# The Effect of Salt Solutions and Absorption Cycles in the Capillary and Drying Coefficient of Red Brick Samples with Different Joints

Authors: A. S. Guimarães; J. M. P. Q. Delgado; V. P. de Freitas; A. P. Albuquerque
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

Rising damp can reduce building’s aesthetical value, comfort, and health mark when combined with the existence of soluble salts in the building components and in the ground water can even lead to material decomposition and compromise its structural performance. This research work intended to study the effect of different absorption cycles of two saturated solutions of sodium sulphate and potassium chloride in the capillary absorption curves obtained through the partial immersion of red brick samples without and with different joints. The results revealed significant differences in the capillary coefficients obtained when samples were tested with salt solutions. In the end of this paper an evaluation of the drying kinetics was presented for all the tested samples. Four different first-order kinetics models, available in the literature, were adjusted to describe the drying process and the results point that the Page and Logarithmic models allow the best fit. The apparent molecular diffusion coefficient for solid red brick samples saturated with different solutions and joints was also estimated.


---

## Body

## 1. Introduction

Rising damp is one of construction’s major problems especially in old, ancient, and historical buildings associated porous materials used in this industry. This happens due to the migration of the salt ions dissolved in water into the porous network of the building’s walls where they remain and crystalize after water evaporates, dealing great pressures against the pore walls and eventually resulting in their fracture after many cycles of crystallization/dissolution [1, 2]. This mechanism has a massive influence on the degradation of historical buildings since they were built in a time when construction technologies made no effort to prevent this kind of pathologies.The materials used in the construction industry exhibit porous characteristics that favour the moisture fixation through mechanisms like capillary, hygroscopicity, and condensation [3–7]. The experiments reported in this paper are directly related to rising damp, one of the moisture propagation phenomena that cause further deterioration in buildings. Rising damp may be explained by the capillary migration of water from the soil through the porous network of the materials that compose building elements. This kind of damp assumes a greater expression in old buildings, mostly constructed in masonry, in which porous materials such as ceramic bricks, mortars, and stones are used [1, 2].The presence of dissolved salts in the water, which uprises through the porous network of building elements, constitutes an annoying factor for its degradation [8, 9]. If, on one hand, salts follow the water during its rise in liquid phase, the same does not occur when the water evaporates. Therefore, the salts remain in the porous structure of the building materials and eventually crystallize after the solution has reached its supersaturation state. Salt can crystallize on the surface of the materials developing efflorescence with aesthetical consequences for the building or inside the porous structure, inflicting great pressures over the pore walls that can disintegrate them when surpassing its mechanical resistance [10, 11]. Hygrothermal oscillation of the surrounding environment may promote cycles of crystallization/dissolution and potentially developing wrecking tensions in different pores in each cycle.Adding to this, the constructive systems, elements, and components, particularly the masonry, base their functional efficiency on the combination of materials with different characteristics. However, this heterogeneity makes moisture transfer analysis much more complex, demanding the knowledge, not only about the individual characteristics of the materials but also about the continuity conditions of the interface that separates the distinct materials and that is why the knowledge about the joints influence in those transport phenomena is considered crucial [12–14].This paper intends to report the experimental work carried out with brick specimens, aiming to evaluate the effect of salt solutions in the capillary absorption of monolithic brick specimens in comparison with water. Sodium sulphate and potassium chloride were the chosen salts to perform the experiments. The first is one of the salts that impose more degradation to buildings; the second was chosen for being very commonly found in building materials, especially the ion chloride. It also presents the drying kinetics and five models were adjusted to describe the drying process. Finally, in the capillary absorption and drying tests, different joints as perfect contact (just in contact), hydraulic continuity (with interpenetration of both materials), and air space (with an air layer between different materials) were also tested to evaluate the interface effect in moisture transference processes.


## 2. Materials and Methods

The test specimens used were nine red brick monolithic samples with the dimensions 5 × 5 × 10 cm3 (three for each solution including water). All the specimens were sealed in the lateral faces with an epoxy coating to avoid the evaporation through these sides and assure the unidirectional moisture flow from the bottom to the specimens’ top surface. Tests were performed only for pure water and two saturated salt solutions (KCl and Na2SO4). The solutions were saturated with salt excess in order to avoid the decrease of ions during the absorption process.


### 2.1. Capillary Coefficient

The capillary absorption tests followed the procedure n° II.6 “Water Absorption Coefficient (Capillary)” of RILEM [15]. The tests were preceded by the drying of the specimens in an oven at about 60°C until obtaining constant mass, in order to calculate the dry mass of the specimens. After this step, specimens were stored in the test room for some days, until they reach the hygrothermal equilibrium.Mukhopadhyaya et al. [16] confirmed the temperature influence on capillary absorption coefficient of brick specimens in their study with different porous materials. In order to minimize the effect of temperature on our results, tests were performed in a room with controlled temperature. The values of temperature and relative humidity (RH) of the air were measured every ten minutes for 33 days using a sequential data recording device. The mean values obtained were 22.8°C for the temperature and 52.7% for the RH.Tests began with the partial immersion of the specimens 5 mm deep. After the immersion, weightings were performed periodically in order to determine the amount of water absorbed during the test. On the first day, weightings were performed on all samples at minutes 1, 3, 5, 10, 15, 30, and 60 and afterwards at least once an hour. In general, weightings were attempted every two hours on the second day, every three hours on the third day, and once a day for the remaining days of testing. This timing had yet to suffer some adjustments for some combinations tested. For instance, for the specimens with air space between layers, after the wet front has reached the interface the time between weightings was extended since the moisture transport at the interface took place in the vapor phase and was therefore much slower.The amount of absorbed water per unit area at timet assay M
w (kg/m2) is calculated using (1), where M
0 (kg) is the dry mass of the sample, M
i (kg) is of the mass of sample at time t, and A (m2) is the area of the base of the specimen:(1)
M
w
=
M
i
-
M
0
A
.Once the amount of water absorbed over the time until the saturation of the porous media was determined, it was then possible to calculate the capillary absorption coefficient,A
w, and the maximum moisture flow through the interface. The earlier one corresponds to the slope of the first linear portion of the imbibition curve that expresses the amount of water absorbed per unit area (kg/m2) as a function of the root of time (s1/2). The second corresponds to the slope of the linear approximation of the imbibition curve that expresses the amount of water absorbed per unit area (kg/m2) as a function of time (s) once reached the interface.The results of capillary absorption are given by the sorptivityS (m/s0.5). This property, which depends on both the material and the liquid, expresses the tendency of a building material to absorb and transmit a liquid by capillarity [6], as shown by (2)
S
=
σ
η
1
/
2
S
˙
,where σ is the surface tension of the liquid, η is the viscosity of the liquid, and S is the intrinsic sorptivity of the material. It is important to be in mind that the relation between capillary absorption coefficient and sorptivity is given by A
w
=
S
·
ρ
w, where ρ
w is the water density (kg/m3).


### 2.2. Drying Kinetics

Drying was assessed following the experimental procedure of RILEM [15]. It consists in soaking the specimens and then letting them dry through their top surface under controlled environmental conditions. Meanwhile, the loss of water is monitored by periodical weighing. The results are expressed by the so-called mass drying curve which depicts the variation in moisture content over time.Frequently, quite simple models [17, 18] are presented to describe the drying curves that can provide an adequate representation of the experimental results. One of the most simplified models is the exponential model:(3)
MR
=
w
-
w
e
w
0
-
w
e
=
e
-
k
t
,where w is the average moisture content at any time, w
0 is the initial moisture content, w
e is the equilibrium moisture content, k is the drying rate constant, and t is the drying time. Usually, this model does not provide an accurate simulation of drying curves of many building materials, underestimating the beginning of the drying curve and overestimating the later stages. To soften this minor accuracy, the Page model is applied with an empirical modification to the time term by introducing an exponent, n:(4)
MR
=
w
-
w
e
w
0
-
w
e
=
e
-
k
t
n
.These empirical models derive a direct relationship between average moisture content and drying time. However, they neglect the fundamentals of the drying process and their parameters have no physical meaning.In this work, the drying curves were fitted with four different empirical and semiempirical drying models (see Table1). Regression analyses of these equations were done by using STATISTICA routine. The regression coefficient (R
2) was primary criterion for selecting the best equation to describe the drying curves of ETICS. The performance of derived new models was evaluated using various statistical parameters such as the mean bias error (MBE), the root mean square error (RMSE), and chi-square (χ
2), in addition to the regression coefficient (R
2). These parameters can be calculated as follows:(5a)
MBE
=
1
N
∑
i
=
1
N
MR
pre
,
i
-
MR
exp
⁡
,
i
,
(5b)
RMSE
=
1
N
∑
i
=
1
N
MR
pre
,
i
-
MR
exp
⁡
,
i
,
(5c)
χ
2
=
∑
i
=
1
N
MR
e
x
p
,
i
-
MR
pre
,
i
2
N
-
p
.Table 1
Mathematical models given by various authors for drying curves.
Model equation
Model name
M
R
=
e
-
k
t
Exponential
M
R
=
e
-
k
t
n
Page
M
R
=
a
×
e
-
k
t
+
b
Logarithmic
M
R
=
a
×
e
-
k
t
n
+
b
×
t
Midilli et al.The mechanisms of mass transfer in building materials are complex and frequently the modelling of the drying curves during the falling rate period is carried out by assuming that the main mechanism is of diffusional nature. In accordance with this, the experimental drying data for determination of apparent molecular diffusion coefficient was interpreted by using Fick’s diffusion model. In a one-dimensional formulation with the diffusing substance moving in the direction normal to a sheet of medium of thicknessL, the diffusion equation can be written as [19](6)
∂
w
∂
t
=
D
eff
∂
2
w
∂
x
2subject to the following boundary conditions:(7a)
t
=
0
,
0
<
x
<
∞
,
w
=
w
0
,
(7b)
t
>
0
,
x
=
0
,
w
=
w
e
,
(7c)
t
>
0
,
x
⟶
∞
,
w
=
w
0
.The analytical solution of (6) with the initial and boundary conditions (7a)–(7c) is(8)
MR
=
w
-
w
0
w
e
-
w
0
=
1
-
erf
⁡
x
2
D
eff
t
.Integrating in respect oft the rate of the penetration of sample face unit area (x
=
0) by water vapor, the total amount of diffusing substance in time t is obtained; then the appropriate solution of the diffusion equation (8) may be written as follows:(9)
MR
=
8
π
2
×
∑
n
=
0
∞
1
2
n
+
1
2
exp
⁡
-
2
n
+
1
2
π
2
D
eff
t
L
2and for long drying times (neglecting the higher order term by setting n
=
0) it has been simplified as follows:(10)
ln
⁡
MR
=
l
n
8
π
2
-
π
2
D
eff
t
L
2
.


## 2.1. Capillary Coefficient

The capillary absorption tests followed the procedure n° II.6 “Water Absorption Coefficient (Capillary)” of RILEM [15]. The tests were preceded by the drying of the specimens in an oven at about 60°C until obtaining constant mass, in order to calculate the dry mass of the specimens. After this step, specimens were stored in the test room for some days, until they reach the hygrothermal equilibrium.Mukhopadhyaya et al. [16] confirmed the temperature influence on capillary absorption coefficient of brick specimens in their study with different porous materials. In order to minimize the effect of temperature on our results, tests were performed in a room with controlled temperature. The values of temperature and relative humidity (RH) of the air were measured every ten minutes for 33 days using a sequential data recording device. The mean values obtained were 22.8°C for the temperature and 52.7% for the RH.Tests began with the partial immersion of the specimens 5 mm deep. After the immersion, weightings were performed periodically in order to determine the amount of water absorbed during the test. On the first day, weightings were performed on all samples at minutes 1, 3, 5, 10, 15, 30, and 60 and afterwards at least once an hour. In general, weightings were attempted every two hours on the second day, every three hours on the third day, and once a day for the remaining days of testing. This timing had yet to suffer some adjustments for some combinations tested. For instance, for the specimens with air space between layers, after the wet front has reached the interface the time between weightings was extended since the moisture transport at the interface took place in the vapor phase and was therefore much slower.The amount of absorbed water per unit area at timet assay M
w (kg/m2) is calculated using (1), where M
0 (kg) is the dry mass of the sample, M
i (kg) is of the mass of sample at time t, and A (m2) is the area of the base of the specimen:(1)
M
w
=
M
i
-
M
0
A
.Once the amount of water absorbed over the time until the saturation of the porous media was determined, it was then possible to calculate the capillary absorption coefficient,A
w, and the maximum moisture flow through the interface. The earlier one corresponds to the slope of the first linear portion of the imbibition curve that expresses the amount of water absorbed per unit area (kg/m2) as a function of the root of time (s1/2). The second corresponds to the slope of the linear approximation of the imbibition curve that expresses the amount of water absorbed per unit area (kg/m2) as a function of time (s) once reached the interface.The results of capillary absorption are given by the sorptivityS (m/s0.5). This property, which depends on both the material and the liquid, expresses the tendency of a building material to absorb and transmit a liquid by capillarity [6], as shown by (2)
S
=
σ
η
1
/
2
S
˙
,where σ is the surface tension of the liquid, η is the viscosity of the liquid, and S is the intrinsic sorptivity of the material. It is important to be in mind that the relation between capillary absorption coefficient and sorptivity is given by A
w
=
S
·
ρ
w, where ρ
w is the water density (kg/m3).


## 2.2. Drying Kinetics

Drying was assessed following the experimental procedure of RILEM [15]. It consists in soaking the specimens and then letting them dry through their top surface under controlled environmental conditions. Meanwhile, the loss of water is monitored by periodical weighing. The results are expressed by the so-called mass drying curve which depicts the variation in moisture content over time.Frequently, quite simple models [17, 18] are presented to describe the drying curves that can provide an adequate representation of the experimental results. One of the most simplified models is the exponential model:(3)
MR
=
w
-
w
e
w
0
-
w
e
=
e
-
k
t
,where w is the average moisture content at any time, w
0 is the initial moisture content, w
e is the equilibrium moisture content, k is the drying rate constant, and t is the drying time. Usually, this model does not provide an accurate simulation of drying curves of many building materials, underestimating the beginning of the drying curve and overestimating the later stages. To soften this minor accuracy, the Page model is applied with an empirical modification to the time term by introducing an exponent, n:(4)
MR
=
w
-
w
e
w
0
-
w
e
=
e
-
k
t
n
.These empirical models derive a direct relationship between average moisture content and drying time. However, they neglect the fundamentals of the drying process and their parameters have no physical meaning.In this work, the drying curves were fitted with four different empirical and semiempirical drying models (see Table1). Regression analyses of these equations were done by using STATISTICA routine. The regression coefficient (R
2) was primary criterion for selecting the best equation to describe the drying curves of ETICS. The performance of derived new models was evaluated using various statistical parameters such as the mean bias error (MBE), the root mean square error (RMSE), and chi-square (χ
2), in addition to the regression coefficient (R
2). These parameters can be calculated as follows:(5a)
MBE
=
1
N
∑
i
=
1
N
MR
pre
,
i
-
MR
exp
⁡
,
i
,
(5b)
RMSE
=
1
N
∑
i
=
1
N
MR
pre
,
i
-
MR
exp
⁡
,
i
,
(5c)
χ
2
=
∑
i
=
1
N
MR
e
x
p
,
i
-
MR
pre
,
i
2
N
-
p
.Table 1
Mathematical models given by various authors for drying curves.
Model equation
Model name
M
R
=
e
-
k
t
Exponential
M
R
=
e
-
k
t
n
Page
M
R
=
a
×
e
-
k
t
+
b
Logarithmic
M
R
=
a
×
e
-
k
t
n
+
b
×
t
Midilli et al.The mechanisms of mass transfer in building materials are complex and frequently the modelling of the drying curves during the falling rate period is carried out by assuming that the main mechanism is of diffusional nature. In accordance with this, the experimental drying data for determination of apparent molecular diffusion coefficient was interpreted by using Fick’s diffusion model. In a one-dimensional formulation with the diffusing substance moving in the direction normal to a sheet of medium of thicknessL, the diffusion equation can be written as [19](6)
∂
w
∂
t
=
D
eff
∂
2
w
∂
x
2subject to the following boundary conditions:(7a)
t
=
0
,
0
<
x
<
∞
,
w
=
w
0
,
(7b)
t
>
0
,
x
=
0
,
w
=
w
e
,
(7c)
t
>
0
,
x
⟶
∞
,
w
=
w
0
.The analytical solution of (6) with the initial and boundary conditions (7a)–(7c) is(8)
MR
=
w
-
w
0
w
e
-
w
0
=
1
-
erf
⁡
x
2
D
eff
t
.Integrating in respect oft the rate of the penetration of sample face unit area (x
=
0) by water vapor, the total amount of diffusing substance in time t is obtained; then the appropriate solution of the diffusion equation (8) may be written as follows:(9)
MR
=
8
π
2
×
∑
n
=
0
∞
1
2
n
+
1
2
exp
⁡
-
2
n
+
1
2
π
2
D
eff
t
L
2and for long drying times (neglecting the higher order term by setting n
=
0) it has been simplified as follows:(10)
ln
⁡
MR
=
l
n
8
π
2
-
π
2
D
eff
t
L
2
.


## 3. Results and Discussion

### 3.1. Capillary Coefficient

Figure1 sketches a representation of the monolithic specimen, hydraulic continuity interface, perfect contact interface, and air space interface.Figure 1
Virtual representation of the different types of specimen tested.The capillary absorption curves obtained in those specimens for each one of the three solutions tested are represented in Figures2 and 3. The capillary absorption coefficients determined from these curves are represented in Table 2.Table 2
Capillary absorption coefficient of monolithic red brick specimens partially immersed in pure water and saturated solutions of KCl and Na2SO4.
Solution
Capillary absorption coefficient [kg/(m2·s1/2)]
Mean
Standard deviation
Variation coeff (%)
Water
0.0675
0.0035
5.2%
Water + Na2SO4
0.0551
0.0025
4.5%
Water + KCl
0.0660
0.0025
10.6%Figure 2
Illustration of some samples before the beginning of the 2° cycle tests: (a) monolithic specimens, (b) hydraulic continuity interface, and (c) perfect contact interface.
(a)
(b)
(c)Figure 3
Illustration of some samples after several weeks of the 2° cycle tests: (a) monolithic specimens and (b) perfect contact interface.
(a)
(b)The results exposed in this paper regarding the capillary absorption coefficient support the hypothesis that the presence of soluble salts dissolved in water influences the wetting kinetics of porous materials, at least of brick material as it was the porous material in study. The capillary absorption coefficient determined for the specimens immersed in saturated solution of sodium sulphate was way lower than the one obtained for the reference test (pure water). On the other hand, potassium chloride appears to induce an increase in this coefficient in comparison with the reference solution. However, the difference between the capillary absorption coefficient of sodium sulphate solution and the reference solution is higher than the one between the potassium chloride and the latter. Our results are in line with that observed by Azevedo [11] who concluded that salts with potassium ion (K+) lead to the decrease of the capillary absorption coefficient when compared with pure water, while salts with sodium ion (Na+) induce a decrease in the capillary absorption coefficient.In Figure4 it is possible to see the capillary absorption curve of red brick samples as a function of the root of time, after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for each joint type. A more detailed analysis was done in Figure 5, and the results obtained show that comparing the 1st and 2nd absorption cycles, it is possible to conclude that the specimens immersed in water practically absorbed the same amount of water, but when the samples are immersed in salt solutions (Na2SO4 and KCl) the mass gain in the absorption process is lesser in the 2nd cycle than in the 1st cycle.Figure 4
Capillary absorption curve of red brick samples as a function of the root of time, after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Figure 5
Water absorption coefficient of red brick samples after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Figure6 shows the mass gain by the samples tested in water and both salts solutions, for the three different joints analysed. For hydraulic continuity interface, the contact between layers was done with a mortar joint of 3 mm and with an interpenetration of both layers. Figure 6 shows slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance. This result reveals the existence of a resistance associated with the maximum flow transmitted (FLUMAX) that presents the higher value FLUMAX, as showed in Figure 7. The maximum flow transmitted value is a parameter easy to obtain experimentally and an important input for the hygrothermal programs available in literature [20].Figure 6
Representation of the absorption in the monolithic specimens and specimens with hydraulic continuity interface, perfect contact interface, and air space interface, for (a) pure water, (b) saturated solution of KCl, and (c) saturated solution of Na2SO4.
(a)
(b)
(c)Figure 7
Effect of the different interfaces on the FLUMAX: monolithic specimens, hydraulic continuity interface, perfect contact interface, and air space interface.In the situation of perfect contact interface, the experiments detailed in Figure6 show slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance. Once again, this result reveals the existence of resistance associated with the maximum flow transmitted, but the lower slow mass gain by the samples indicates a high hygric resistance and an expectable lower maximum flow transmitted value than the obtained one in the hydraulic continuity interface situation.Finally, for the samples with air space interface, the samples are separated by about 3 mm of an air space in order to have hydric cut that prevents the moisture transfer in liquid phase. Figure6 shows a slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance; however, this hygric resistance is higher than the resistance observed in the perfect contact interface. This phenomenon is observed by the extremely slow weight gain presented in Figure 6, for the situation described, and once again reveals the existence of resistance associated with the maximum flow transmitted. This value is expected to be lower than the obtained one with a perfect contact interface (see Figure 7).


### 3.2. Drying Kinetics

Figure8 shows the changes in the moisture variation with time during the drying process for different joints and liquid solutions. The common feature of the curves seen in Figure 8 is their similarity as being typical drying curve, as moisture content decreased exponentially with time.Figure 8
Drying curves of red brick samples with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Drying rate decreases continuously with time and decreasing moisture content. This result shows that dominant physical mechanism governing moisture movement in red brick samples is the second drying stage. During the second stage of the drying process the diffusion within the building material limits the rate of evaporation.Five drying models have been used to describe drying curves and the applicability of these models is presented in Tables3 and 4. The criterion used for selecting the models that better describe the drying process was the magnitude of the relative error for each one (see Table 4). The Page and Logarithmic models presented the best results.Table 3
Values of empirical constants and drying constant for the models tested.
Joints
Solution
Exponential
Page
Logarithmic
Midilli et al.
Diffusional
Monolithic
Water
k = 1.62 × 10−3
k = 9.24 × 10−3
n = 0.726
k = 1.95 × 10−3
a = 0.881
b = 9.12 × 10−2
k = 5.96 × 10−3
n = 0.818
a = 1.05
b = 1.73 × 10−5
D
e
f
f (m2/s) =  3.34 × 10−10
Water + Na2SO4
k = 3.17 × 10−4
k = 1.03 × 10−3
n = 0.839
k = 4.09 × 10−4
a = 0.792
b = 0.188
k = 6.26 × 10−4
n = 0.903
a = 0.985
b = 9.47 × 10−7
D
e
f
f (m2/s) =  0.48. × 10−10
Water + KCl
k = 3.75 × 10−4
k = 2.24 × 10−4
n = 1.07
k = 3.64 × 10−4
a = 0.986
b = 0
k = 3.53 × 10−5
n = 1.31
a = 0.966
b = 0
D
e
f
f (m2/s) =  0.61 × 10−10
Hydraulic continuity
Water
k = 4.14 × 10−4
k = 1.15 × 10−3
n = 0.858
k = 5.49 × 10−4
a = 0.842
b = 0.156
k = 8.72 × 10−4
n = 0.908
a = 1.00
b = 1.26 × 10−5
D
e
f
f (m2/s) =  0.70 × 10−10
Water + Na2SO4
k = 4.14 × 10−4
k = 1.26 × 10−3
n = 0.846
k = 4.45 × 10−4
a = 0.885
b = 8.71 × 10−2
k = 7.65 × 10−4
n = 0.909
a = 0.981
b = 9.47 × 10−7
D
e
f
f (m2/s) =  0.69 × 10−10
Water + KCl
k = 2.51 × 10−4
k = 6.38 × 10−4
n = 0.875
k = 3.29 × 10−4
a = 0.783
b = 0.203
k = 3.53 × 10−5
n = 1.31
a = 0.966
b = 6.75 × 10−5
D
e
f
f (m2/s) =  0.34 × 10−10
Perfect contact
Water
k = 2.51 × 10−3
k = 2.77 × 10−2
n = 0.601
k = 3.65 × 10−3
a = 0.827
b = 0.125
k = 4.15 × 10−2
n = 0.545
a = 1.06
b = 1.48 × 10−6
D
e
f
f (m2/s) =  5.08 × 10−10
Water + Na2SO4
k = 4.46 × 10−4
k = 1.04 × 10−2
n = 0.559
k = 9.15 × 10−4
a = 0.574
b = 0.367
k = 7.65 × 10−4
n = 0.909
a = 0.981
b = 5.61 × 10−6
D
e
f
f (m2/s) =  0.76 × 10−10
Water + KCl
k = 3.69 × 10−4
k = 3.25 × 10−4
n = 1.02
k = 3.57 × 10−4
a = 0.986
b = 0
k = 8.60 × 10−8
n = 1.19
a = 0.973
b = 0
D
e
f
f (m2/s) =  0.59 × 10−10
Air space interface
Water
k = 4.30 × 10−3
k = 1.89 × 10−2
n = 0.725
k = 5.26 × 10−3
a = 0.907
b = 7.31 × 10−2
k = 2.44 × 10−2
n = 0.692
a = 1.04
b = 1.13 × 10−5
D
e
f
f (m2/s) =  8.51 × 10−10
Water + Na2SO4
k = 9.77 × 10−4
k = 1.47 × 10−2
n = 0.585
k = 1.72 × 10−3
a = 0.693
b = 0.261
k = 7.77 × 10−4
n = 1.05
a = 0.929
b = 7.62 × 10−5
D
e
f
f (m2/s) =  1.72 × 10−10
Water + KCl
k = 3.99 × 10−4
k = 2.58 × 10−3
n = 0.744
k = 6.59 × 10−4
a = 0.686
b = 0.284
k = 7.48 × 10−4
n = 0.938
a = 0.974
b = 4.38 × 10−5
D
e
f
f (m2/s) =  0.66 × 10−10Table 4
Results of the statistical analyses obtained with the drying models tested.
Joints
Solution
Chi-square (χ
2) error
Exponential
Page
Logarithmic
Midilli et al.
Diffusional
Monolithic
Water
12.75%
1.54%
5.51%
7.19%
5.93%
Water + Na2SO4
9.01%
1.68%
1.58%
1.10%
20.01%
Water + KCl
2.28%
2.25%
2.12%
0.86%
11.75%
Hydraulic continuity
Water
1.83%
0.67%
0.60%
0.61%
4.65%
Water + Na2SO4
7.53%
2.23%
2.05%
1.45%
15.90%
Water + KCl
2.44%
1.46%
0.91%
2.50%
12.66%
Perfectcontact
Water
38.75%
4.14%
17.57%
2.76%
14.10%
Water + Na2SO4
73.16%
3.12%
16.67%
57.93%
7.03%
Water + KCl
1.07%
1.12%
0.89%
0.49%
7.70%
Air space interface
Water
3.93%
1.10%
1.24%
0.54%
2.74%
Water + Na2SO4
69.91%
5.83%
7.69%
18.98%
20.76%
Water + KCl
8.85%
1.61%
1.04%
1.00%
4.94%
Sum
251.51%
26.75%
57.87%
95.41%
128.17%The results reported in Table3 show that the drying constant obtained is greater for red brick samples with pure water than with the salt solution analysed. It is important to be in mind that with salt solutions the drying process is more complex considering the salt ions stays in the material and the difficult transport process. Another important conclusion is the influence of the joints in the drying process, and it is possible to observe that the monolithic samples and the samples with perfect contact present higher values of drying constant than the samples with hydraulic continuity. Figure 8 also shows that monolithic samples and samples with perfect contact interface present a similar drying process, which should be expected due to the nature of the perfect contact joint. The samples with air space interface present the higher drying constant value which, considering the highest contact with air that they have, to eliminate water, seems to be expected and a realistic result.Finally, in order to establish the diffusional model, the effective diffusivity coefficient was identified by using (9) and the experimental drying curves of red brick samples were obtained. Effective diffusivity coefficient determination results from plot of dimensionless moisture ratio which is obtained from experimental data plotted against time on a semilogarithmic diagram. This plot is straight over the first falling period. The slope of this straight line is equal to quantity π
2
D
e
f
f
/
L
2 in case of slab geometry.The effective diffusivity coefficient (D
e
f
f) obtained is greater for the red brick samples with pure water than the samples with salt solutions, and the sample with hydraulic continuity interface presents lower values of D
e
f
f, as showed in Table 3.


## 3.1. Capillary Coefficient

Figure1 sketches a representation of the monolithic specimen, hydraulic continuity interface, perfect contact interface, and air space interface.Figure 1
Virtual representation of the different types of specimen tested.The capillary absorption curves obtained in those specimens for each one of the three solutions tested are represented in Figures2 and 3. The capillary absorption coefficients determined from these curves are represented in Table 2.Table 2
Capillary absorption coefficient of monolithic red brick specimens partially immersed in pure water and saturated solutions of KCl and Na2SO4.
Solution
Capillary absorption coefficient [kg/(m2·s1/2)]
Mean
Standard deviation
Variation coeff (%)
Water
0.0675
0.0035
5.2%
Water + Na2SO4
0.0551
0.0025
4.5%
Water + KCl
0.0660
0.0025
10.6%Figure 2
Illustration of some samples before the beginning of the 2° cycle tests: (a) monolithic specimens, (b) hydraulic continuity interface, and (c) perfect contact interface.
(a)
(b)
(c)Figure 3
Illustration of some samples after several weeks of the 2° cycle tests: (a) monolithic specimens and (b) perfect contact interface.
(a)
(b)The results exposed in this paper regarding the capillary absorption coefficient support the hypothesis that the presence of soluble salts dissolved in water influences the wetting kinetics of porous materials, at least of brick material as it was the porous material in study. The capillary absorption coefficient determined for the specimens immersed in saturated solution of sodium sulphate was way lower than the one obtained for the reference test (pure water). On the other hand, potassium chloride appears to induce an increase in this coefficient in comparison with the reference solution. However, the difference between the capillary absorption coefficient of sodium sulphate solution and the reference solution is higher than the one between the potassium chloride and the latter. Our results are in line with that observed by Azevedo [11] who concluded that salts with potassium ion (K+) lead to the decrease of the capillary absorption coefficient when compared with pure water, while salts with sodium ion (Na+) induce a decrease in the capillary absorption coefficient.In Figure4 it is possible to see the capillary absorption curve of red brick samples as a function of the root of time, after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for each joint type. A more detailed analysis was done in Figure 5, and the results obtained show that comparing the 1st and 2nd absorption cycles, it is possible to conclude that the specimens immersed in water practically absorbed the same amount of water, but when the samples are immersed in salt solutions (Na2SO4 and KCl) the mass gain in the absorption process is lesser in the 2nd cycle than in the 1st cycle.Figure 4
Capillary absorption curve of red brick samples as a function of the root of time, after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Figure 5
Water absorption coefficient of red brick samples after 1 and 2 cycles, with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Figure6 shows the mass gain by the samples tested in water and both salts solutions, for the three different joints analysed. For hydraulic continuity interface, the contact between layers was done with a mortar joint of 3 mm and with an interpenetration of both layers. Figure 6 shows slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance. This result reveals the existence of a resistance associated with the maximum flow transmitted (FLUMAX) that presents the higher value FLUMAX, as showed in Figure 7. The maximum flow transmitted value is a parameter easy to obtain experimentally and an important input for the hygrothermal programs available in literature [20].Figure 6
Representation of the absorption in the monolithic specimens and specimens with hydraulic continuity interface, perfect contact interface, and air space interface, for (a) pure water, (b) saturated solution of KCl, and (c) saturated solution of Na2SO4.
(a)
(b)
(c)Figure 7
Effect of the different interfaces on the FLUMAX: monolithic specimens, hydraulic continuity interface, perfect contact interface, and air space interface.In the situation of perfect contact interface, the experiments detailed in Figure6 show slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance. Once again, this result reveals the existence of resistance associated with the maximum flow transmitted, but the lower slow mass gain by the samples indicates a high hygric resistance and an expectable lower maximum flow transmitted value than the obtained one in the hydraulic continuity interface situation.Finally, for the samples with air space interface, the samples are separated by about 3 mm of an air space in order to have hydric cut that prevents the moisture transfer in liquid phase. Figure6 shows a slowing of the wetting process when the moisture reaches the interface due to the interface hygric resistance; however, this hygric resistance is higher than the resistance observed in the perfect contact interface. This phenomenon is observed by the extremely slow weight gain presented in Figure 6, for the situation described, and once again reveals the existence of resistance associated with the maximum flow transmitted. This value is expected to be lower than the obtained one with a perfect contact interface (see Figure 7).


## 3.2. Drying Kinetics

Figure8 shows the changes in the moisture variation with time during the drying process for different joints and liquid solutions. The common feature of the curves seen in Figure 8 is their similarity as being typical drying curve, as moisture content decreased exponentially with time.Figure 8
Drying curves of red brick samples with pure water and saturated solutions of KCl and Na2SO4, for (a) monolithic specimens, (b) hydraulic continuity interface, (c) perfect contact interface, and (d) air space interface.
(a)
(b)
(c)
(d)Drying rate decreases continuously with time and decreasing moisture content. This result shows that dominant physical mechanism governing moisture movement in red brick samples is the second drying stage. During the second stage of the drying process the diffusion within the building material limits the rate of evaporation.Five drying models have been used to describe drying curves and the applicability of these models is presented in Tables3 and 4. The criterion used for selecting the models that better describe the drying process was the magnitude of the relative error for each one (see Table 4). The Page and Logarithmic models presented the best results.Table 3
Values of empirical constants and drying constant for the models tested.
Joints
Solution
Exponential
Page
Logarithmic
Midilli et al.
Diffusional
Monolithic
Water
k = 1.62 × 10−3
k = 9.24 × 10−3
n = 0.726
k = 1.95 × 10−3
a = 0.881
b = 9.12 × 10−2
k = 5.96 × 10−3
n = 0.818
a = 1.05
b = 1.73 × 10−5
D
e
f
f (m2/s) =  3.34 × 10−10
Water + Na2SO4
k = 3.17 × 10−4
k = 1.03 × 10−3
n = 0.839
k = 4.09 × 10−4
a = 0.792
b = 0.188
k = 6.26 × 10−4
n = 0.903
a = 0.985
b = 9.47 × 10−7
D
e
f
f (m2/s) =  0.48. × 10−10
Water + KCl
k = 3.75 × 10−4
k = 2.24 × 10−4
n = 1.07
k = 3.64 × 10−4
a = 0.986
b = 0
k = 3.53 × 10−5
n = 1.31
a = 0.966
b = 0
D
e
f
f (m2/s) =  0.61 × 10−10
Hydraulic continuity
Water
k = 4.14 × 10−4
k = 1.15 × 10−3
n = 0.858
k = 5.49 × 10−4
a = 0.842
b = 0.156
k = 8.72 × 10−4
n = 0.908
a = 1.00
b = 1.26 × 10−5
D
e
f
f (m2/s) =  0.70 × 10−10
Water + Na2SO4
k = 4.14 × 10−4
k = 1.26 × 10−3
n = 0.846
k = 4.45 × 10−4
a = 0.885
b = 8.71 × 10−2
k = 7.65 × 10−4
n = 0.909
a = 0.981
b = 9.47 × 10−7
D
e
f
f (m2/s) =  0.69 × 10−10
Water + KCl
k = 2.51 × 10−4
k = 6.38 × 10−4
n = 0.875
k = 3.29 × 10−4
a = 0.783
b = 0.203
k = 3.53 × 10−5
n = 1.31
a = 0.966
b = 6.75 × 10−5
D
e
f
f (m2/s) =  0.34 × 10−10
Perfect contact
Water
k = 2.51 × 10−3
k = 2.77 × 10−2
n = 0.601
k = 3.65 × 10−3
a = 0.827
b = 0.125
k = 4.15 × 10−2
n = 0.545
a = 1.06
b = 1.48 × 10−6
D
e
f
f (m2/s) =  5.08 × 10−10
Water + Na2SO4
k = 4.46 × 10−4
k = 1.04 × 10−2
n = 0.559
k = 9.15 × 10−4
a = 0.574
b = 0.367
k = 7.65 × 10−4
n = 0.909
a = 0.981
b = 5.61 × 10−6
D
e
f
f (m2/s) =  0.76 × 10−10
Water + KCl
k = 3.69 × 10−4
k = 3.25 × 10−4
n = 1.02
k = 3.57 × 10−4
a = 0.986
b = 0
k = 8.60 × 10−8
n = 1.19
a = 0.973
b = 0
D
e
f
f (m2/s) =  0.59 × 10−10
Air space interface
Water
k = 4.30 × 10−3
k = 1.89 × 10−2
n = 0.725
k = 5.26 × 10−3
a = 0.907
b = 7.31 × 10−2
k = 2.44 × 10−2
n = 0.692
a = 1.04
b = 1.13 × 10−5
D
e
f
f (m2/s) =  8.51 × 10−10
Water + Na2SO4
k = 9.77 × 10−4
k = 1.47 × 10−2
n = 0.585
k = 1.72 × 10−3
a = 0.693
b = 0.261
k = 7.77 × 10−4
n = 1.05
a = 0.929
b = 7.62 × 10−5
D
e
f
f (m2/s) =  1.72 × 10−10
Water + KCl
k = 3.99 × 10−4
k = 2.58 × 10−3
n = 0.744
k = 6.59 × 10−4
a = 0.686
b = 0.284
k = 7.48 × 10−4
n = 0.938
a = 0.974
b = 4.38 × 10−5
D
e
f
f (m2/s) =  0.66 × 10−10Table 4
Results of the statistical analyses obtained with the drying models tested.
Joints
Solution
Chi-square (χ
2) error
Exponential
Page
Logarithmic
Midilli et al.
Diffusional
Monolithic
Water
12.75%
1.54%
5.51%
7.19%
5.93%
Water + Na2SO4
9.01%
1.68%
1.58%
1.10%
20.01%
Water + KCl
2.28%
2.25%
2.12%
0.86%
11.75%
Hydraulic continuity
Water
1.83%
0.67%
0.60%
0.61%
4.65%
Water + Na2SO4
7.53%
2.23%
2.05%
1.45%
15.90%
Water + KCl
2.44%
1.46%
0.91%
2.50%
12.66%
Perfectcontact
Water
38.75%
4.14%
17.57%
2.76%
14.10%
Water + Na2SO4
73.16%
3.12%
16.67%
57.93%
7.03%
Water + KCl
1.07%
1.12%
0.89%
0.49%
7.70%
Air space interface
Water
3.93%
1.10%
1.24%
0.54%
2.74%
Water + Na2SO4
69.91%
5.83%
7.69%
18.98%
20.76%
Water + KCl
8.85%
1.61%
1.04%
1.00%
4.94%
Sum
251.51%
26.75%
57.87%
95.41%
128.17%The results reported in Table3 show that the drying constant obtained is greater for red brick samples with pure water than with the salt solution analysed. It is important to be in mind that with salt solutions the drying process is more complex considering the salt ions stays in the material and the difficult transport process. Another important conclusion is the influence of the joints in the drying process, and it is possible to observe that the monolithic samples and the samples with perfect contact present higher values of drying constant than the samples with hydraulic continuity. Figure 8 also shows that monolithic samples and samples with perfect contact interface present a similar drying process, which should be expected due to the nature of the perfect contact joint. The samples with air space interface present the higher drying constant value which, considering the highest contact with air that they have, to eliminate water, seems to be expected and a realistic result.Finally, in order to establish the diffusional model, the effective diffusivity coefficient was identified by using (9) and the experimental drying curves of red brick samples were obtained. Effective diffusivity coefficient determination results from plot of dimensionless moisture ratio which is obtained from experimental data plotted against time on a semilogarithmic diagram. This plot is straight over the first falling period. The slope of this straight line is equal to quantity π
2
D
e
f
f
/
L
2 in case of slab geometry.The effective diffusivity coefficient (D
e
f
f) obtained is greater for the red brick samples with pure water than the samples with salt solutions, and the sample with hydraulic continuity interface presents lower values of D
e
f
f, as showed in Table 3.


## 4. Conclusions

In this work an extensive experimental campaign was presented to study the effect of different absorption cycles of two different saturated solutions of sodium sulphate and potassium chloride in the capillary absorption curves obtained through the partial immersion of red brick samples without and with different joints. The drying kinetic process was also analysed for all the samples tested.The main conclusions were as follows:(i)
Both salts influence the capillary absorption coefficient in a distinct way. The presence of sodium sulphate induces a decrease in this coefficient compared to tests performed with pure water, while the tests performed with potassium chloride showed an increase of the capillary absorption coefficient compared to pure water, despite presenting a lower difference.
(ii)
All three types of interface studied presented hydric resistance during the capillary absorption tests, although with different levels of magnitude. Specimens with air space between layers offered much more resistance to moisture transport through their interface compared to both perfect contact and hydraulic contact specimens due to the fact that moisture only flows in vapor phase unlike the other two which also support liquid phase transport.
(iii)
Comparing our results with those obtained by de Freitas [12] helped sustaining the author’s theory that maximum moisture flow through the air space and perfect contact interfaces (individually) may be fixed within a close range of values for the same material, since the maximum moisture flow values determined in this work were very close to the author’s for a similar used material.
(iv)
Specimens with hydraulic contact interface presented more heterogeneous results. Furthermore this kind of interface’s hydric resistance depends on several factors like the water/cement ratio and curing conditions. Despite the difference between the specimen’s characteristics, a comparison between ours and Cunha’s results shows distinct behaviours in moisture transport through the interface despite using the same cement material.
(v)
Different first-order kinetics models were adjusted to describe the drying process and the results point that the Page and Logarithmic models allow the best fit.



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*Source: 7868194-2016-04-13.xml*