−9}–2 × 10

^{−9}m

^{2}/s [10].

## 3. Results

- The water mass dynamics of the drops from the plate;
- The state of the evaporating drops’ shape;
- The air parameters near to the plate with the evaporating drops;
- The increase in plate mass due to rust deposition from corrosion process.

_{p}) this fact, now supported experimentally, was used: namely that the drop shrinks while keeping its initial diameter.

^{−}is reported in many works [34,35], so our data are in agreement with them.

_{Fe}·cm

^{−2}h

^{−1}(Table 5 and Table 6, column F) to 0.05–0.06 mg

_{Fe}·cm

^{−2}h

^{−1}(Table 7 and Table 8, column F).

## 4. Discussion

- Completing the model with additional data (temperature dependence of dissolved oxygen concentration in water droplet, temperature dependence of water surface tension, densities, molecular masses, etc.) and conditions’ initials;
- The numerical transposition of the model with the micro sequences: (a) the choice of the parameters of the model that require calibration, namely the coefficient α and the power m in relation (21), the coefficient a in Equation (24), k
_{rs}and the relation D_{O2efin}(Equation (25)), respectively; (b) selection, from the beginning of the investigation, of the tests with all their data, which are used in the calibration (Table 5 and Table 6 for corrosion in water droplets, respectively, and Table 8 for corrosion with droplets containing NaCl); (c) setting an option regarding air parameters’ (relative humidity and temperature according to Table 5, Table 6, Table 7 and Table 8) use in the model, i.e., as functions of time or as average values; (d) the effective expression of the numerical model from the import of the test data file to the Runge–Kutta integration of the differential equations that provides the dynamics of the mass of the droplet and the dynamics of the mass of rust deposited under the droplet, respectively; - The effective use of the numerical model in order to establish values for certain parameters, and strategies for expressing others, respectively.

_{g}) near the plate is supported by the recorded data (Table 5, Table 6, Table 7 and Table 8, column G and H), which show extremely small time variations. The values identified for the surface reaction rate constant (k

_{rs}) and for the effective diffusion coefficient of oxygen through the rust layer (D

_{O2ef}) are consistent with those from film corrosion [9] when evaporation–corrosion occurs in water droplets. The higher values of k

_{rsin}corrosion by NaCl water droplets show the intensification of the anodic reaction on the steel surface, as reported in other works [34,35,36]. The high value of D

_{O2efin}in this case indicates a fairly permeable structure of the rust formed in the corrosion process, as well as that here the transport of oxygen is facilitated by the action of the Cl

^{−}ions. For the constant α in Equation (24) the model worked well with a higher value compared to those found in the literature (3.75 × 10

^{−5}).

_{g}.

_{i}is the number of time steps since model integration for the i evaporation-corrosion test.

_{g}/20 finds the values 0.7551 and −0.2900, respectively, showing that a can, in the limit, be linearly related to φ and can be considered independent of t

_{g}. Figure 18 supports these results. The line a vs. φ in this figure is given by Equation (32). Adding Equation (32) to Table 9 means that all parameters of the evaporation–corrosion model are known.

_{mpM}) together with graphical representations from Figure 13, Figure 14 and Figure 15.

## 5. Conclusions

^{−5}m/s, oxygen diffusion coefficient through the rust layer at 9.1 × 10

^{−10}m

^{2}/s, m constant from the Equation (21) to 0.33, respectively, and α from Equation (24) to 2.63 × 10

^{−4}m

^{2}·s (Table 9). When NaCl was present in the corrosion medium, at the concentration level of 1 g/L, the surface reaction rate constant increased 21 times. The same increase was identified for the oxygen diffusion coefficient through the crust.

_{mpM}r and ε

_{mruM}

_{,}respectively).

^{-}ions in the anodic corrosion process, led to a strong change in the reaction rate constant and the oxygen diffusion coefficient through the rust layer values, so that we could obtain, for the dynamics of the mass deposited by the rust, a good agreement between the model and the experiment.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Experimental laboratory setup for corrosion in water droplets: (1) black steel plate for corrosion tests; (2) precision balance; (3) water droplets to corrode; (4) balance protection enclosure; (5) temperature humidity dew point Data Logger; (6) laboratory meteorological micro station; (7) filming device; (8) data registration and processing system; (9) stand; (10) clamp stand.

**Figure 2.**Possible models for the evolution of droplets shape during their evaporation, hemisphere shape: (

**A**) descending hemisphere; (

**B**) spherical cap with trace preservation; (

**C**) spherical cap without trace preservation. Rust is brown color.

**Figure 4.**Representation of mass and heat transfer when evaporating the droplet from the steel surface (boundary layer limit as dotted line).

**Figure 5.**The process of oxygen transfer and corrosion inside the droplet with Marangoni flow (boundary layer limit as dotted line).

**Figure 6.**Determination of the average diameter of the water droplet and its associated standard deviation (Test 1, d

_{0}= 7.71 ± 0.8 mm).

**Figure 7.**Frames from droplet evaporation–corrosion on a steel surface in Test 1, showing that droplet shrinkage occurs with droplet diameter maintained: (φ = 36.5%, d

_{0}= 7.2 mm): (

**a**) blank black steel plate, starting droplet’s deposition; (

**b**) droplet already in position; (

**c**) evaporation evolution after 21 min; (

**d**) end of evaporation and shape formation; (

**d**) bottom-third deposition of the drop, φ = 43.5%, d

_{0}= 7.2 mm.

**Figure 8.**Frames from droplet evaporation–corrosion on a steel surface in Test 3, showing that droplet shrinkage occurs with droplet diameter maintained: (φ = 43.5%, d

_{0}= 7.2 mm): (

**a**) starting droplet’s deposition onto rusted old trails; (

**b**) droplet already in position; (

**c**) evaporation evolution after 21 min; (

**d**) end of evaporation with the new layer of rust.

**Figure 9.**Droplet shape and diameter during their evaporation from the steel surface in evaporation-corrosion Test 1: (

**a**) initial; (

**b**) after 120 min; (

**c**) after 210 min (end of test). Mean diameter and standard deviation are shown in Table 5.

**Figure 10.**Droplet shape and diameter during their evaporation from the steel surface in evaporation-corrosion Test 4: (

**a**) initial; (

**b**) after 120 min; and (

**c**) after 210 min (end of test). Mean diameter and standard deviation are shown in Table 6.

**Figure 11.**Droplet shape and diameter during their evaporation from the steel surface in the evaporation-corrosion test 28: (

**a**) initial; (

**b**) after 120 min; (

**c**) after 330 min (end of test). Mean diameter and standard deviation are shown in Table 7).

**Figure 12.**Droplet shape and diameter during their evaporation from the steel surface in the fourth evaporation-corrosion test 30: (

**a**) initial; (

**b**) after 120 min; (

**c**) after 210 min (end of test). Mean diameter and standard deviation are shown in Table 8).

**Figure 13.**Dynamics of droplets mass during their evaporation for tests 1 to 10 (T

_{1}…T

_{10}): (

**a**) T

_{1}–red; T

_{3}—blue; T

_{5}—green; T

_{7}—black; T

_{9}—brown; (

**b**) T

_{2}–red; T

_{4}–blue; T

_{6}–green; T

_{8}–black; T

_{10}–brown; continuous curves–model, dashed curves–experimental.

**Figure 14.**Dynamics of droplets mass during their evaporation for tests 11 to 20 (T

_{11}…T

_{20}): (

**a**) T

_{11}—red; T

_{13}—blue; T

_{15}—green; T

_{17}—black; T

_{19}—brown; (

**b**) T

_{12}—red; T

_{14}—blue; T

_{16}—green; T

_{18}—black; T

_{20}—brown; continuous curves—model, dashed curves—experimental.

**Figure 15.**Dynamics of droplets mass during their evaporation for tests 21 to 30 (T

_{21}…T

_{30}): (

**a**) T

_{21}—red; T

_{23}—blue; T

_{25}—green; T

_{27}—black; T

_{29}—brown; (

**b**) T

_{22}—red; T

_{24}—blue; T

_{26}—green; T

_{28}—black; T

_{30}—brown; Continuous curves—model, dashed curves—experimental.

**Figure 16.**Dynamics of deposited rust mass during droplets evaporation-corrosion, from one droplet, experimental for tests T

_{1}…T

_{20}: (

**a**) T

_{1}to T

_{10}; (

**b**) T

_{11}to T

_{20}; continuous curves—model, dashed curves—experimental.

**Figure 17.**Dynamics of deposited rust mass during droplets evaporation—corrosion: (

**a**) in experimental tests T1

_{21}…T

_{30}; (

**b**) cumulated mass rust vs. effective corrosion time; line—model, dashed line—experimental).

**Figure 18.**The evolution of a coefficient of Equation (21) in respect to the relative humidity of the air (

**a**) and its temperature (

**b**).

**Table 1.**Black weathering steel sheet composition used in water droplet corrosion research (according to manufacturer) [10].

Element | Composition (wt%) |
---|---|

Manganese (Mn) | 0.166 |

Phosphorus (P) | 0.028 |

Sulfur (S) | 0.028 |

Carbon (C) | 0.206 |

Chromium (Cr) | 0.078 |

Molybdenum (Mo) | 0.114 |

Vanadium (V) | 0.003 |

Silicon (Si) | 0.004 |

Copper (Cu) | 0.082 |

Nickel (Ni) | 0.088 |

Titanium (Ti) | 0.004 |

Iron (Fe) | 0.199 |

C.N. | Experimental Factors | Values | Observations |
---|---|---|---|

1 | Number of drops on the plate | 100 | Selected |

2 | The initial mass of the drops on the plate (g) | 4.5–15.5 | Selected |

3 | Average droplet volume (μL) | 45–55 | Computed |

4 | The initial shape of the drop | Spherical cap | Observed |

5 | Electrical conductivity and water pH (μS/cm) | 100 | Selected |

6 | Number of successive tests for corrosion in water | 26 | Selected |

7 | NaCl concentration (g/L) in water (accelerated corrosion) | 1 | Selected |

8 | Number of accelerated corrosion tests | 4 | Selected |

**Table 3.**Calculation of droplet evaporation surface value as a function of droplet mass for the case of paraboloid cap with constant cap radius.

Parameters | Surface Values as Function of Droplet Mass | ||||||
---|---|---|---|---|---|---|---|

R (cm) | 0.30 | ||||||

m_{p} (g) | 0.060 | 0.050 | 0.040 | 0.030 | 0.020 | 0.010 | 0.005 |

h or h_{τ} (cm) | 0.312 | 0.276 | 0.235 | 0.183 | 0.133 | 0.069 | 0.035 |

S or S(τ) (cm^{2}) | 0.588 | 0.528 | 0.453 | 0.378 | 0.286 | 0.283 | 0.283 |

$\alpha f({m}_{p}$) | $\alpha =\pi {R}^{2}$ $f\left({m}_{p}\right)=0.908+7.08{m}_{p}+221.2{m}_{p}^{2}$ | ||||||

R (cm) | 0.35 | ||||||

m_{p} (g) | 0.060 | 0.050 | 0.040 | 0.030 | 0.020 | 0.010 | 0.005 |

h or h_{τ} (cm) | 0.252 | 0.228 | 0.189 | 0.147 | 0.101 | 0.052 | 0.022 |

S or S(τ) (cm^{2}) | 0.595 | 0.530 | 0.458 | 0.385 | 0.385 | 0.385 | 0.385 |

$\alpha f({m}_{p}$) | $\alpha =\pi {R}^{2}$ $f\left({m}_{p}\right)=1.037-7.79{m}_{p}+277.5{m}_{p}^{2}$ | ||||||

R (cm) | 0.40 | ||||||

m_{p} (g) | 0.060 | 0.050 | 0.040 | 0.030 | 0.020 | 0.010 | 0.005 |

h or h_{τ} (cm) | 0.217 | 0.185 | 0.152 | 0.116 | 0.078 | 0.040 | 0.020 |

S or S(τ) (cm^{2}) | 0.601 | 0.529 | 0.505 | 0.503 | 0.503 | 0.503 | 0.503 |

$\alpha f({m}_{p}$) | $\alpha =\pi {R}^{2}$ $f\left({m}_{p}\right)=1.043-5.98{m}_{p}+135.7{m}_{p}^{2}$ | ||||||

R (cm) | 0.45 | ||||||

m_{p} (g) | 0.060 | 0.050 | 0.040 | 0.030 | 0.020 | 0.010 | 0.005 |

h or h_{τ} (cm) | 0.179 | 0.157 | 0.123 | 0.093 | 0.062 | 0.031 | 0.016 |

S or S(τ) (cm^{2}) | 0.666 | 0.656 | 0.642 | 0.636 | 0.636 | 0.636 | 0.636 |

$\alpha f({m}_{p}$) | $\alpha =\pi {R}^{2}$ $f\left({m}_{p}\right)=1.005-0.933{m}_{p}+27.5{m}_{p}^{2}$ |

C.N. | Parameter | Vertical Surface | Horizontal Upper Surface | Horizontal Lower Surface |
---|---|---|---|---|

1 | $a$ | 1.420 | 1.320 | 1.520 |

2 | $m$ | 0.250 | 0.250 | 0.330 |

3 | ${l}_{c}$ | 0.112 | 0.055 | 0.055 |

**Table 5.**Experimental data characterizing the evaporation of droplets from the steel surface and its corrosion (Test 1, d

_{0}= 7.78 ± 0.31 mm, d

_{u}= 8.05 ± 0.45 mm).

A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 482.15 | 487.25 | 0.00 | 0.05 | 27.7 | 53.9 | 17.5 | 26.0 | 55.0 | 757.6 | 0.0 |

2 | 30 | 486.35 | 0.90 | 27.8 | 52.9 | 17.3 | 0.5 | |||||

3 | 60 | 485.30 | 1.05 | 27.9 | 53.3 | 17.5 | 1.0 | |||||

4 | 90 | 484.00 | 1.30 | 27.9 | 52.8 | 17.3 | 1.5 | |||||

5 | 120 | 483.50 | 0.50 | 28.0 | 52.1 | 17.2 | 2.0 | |||||

6 | 150 | 482.80 | 0.70 | 27.8 | 52.8 | 17.2 | 2.5 | |||||

7 | 180 | 482.20 | 0.60 | 27.8 | 52.9 | 17.3 | 3.0 | |||||

8 | 210 | 482.20 | 0.00 | 27.8 | 53.2 | 17.3 | 3.5 |

**Table 6.**Experimental data characterizing the evaporation of droplets from the steel surface, and its corrosion (Test 4, d

_{0}= 7.79 ± 0.54 mm, d

_{u}= 8.38 ± 0.55 mm).

A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 482.30 | 486.85 | 0.00 | 0.05 | 27.2 | 43.2 | 13.6 | 2.0 | 44.0 | 756 | 81.0 |

2 | 30 | 484.35 | 2.50 | 27.4 | 42.8 | 13.6 | 81.5 | |||||

3 | 60 | 484.10 | 0.25 | 27.5 | 42.5 | 13.6 | 82.0 | |||||

4 | 90 | 482.80 | 1.30 | 27.7 | 41.9 | 13.5 | 82.5 | |||||

5 | 120 | 482.35 | 0.00 | 27.9 | 40.9 | 13.3 | 83.0 | |||||

6 | 150 | 482.35 | 0.00 | 27.8 | 40.9 | 13.3 | 83.5 |

**Table 7.**Experimental data characterizing the evaporation of droplets from the steel surface and its corrosion (Test 28, d

_{0}= 8.70 ± 0.44 mm, d

_{u}= 8.93 ± 0.50 mm).

A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 484.45 | 501.60 | 0.00 | 0.25 | 28.5 | 32.2 | 10.3 | 32 | 45 | 759 | 9711.5 |

2 | 30 | 498.00 | 3.60 | 28.3 | 31.7 | 9.8 | 9712.0 | |||||

3 | 60 | 497.30 | 0.70 | 28.2 | 33.4 | 10.5 | 9712.5 | |||||

4 | 90 | 495.40 | 1.90 | 28.3 | 32.6 | 10.3 | 9713.0 | |||||

5 | 120 | 492.35 | 3.05 | 28.1 | 32.2 | 9.9 | 9713.5 | |||||

6 | 150 | 490.20 | 2.15 | 28.1 | 32.1 | 9.9 | 9714.0 | |||||

7 | 180 | 488.40 | 1.80 | 28.0 | 31.7 | 9.6 | 9714.5 | |||||

8 | 210 | 487.65 | 0.75 | 28.0 | 31.8 | 9.6 | 9715.0 | |||||

9 | 240 | 486.30 | 1.35 | 27.9 | 32.4 | 9.8 | 9715.5 | |||||

10 | 270 | 485.40 | 0.90 | 27.8 | 33.1 | 10.1 | 9716.0 | |||||

11 | 300 | 484.85 | 0.55 | 27.7 | 33.6 | 10.2 | 9716.5 | |||||

12 | 330 | 484.85 | 0.00 | 27.6 | 34.1 | 10.3 | 9717.0 |

**Table 8.**Experimental data characterizing the evaporation of droplets from the steel surface and its corrosion (Test 30, d

_{0}= 9.05 ± 0.47 mm, d

_{u}= 9.32 ± 0.49 mm).

A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 485.20 | 496.15 | 0.00 | 0.30 | 28.9 | 37.8 | 13 | 30 | 35 | 757 | 9769.0 |

2 | 30 | 493.10 | 3.05 | 29.1 | 37.6 | 13.1 | 9769.5 | |||||

3 | 60 | 491.20 | 1.90 | 29.2 | 37.7 | 13.3 | 9770.0 | |||||

4 | 90 | 489.35 | 1.85 | 29.0 | 36.9 | 12.7 | 9770.5 | |||||

5 | 120 | 488.15 | 1.20 | 28.8 | 37.1 | 12.7 | 9771.0 | |||||

6 | 150 | 486.70 | 1.45 | 28.7 | 37.1 | 12.6 | 9771.5 | |||||

7 | 180 | 485.50 | 1.20 | 28.6 | 37.1 | 12.5 | 9772.0 | |||||

8 | 210 | 485.50 | 0.00 | 28.5 | 36.7 | 12.2 | 9772.5 |

C.N. | Case | Data | φ | t_{g} | ${\mathit{k}}_{\mathit{r}\mathit{s}}$ (Equation (25)) | ${\mathit{D}}_{\mathit{O}2\mathit{e}\mathit{f}}$ (Equation (23)) | a (Equation (21)) | m (Equation (21)) | α (Equation (24)) |
---|---|---|---|---|---|---|---|---|---|

1 | Water droplet | Table 5 Table 6 | mean | mean | 4.5 × 10^{−5} (m/s) | 9.1 × 10^{−10} (m^{2}/s) | f(φ,t_{g}) | 0.33 | 2.63 × 10^{−4} (m^{2}·s) |

2 | Water droplet with NaCl | Table 8 | mean | mean | 9.5 × 10^{−4} (m/s) | 5.1 × 10^{−9} (m^{2}/s) | f(φ,t_{g}) | 0.33 | 2.63 × 10^{−4} (m^{2}·s) |

**Table 10.**Corrosion tests and comparison of experimental results with those according to the model by relative deviations (ε

_{mpM}, ε

_{mruM}).

Test | m_{p0}(g) | φ (/) | t_{g} (^{°}C) | a (20) | ε_{mpM}(%) | ε_{mruM}(%) | τ_{t}(h) | τ_{c}(h) | τ_{p}(h) |
---|---|---|---|---|---|---|---|---|---|

1 | 0.0500 | 0.531 | 27.8 | 7.66 | −8.14 | −9.31 | 3.5 | 3.5 | 3.5 |

2 | 0.0480 | 0.454 | 28.2 | 7.69 | −7.65 | −2.85 | 3.0 | 6.5 | 30.5 |

3 | 0.0360 | 0.354 | 28.3 | 5.18 | 11.31 | 2.94 | 2.5 | 9.0 | 57.5 |

4 | 0.0455 | 0.427 | 27.6 | 5.95 | 18.62 | 1.94 | 2.5 | 11.5 | 83.5 |

5 | 0.0490 | 0.328 | 27.7 | 5.23 | 15.18 | 4.39 | 3.0 | 14.5 | 134 |

6 | 0.0480 | 0.306 | 27.4 | 5.41 | −11.50 | 15.55 | 2.5 | 17.0 | 161 |

7 | 0.0535 | 0.312 | 28.2 | 5.33 | 14.14 | 8.65 | 2.5 | 19.5 | 187 |

8 | 0.0535 | 0.350 | 28.9 | 5.19 | 0.717 | 11.02 | 3.0 | 22.5 | 214 |

9 | 0.0630 | 0.383 | 25.6 | 5.41 | 15.29 | 5.62 | 4.0 | 26.5 | 1658 |

10 | 0.0700 | 0.339 | 26.3 | 4.39 | 1.81 | −161 | 4.5 | 31.0 | 1687 |

11 | 0.0915 | 0.479 | 21.4 | 6.80 | 8.45 | 2.35 | 5.0 | 36.0 | 2892 |

12 | 0.1040 | 0.441 | 21,5 | 7.16 | −12.74 | 3.83 | 4.0 | 40.0 | 2920 |

13 | 0.1020 | 0.301 | 24.9 | 4.39 | 18.00 | 4.79 | 5.0 | 45.0 | 5517 |

14 | 0.1150 | 0.261 | 25.4 | 3.79 | −0.96 | 2.45 | 5.0 | 50.0 | 5645 |

15 | 0.1230 | 0.950 | 25.8 | 4.65 | −13.42 | 4.68 | 5.0 | 55.0 | 5575 |

16 | 0.1310 | 0.299 | 24.9 | 4.88 | −1.39 | 2.92 | 5.0 | 60.0 | 6252 |

17 | 0.1320 | 0.349 | 23.9 | 6.26 | −3.21 | 4.86 | 5.0 | 64.0 | 6282 |

18 | 0.1240 | 0.361 | 23.2 | 6.25 | −3.49 | 7.19 | 5.5 | 69.5 | 6584 |

19 | 0.1260 | 0.306 | 21.3 | 6.97 | −3.31 | 7.96 | 5.0 | 74.5 | 6603 |

20 | 0.1350 | 0.326 | 22.9 | 5.21 | −4.41 | 8.72 | 6.0 | 80.5 | 6663 |

21 | 0.1460 | 0.312 | 23.1 | 5.01 | 0.48 | 9.66 | 5.5 | 86.0 | 6903 |

22 | 0.1670 | 0.498 | 20.9 | 5.31 | 1.75 | 9.92 | 7.5 | 93.5 | 7014 |

23 | 0.1390 | 0.498 | 20.2 | 6.99 | 3.04 | 9.71 | 7.0 | 100.5 | 7654 |

24 | 0.1500 | 0.489 | 20,0 | 6.30 | −6.20 | 11.24 | 7.5 | 108.0 | 7684 |

25 | 0.1670 | 0.487 | 20.9 | 6.05 | 16.75 | 12.89 | 8.5 | 116.5 | 7719 |

26 | 0.1650 | 0.577 | 20,3 | 7.26 | 5.16 | 11.08 | 8.5 | 125.0 | 7789 |

27 | 0.2080 | 0.495 | 20.8 | 5.19 | 17.87 | 8.95 | 9.5 | 134.5 | 7820 |

28 | 0.1250 | 0.326 | 28.1 | 5.95 | 15.18 | 12.27 | 5.5 | 140.0 | 7860 |

29 | 0.1550 | 0.337 | 28.4 | 6.21 | 15.28 | 13.27 | 4.0 | 144.0 | 7884 |

30 | 0.1090 | 0.372 | 28.8 | 6.86 | −19.98 | 17.31 | 3.5 | 147.5 | 7908 |

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## Share and Cite

**MDPI and ACS Style**

Ilie, M.C.; Chiş, T.V.; Maior, I.; Răducanu, C.E.; Deleanu, I.M.; Dobre, T.; Pârvulescu, O.C.
Experimental Investigation and Modeling: Considerations of Simultaneous Surface Steel Droplets’ Evaporation and Corrosion. *Metals* **2023**, *13*, 1733.
https://doi.org/10.3390/met13101733

**AMA Style**

Ilie MC, Chiş TV, Maior I, Răducanu CE, Deleanu IM, Dobre T, Pârvulescu OC.
Experimental Investigation and Modeling: Considerations of Simultaneous Surface Steel Droplets’ Evaporation and Corrosion. *Metals*. 2023; 13(10):1733.
https://doi.org/10.3390/met13101733

**Chicago/Turabian Style**

Ilie, Marius Ciprian, Timur Vasile Chiş, Ioana Maior, Cristian Eugen Răducanu, Iuliana Mihaela Deleanu, Tănase Dobre, and Oana Cristina Pârvulescu.
2023. "Experimental Investigation and Modeling: Considerations of Simultaneous Surface Steel Droplets’ Evaporation and Corrosion" *Metals* 13, no. 10: 1733.
https://doi.org/10.3390/met13101733