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Capillary rise kinetics of some building materials
Journal of Colloid and Interface Science 284 (2005) 260–264 www.elsevier.com/locate/jcis
Capillary rise kinetics of some building materials M. Karoglou ∗ , A. Moropoulou, A. Giakoumaki, M.K. Krokida School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece Received 7 June 2004; accepted 28 September 2004
Abstract The presence of water in masonry is one of the main factors in deterioration. Capillary rise is the most usual mechanism of water penetration into building materials. In this study the kinetics of the capillary rise phenomenon was studied for various building materials: four stones, two bricks, and six plasters. A first-order kinetic model was proposed, in which the equilibrium moisture height derived from Darcy law. The capillary height time constant found to be strongly affected by the material characteristics. Moreover, the capillary height time constant can be predicted if the average pore radius of the materials is known. 2004 Elsevier Inc. All rights reserved. Keywords: Brick; Capillary height; Plaster; Stone
1. Introduction Water is an important weathering factor for building materials. Specifically, many chemical reactions take place in building materials only in the presence of water. Also, the transport, crystallization, and hydration of salts are controlled by water. Moreover, below the freezing point, water migrates to narrow pores and tight crays stays wet [1]. In addition, atmospheric precipitation or air humidity carry pollutants into building materials, leading to their deterioration, and biological decay can occur only in the presence of water. Water can reach a building material through capillary rise of ground moisture, rain, and condensation of air humidity. The mechanism of capillary rise is important in masonry, because it carries soluble salts at the masonry. The maximum salt concentration, and thus the maximum deterioration, is observed in a specific zone of the masonry, which depends on the type of the building material and on the environmental conditions [2]. Thus the capillary rise kinetics is indicative of the susceptibility of materials to decay factors and can provide important information for the selection of compatible building materials for masonry. * Corresponding author. Fax: +30-210-7723215.
E-mail address: [email protected] (M. Karoglou). 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.09.065
In the present work, six masonry substrate materials (four stones and two bricks) and six plasters were selected, in order to assess the capillary rise kinetics over a wide range of pore size distributions and reveal the effect of materials’ microstructures on the capillary rise kinetics.
2. Mathematical modeling In the literature several studies attempt to optimize the existing theoretical models of capillary rise height kinetics. The simplest theoretical model, which relates the height penetration H of a liquid into a capillary with pore radius r to time, is the Lucas–Washburn equation, γ cos θ r t, (1) 2n where γ is the water surface tension, θ the liquid–solid contact angle, and n the fluid viscosity [3]. However, the main deficiency of this model is that only the product r cos ϑ can be calculated and not each element separately. Marmur and Cohen [4] present an equation for the kinetics of vertical capillary penetration using capillary height related to time in an assembly of cylindrical capillaries of various radii and the same contact angles. Hamraoui and Nylander [5] introduce another model for the invasion of a
H2 =
M. Karoglou et al. / Journal of Colloid and Interface Science 284 (2005) 260–264
porous medium by a liquid, although the porous medium is not a building material. In contrast to the Lucas–Washburn equation, the analytical solution predicts linear time dependence on height, rather than the usual square root of time. Their analytical approach is in good agreement with both experimental and numerical solutions. However, the major part of the studies in the literature concentrates on the capillary moisture kinetics. Hoffmann and Niesel [6] present an exponential model, the main equation of which is xt = xmax (1 − e−bt ), 0.5
(2)
where xt expresses the liquid content in time t (g/cm2 ), xmax the maximum liquid content reached by capillary action (g/cm2 ), and b is the factor involving suction velocity and pore space filling. Mosquera et al. [7] also suggest a model that relates moisture content to time. More specifically, they apply a three-sized single-pore model and calculate an effective pore radius. Good agreement was found between the effective pore radius calculated and the radius estimated using a capillary rate value measured experimentally. Consequently, for the materials used in that study (granites), it is possible to predict the process rate for the capillary rise from only two characteristic pore sizes, corresponding to the radii of macrofissures and microfissures. In addition, other studies predict both waterfront (height) and moisture content of masonries. A study in this direction was made by the Frauenhofer Institute for Building Physics (Frauenhofer Institut für Bauphysik) [8], where twodimensional simulations were built with a program for calculating transient heat and moisture transport (WUFIZ). Using this program, it is possible to predict both waterfront (height) and moisture content of a masonry depending on the microstructural characteristics of the building materials and the environmental conditions. Furthermore, Torres and Freitas [9] verify this model for historical buildings. In the above-mentioned studies the drying process is not taken into consideration. Ianson and Hoff [10] presented a theoretical analysis of the effect of the continuous loss of water by evaporation on the rising damp equilibrium in masonry walls. The analysis predicts capillary rise heights in good agreement with those observed in walls that lack an effective dampproof course. The present study demonstrates that a simple first-order kinetic model can be used to predict the capillary rise height as a function of average pore radius. The theoretical model used in the present work follows first-order kinetics, dH 1 = (He − H ), dt tc
(3)
where He is the equilibrium height (cm) and tc the time constant (s). Practically, the capillary height constant tc represents the time required for the waterfront of a material to reach 2/3 of the equilibrium height.
261
It should be noted that the pores of the materials are assumed to have a cylindrical shape and present a homogeneous microstructure. Furthermore, evaporation effects are disregarded and only vertical rise of water is considered. The solution of Eq. (3) provides the development of height related to time, H = He − (He − H0 )e−t/τc ,
(4)
where H0 is a correction factor. For the estimation of moisture equilibrium height He (cm) the Darcy law [11] is used, r2 2γ dH = pg cos α + , u= (5) dt 8nH r where u expresses the velocity of the liquid rise, n the viscosity of the liquid, H the height, r the mean radius of the capillary, γ the surface tension of the liquid, and α the angle of the capillary to the vertical. For vertical rise cos α = −1 and the formula turns into r 2 2γ u= (6) − pgH . 8nH r In the steady state u = 0 and H = He , so the equilibrium height equals He =
2γ . pgr
(7)
For water, the equilibrium height at a temperature of 18 ◦ C is equal to 15 × 10−2 (8) , r where both He and r are given in cm. Therefore if the material pore radius is known, the equilibrium height is possible. He =
3. Materials and methods The building materials investigated are shown in Table 1. Four of them were quarry limestones; two originated from Rethymno, Crete with white and yellow color respectively (SRW, SRY), one from Rhodes (SRH) and one from Cyprus (SCY). The bricks were of traditional type; one produced by an Italian company (BRI) and the other by a Greek company (BRM). Four types of plasters were also investigated; one was a cement-based plaster commonly used in new construction and restoration work (PTI), one a traditional lime plaster taken from a neoclassical building from the center of Athens (PZN), and the rest were modern plasters with different chemical compositions produced in Italy, suitable for masonries suffering from rising damp (PMP, PRL). There is no standard describing an experimental procedure for obtaining the capillary rise height related to time. For that reason, it is possible to measure, instead of height,
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Table 1 Materials properties Code
Plasters PMP PRL PTI PZN
SRH SRY SRW
He (cm)
ε (%)
Porosity sd
εc (%)
ε/εc (%)
0.45
0.02
3333
49.2
0.84
48
97.6
2.01
0.36
667
32.6
0.75
27
82.9
Premixed plaster Premixed plaster Premixed plaster Traditional plaster
2.42 0.87 1.46 0.51
0.78 0.02 0.07 0.006
649 1724 1030 2941
32.4 34.8 42.1 38.8
1.85 0.39 0.72 2.46
25.1 31.6 39.3 34.7
77.5 90.9 93.5 89.4
Cyprus quarry sandstone Rhodes quarry sandstone Rethymno yellow quarry sandstone Rethymno white quarry sandstone
4.86
0.3
309
27.7
0.51
19
68.3
4.87
38
22.0
1.85
18.6
84.4
2.83
1.17
564
35.2
2.6
30.8
87.3
4.45
0.44
320
33.7
3
29.8
88.4
Traditional handmade clay brick Traditional handmade clay brick
BRM
Stones SCY
Pore radius sd
Materials
Bricks BRI
r (µm)
39.8
the moisture content related to time, for which there are national and international regulations, such as the German DIN 52 617, the Italian Normal 11/85, and the European EN 1925 for building stones and the EN 1015-18 for mortars and renders [12–15]. These standards describe the experimental procedure for calculating the capillary rise coefficient in kg/m2 s1/2 or g/cm2 s1/2 . This coefficient describes the water uptake rate, but it does not give any information about the corresponding capillary rise height. In the present work, the experimental procedure for the calculation of the moisture content of the materials followed the instructions of the Italian Normal 11/85. The dry mass, the height, and the surface of each sample were measured. Then the sample was put on a paper layer, saturated with distilled water. Its mass, mt , was weighed at fixed time intervals until the sample was saturated with water. At the end of the experiment the capillary moisture content, xc , was calculated on a dry basis (mt − mdry /mdry ) (%) related to time for each sample. The height in each time interval can be extracted using the equation H=
x Hsample , xc
(9)
where x is the moisture content at time t (g/g dry base), xc the capillary saturation moisture content (g/g dry base), and Hsample the geometric height of the sample, assuming that moisture content and height are proportional magnitude. The capillary saturation moisture content is the amount of water obtained by capillary rise until the water reaches the upper surface of the sample, without creation of a “knick point.” The capillaries are the pores, which play the most significant role in the capillary rise kinetics. If a material has a high percentage of capillaries, it is obvious that the capillary rise rate will be also high. Consequently, this percentage
could explain the reason for the differences in the capillary rise kinetics for different materials. A way to estimate this percentage is to calculate the capillary active porosity εcap , which is a factor that can be indicative for the capillaries, εcap =
xc % ε, xi %
(10)
where xc the capillary saturation moisture content (g/g dry base) obtained by capillary rise, xi the amount of water obtained by total immersion (g/g dry base), and ε is the porosity of the sample, as calculated by mercury porosimetry according to the Italian Normal 4/80 [16]. The latter amount is always higher than the former, because in total immersion water can also reach pores that are not capillaries. The moisture content of the sample after total immersion, xi , is expressed in g/g dry base and can be calculated by performing the experiment of total immersion, according to the Italian Normal 7/81 [17]. The sample is immersed in distilled water at a constant temperature and left there for as long as it takes for saturation. In Table 1 the average pore radius, along with its standard deviation for each material, the equilibrium height, the total porosity and porosity standard deviation for each material, and the capillary active porosity for each material are apposed. Mercury porosimetry was used for the estimation of the porosity and average pore radius r of each material according to the Italian Normal 4/80. The data of equilibrium height (He ) resulted from the Darcy law (Eq. (8)) using average pore radius taken from porosimetry experimental results (Table 1). Equilibrium height values are given also in Table 1. Table 1 shows also the ratio of capillary active to the total porosity. From these results, it is obvious that the pores of BRI are almost all capillaries (98%). PTI also has a very
M. Karoglou et al. / Journal of Colloid and Interface Science 284 (2005) 260–264
263
high percentage of capillaries (94%), as well as PRL (91%). Most of the materials have a high percentage of capillaries (PZN, SRH, SRY, SWR, BRM, PMP). SCY has a relatively low percentage.
4. Results and discussion The first-order kinetic model was fitted to experimental data and the results of parameter estimation are summarized in Table 2. The parameters of the proposed model, H0 , tc (Eq. (4)), resulted from an optimization technique to minimize the residual sum of squares between experimental and calculated values of capillary height (Eq. (3)). The capillary time constant was calculated for experimental times until 100 s. Each set of parameters corresponds to a different building material. The corresponding values of residual sum of squares are also given in Table 2. SRY and BRM presented the smallest residual sum of squares values. The main results of capillary kinetics for all the examined materials are summarized in Fig. 1. In this figure it is obvious that initial capillary height and capillary time constant vary for the different materials, depending on the materials’ microstructure. The fitting of the proposed model to the experimental data is considered satisfactory for all the examined building materials. The highest value of H0 is found for SRH, the lowest value for SRY. The capillary rise time constant depends on the equilibrium height, although the capillary rise height rate is not directly proportional to the equilibrium height. For example, although BRI presents the greatest equilibrium height (Table 1), PZN presents a higher capillary rise constant. Fig. 2 presents the theoretical capillary kinetics (height versus time) for all the examined materials. The materials are divided into two groups. The first group contains masonry substrate materials such as stones and bricks and the second one contains all plasters. SWR and SRH reach their equilibrium height quicker than the other materials, while BRI needs the most time to reach its equilibrium height.
Fig. 1. Measured and calculated capillary kinetics for some building materials.
Table 2 Estimated parameters Materials
tc (s)
S
Bricks BRI BRM
329,246 162,841
1.94 × 100 4.59 × 10−1
Plasters PMP PRL PTI PZN
60,650 181,907 60,650 512,382
5.03 × 100 1.48 × 100 5.03 × 100 5.61 × 10−1
Stones SCY SRH SRY SRW
68,298 1,869 109,498 21,161
7.72 × 10−1 2.20 × 101 3.62 × 10−1 4.32 × 100
Fig. 2. Theoretical height versus time for the various materials.
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M. Karoglou et al. / Journal of Colloid and Interface Science 284 (2005) 260–264
radius of the materials, and it can be used to forecast the capillary rise kinetics of various building materials.
Acknowledgments The authors thank Dr. A. Bakolas for his contribution to the understanding of the microstructure of materials.
References Fig. 3. Correlation diagram between t c and H e .
SRY, although at the beginning it presents the lowest rate, then presents behavior similar to that of BRM, with which it happens to have similar average pore radius (Table 1). PMP reach its equilibrium height quicker than the other materials. All the other plasters present almost the same behavior. Fig. 3 shows the effect of average pore radius r of the examined material on the capillary height constant tc of the proposed model. This approach is very significant, though it can be used in order to estimate, with a significant accuracy, the capillary height constant of a new building material, knowing only its average pore radius. These data can be used in simulators forecasting the capillary rise kinetics of various building materials.
5. Conclusions A first-order capillary rise kinetic model was developed for predicting the capillary rise height depending on average pore radius of the materials. The model successfully predicted the water capillary rise of several building materials. Moreover, the capillary rise kinetics of a building material can be estimated if its average pore radius in known. The capillary height constant tc was related to average pore
[1] H.K. Christenson, Colloids Surf. 123–124 (1997) 355–357. [2] A. Arnold, in: Fourth International Congress on the Deterioration and Preservation of Stone Objects, Louisville, 1982, pp. 11–28. [3] E. Washburn, Phys. Rev. 17 (1971) 273. [4] A. Marmur, R.D. Cohen, J. Colloid Interface Sci. 189 (1997) 299–304. [5] A. Hamraoui, T. Nylander, J. Colloid Interface Sci. 250 (2002) 415– 421. [6] D. Hoffmann, K. Niesel, Am. Ceram. Soc. Bull. 67 (8) (1988) 1418. [7] M.J. Mosquera, T. Rivas, B. Prieto, B. Silva, J. Colloid Interface Sci. 222 (2000) 41–45. [8] H.M. Künzel, Simultaneous Heat and Moisture Transport in Building Components, Fraunhofer IRB Vertag, 1995. [9] M.I. Torres, V.P. de Freitas, in: P.B. Loureno, P. Roca (Eds.), Historical Constructions, Guimares, 2001, pp. 381–390. [10] S.J. Ianson, W.D. Hoff, Building Environ. 21 (1986) 195–200. [11] R.H. Perry, D.W. Green (Eds.), Perry’s Chemical Engineers’ Handbook, seventh ed., McGraw–Hill, New York, 1997, pp. 6–39. [12] Bestimmung der Wasseraufnahmekoeffizienten [Determination of Water Absorption Coefficient], DIN 52 617. [13] ICR, Assorbimento d’acqua per capillarità—Coefficiente di assorbimento capillare [Water Absorption Coefficient by Capillarity—Water Absorption Coefficient], Italian recommendation NORMAL-11/82. [14] Determination of Water Absorption Coefficient by Capillarity, EN 1925, published March 1999, WI 246006. [15] Methods of Test for Mortar for Masonry, Determination of Water Absorption Coefficient Due to Capillary Action, EN 1015-18. [16] ICR, Distribuzione del volume dei pori in funzione del loro diametro [Pore Volume Distribution as a Function of Their Diameter], Italian recommendation NORMAL-4/80. [17] ICR, Assorbimento d’ acqua per immersione totale—Capacità di imbibizione [Water Absorption with Total Immersion—Immersion Capacity], Italian recommendation NORMAL-7/81.
Capillary rise kinetics of some building materials M. Karoglou ∗ , A. Moropoulou, A. Giakoumaki, M.K. Krokida School of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece Received 7 June 2004; accepted 28 September 2004
Abstract The presence of water in masonry is one of the main factors in deterioration. Capillary rise is the most usual mechanism of water penetration into building materials. In this study the kinetics of the capillary rise phenomenon was studied for various building materials: four stones, two bricks, and six plasters. A first-order kinetic model was proposed, in which the equilibrium moisture height derived from Darcy law. The capillary height time constant found to be strongly affected by the material characteristics. Moreover, the capillary height time constant can be predicted if the average pore radius of the materials is known. 2004 Elsevier Inc. All rights reserved. Keywords: Brick; Capillary height; Plaster; Stone
1. Introduction Water is an important weathering factor for building materials. Specifically, many chemical reactions take place in building materials only in the presence of water. Also, the transport, crystallization, and hydration of salts are controlled by water. Moreover, below the freezing point, water migrates to narrow pores and tight crays stays wet [1]. In addition, atmospheric precipitation or air humidity carry pollutants into building materials, leading to their deterioration, and biological decay can occur only in the presence of water. Water can reach a building material through capillary rise of ground moisture, rain, and condensation of air humidity. The mechanism of capillary rise is important in masonry, because it carries soluble salts at the masonry. The maximum salt concentration, and thus the maximum deterioration, is observed in a specific zone of the masonry, which depends on the type of the building material and on the environmental conditions [2]. Thus the capillary rise kinetics is indicative of the susceptibility of materials to decay factors and can provide important information for the selection of compatible building materials for masonry. * Corresponding author. Fax: +30-210-7723215.
E-mail address: [email protected] (M. Karoglou). 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.09.065
In the present work, six masonry substrate materials (four stones and two bricks) and six plasters were selected, in order to assess the capillary rise kinetics over a wide range of pore size distributions and reveal the effect of materials’ microstructures on the capillary rise kinetics.
2. Mathematical modeling In the literature several studies attempt to optimize the existing theoretical models of capillary rise height kinetics. The simplest theoretical model, which relates the height penetration H of a liquid into a capillary with pore radius r to time, is the Lucas–Washburn equation, γ cos θ r t, (1) 2n where γ is the water surface tension, θ the liquid–solid contact angle, and n the fluid viscosity [3]. However, the main deficiency of this model is that only the product r cos ϑ can be calculated and not each element separately. Marmur and Cohen [4] present an equation for the kinetics of vertical capillary penetration using capillary height related to time in an assembly of cylindrical capillaries of various radii and the same contact angles. Hamraoui and Nylander [5] introduce another model for the invasion of a
H2 =
M. Karoglou et al. / Journal of Colloid and Interface Science 284 (2005) 260–264
porous medium by a liquid, although the porous medium is not a building material. In contrast to the Lucas–Washburn equation, the analytical solution predicts linear time dependence on height, rather than the usual square root of time. Their analytical approach is in good agreement with both experimental and numerical solutions. However, the major part of the studies in the literature concentrates on the capillary moisture kinetics. Hoffmann and Niesel [6] present an exponential model, the main equation of which is xt = xmax (1 − e−bt ), 0.5
(2)
where xt expresses the liquid content in time t (g/cm2 ), xmax the maximum liquid content reached by capillary action (g/cm2 ), and b is the factor involving suction velocity and pore space filling. Mosquera et al. [7] also suggest a model that relates moisture content to time. More specifically, they apply a three-sized single-pore model and calculate an effective pore radius. Good agreement was found between the effective pore radius calculated and the radius estimated using a capillary rate value measured experimentally. Consequently, for the materials used in that study (granites), it is possible to predict the process rate for the capillary rise from only two characteristic pore sizes, corresponding to the radii of macrofissures and microfissures. In addition, other studies predict both waterfront (height) and moisture content of masonries. A study in this direction was made by the Frauenhofer Institute for Building Physics (Frauenhofer Institut für Bauphysik) [8], where twodimensional simulations were built with a program for calculating transient heat and moisture transport (WUFIZ). Using this program, it is possible to predict both waterfront (height) and moisture content of a masonry depending on the microstructural characteristics of the building materials and the environmental conditions. Furthermore, Torres and Freitas [9] verify this model for historical buildings. In the above-mentioned studies the drying process is not taken into consideration. Ianson and Hoff [10] presented a theoretical analysis of the effect of the continuous loss of water by evaporation on the rising damp equilibrium in masonry walls. The analysis predicts capillary rise heights in good agreement with those observed in walls that lack an effective dampproof course. The present study demonstrates that a simple first-order kinetic model can be used to predict the capillary rise height as a function of average pore radius. The theoretical model used in the present work follows first-order kinetics, dH 1 = (He − H ), dt tc
(3)
where He is the equilibrium height (cm) and tc the time constant (s). Practically, the capillary height constant tc represents the time required for the waterfront of a material to reach 2/3 of the equilibrium height.
261
It should be noted that the pores of the materials are assumed to have a cylindrical shape and present a homogeneous microstructure. Furthermore, evaporation effects are disregarded and only vertical rise of water is considered. The solution of Eq. (3) provides the development of height related to time, H = He − (He − H0 )e−t/τc ,
(4)
where H0 is a correction factor. For the estimation of moisture equilibrium height He (cm) the Darcy law [11] is used, r2 2γ dH = pg cos α + , u= (5) dt 8nH r where u expresses the velocity of the liquid rise, n the viscosity of the liquid, H the height, r the mean radius of the capillary, γ the surface tension of the liquid, and α the angle of the capillary to the vertical. For vertical rise cos α = −1 and the formula turns into r 2 2γ u= (6) − pgH . 8nH r In the steady state u = 0 and H = He , so the equilibrium height equals He =
2γ . pgr
(7)
For water, the equilibrium height at a temperature of 18 ◦ C is equal to 15 × 10−2 (8) , r where both He and r are given in cm. Therefore if the material pore radius is known, the equilibrium height is possible. He =
3. Materials and methods The building materials investigated are shown in Table 1. Four of them were quarry limestones; two originated from Rethymno, Crete with white and yellow color respectively (SRW, SRY), one from Rhodes (SRH) and one from Cyprus (SCY). The bricks were of traditional type; one produced by an Italian company (BRI) and the other by a Greek company (BRM). Four types of plasters were also investigated; one was a cement-based plaster commonly used in new construction and restoration work (PTI), one a traditional lime plaster taken from a neoclassical building from the center of Athens (PZN), and the rest were modern plasters with different chemical compositions produced in Italy, suitable for masonries suffering from rising damp (PMP, PRL). There is no standard describing an experimental procedure for obtaining the capillary rise height related to time. For that reason, it is possible to measure, instead of height,
262
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Table 1 Materials properties Code
Plasters PMP PRL PTI PZN
SRH SRY SRW
He (cm)
ε (%)
Porosity sd
εc (%)
ε/εc (%)
0.45
0.02
3333
49.2
0.84
48
97.6
2.01
0.36
667
32.6
0.75
27
82.9
Premixed plaster Premixed plaster Premixed plaster Traditional plaster
2.42 0.87 1.46 0.51
0.78 0.02 0.07 0.006
649 1724 1030 2941
32.4 34.8 42.1 38.8
1.85 0.39 0.72 2.46
25.1 31.6 39.3 34.7
77.5 90.9 93.5 89.4
Cyprus quarry sandstone Rhodes quarry sandstone Rethymno yellow quarry sandstone Rethymno white quarry sandstone
4.86
0.3
309
27.7
0.51
19
68.3
4.87
38
22.0
1.85
18.6
84.4
2.83
1.17
564
35.2
2.6
30.8
87.3
4.45
0.44
320
33.7
3
29.8
88.4
Traditional handmade clay brick Traditional handmade clay brick
BRM
Stones SCY
Pore radius sd
Materials
Bricks BRI
r (µm)
39.8
the moisture content related to time, for which there are national and international regulations, such as the German DIN 52 617, the Italian Normal 11/85, and the European EN 1925 for building stones and the EN 1015-18 for mortars and renders [12–15]. These standards describe the experimental procedure for calculating the capillary rise coefficient in kg/m2 s1/2 or g/cm2 s1/2 . This coefficient describes the water uptake rate, but it does not give any information about the corresponding capillary rise height. In the present work, the experimental procedure for the calculation of the moisture content of the materials followed the instructions of the Italian Normal 11/85. The dry mass, the height, and the surface of each sample were measured. Then the sample was put on a paper layer, saturated with distilled water. Its mass, mt , was weighed at fixed time intervals until the sample was saturated with water. At the end of the experiment the capillary moisture content, xc , was calculated on a dry basis (mt − mdry /mdry ) (%) related to time for each sample. The height in each time interval can be extracted using the equation H=
x Hsample , xc
(9)
where x is the moisture content at time t (g/g dry base), xc the capillary saturation moisture content (g/g dry base), and Hsample the geometric height of the sample, assuming that moisture content and height are proportional magnitude. The capillary saturation moisture content is the amount of water obtained by capillary rise until the water reaches the upper surface of the sample, without creation of a “knick point.” The capillaries are the pores, which play the most significant role in the capillary rise kinetics. If a material has a high percentage of capillaries, it is obvious that the capillary rise rate will be also high. Consequently, this percentage
could explain the reason for the differences in the capillary rise kinetics for different materials. A way to estimate this percentage is to calculate the capillary active porosity εcap , which is a factor that can be indicative for the capillaries, εcap =
xc % ε, xi %
(10)
where xc the capillary saturation moisture content (g/g dry base) obtained by capillary rise, xi the amount of water obtained by total immersion (g/g dry base), and ε is the porosity of the sample, as calculated by mercury porosimetry according to the Italian Normal 4/80 [16]. The latter amount is always higher than the former, because in total immersion water can also reach pores that are not capillaries. The moisture content of the sample after total immersion, xi , is expressed in g/g dry base and can be calculated by performing the experiment of total immersion, according to the Italian Normal 7/81 [17]. The sample is immersed in distilled water at a constant temperature and left there for as long as it takes for saturation. In Table 1 the average pore radius, along with its standard deviation for each material, the equilibrium height, the total porosity and porosity standard deviation for each material, and the capillary active porosity for each material are apposed. Mercury porosimetry was used for the estimation of the porosity and average pore radius r of each material according to the Italian Normal 4/80. The data of equilibrium height (He ) resulted from the Darcy law (Eq. (8)) using average pore radius taken from porosimetry experimental results (Table 1). Equilibrium height values are given also in Table 1. Table 1 shows also the ratio of capillary active to the total porosity. From these results, it is obvious that the pores of BRI are almost all capillaries (98%). PTI also has a very
M. Karoglou et al. / Journal of Colloid and Interface Science 284 (2005) 260–264
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high percentage of capillaries (94%), as well as PRL (91%). Most of the materials have a high percentage of capillaries (PZN, SRH, SRY, SWR, BRM, PMP). SCY has a relatively low percentage.
4. Results and discussion The first-order kinetic model was fitted to experimental data and the results of parameter estimation are summarized in Table 2. The parameters of the proposed model, H0 , tc (Eq. (4)), resulted from an optimization technique to minimize the residual sum of squares between experimental and calculated values of capillary height (Eq. (3)). The capillary time constant was calculated for experimental times until 100 s. Each set of parameters corresponds to a different building material. The corresponding values of residual sum of squares are also given in Table 2. SRY and BRM presented the smallest residual sum of squares values. The main results of capillary kinetics for all the examined materials are summarized in Fig. 1. In this figure it is obvious that initial capillary height and capillary time constant vary for the different materials, depending on the materials’ microstructure. The fitting of the proposed model to the experimental data is considered satisfactory for all the examined building materials. The highest value of H0 is found for SRH, the lowest value for SRY. The capillary rise time constant depends on the equilibrium height, although the capillary rise height rate is not directly proportional to the equilibrium height. For example, although BRI presents the greatest equilibrium height (Table 1), PZN presents a higher capillary rise constant. Fig. 2 presents the theoretical capillary kinetics (height versus time) for all the examined materials. The materials are divided into two groups. The first group contains masonry substrate materials such as stones and bricks and the second one contains all plasters. SWR and SRH reach their equilibrium height quicker than the other materials, while BRI needs the most time to reach its equilibrium height.
Fig. 1. Measured and calculated capillary kinetics for some building materials.
Table 2 Estimated parameters Materials
tc (s)
S
Bricks BRI BRM
329,246 162,841
1.94 × 100 4.59 × 10−1
Plasters PMP PRL PTI PZN
60,650 181,907 60,650 512,382
5.03 × 100 1.48 × 100 5.03 × 100 5.61 × 10−1
Stones SCY SRH SRY SRW
68,298 1,869 109,498 21,161
7.72 × 10−1 2.20 × 101 3.62 × 10−1 4.32 × 100
Fig. 2. Theoretical height versus time for the various materials.
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radius of the materials, and it can be used to forecast the capillary rise kinetics of various building materials.
Acknowledgments The authors thank Dr. A. Bakolas for his contribution to the understanding of the microstructure of materials.
References Fig. 3. Correlation diagram between t c and H e .
SRY, although at the beginning it presents the lowest rate, then presents behavior similar to that of BRM, with which it happens to have similar average pore radius (Table 1). PMP reach its equilibrium height quicker than the other materials. All the other plasters present almost the same behavior. Fig. 3 shows the effect of average pore radius r of the examined material on the capillary height constant tc of the proposed model. This approach is very significant, though it can be used in order to estimate, with a significant accuracy, the capillary height constant of a new building material, knowing only its average pore radius. These data can be used in simulators forecasting the capillary rise kinetics of various building materials.
5. Conclusions A first-order capillary rise kinetic model was developed for predicting the capillary rise height depending on average pore radius of the materials. The model successfully predicted the water capillary rise of several building materials. Moreover, the capillary rise kinetics of a building material can be estimated if its average pore radius in known. The capillary height constant tc was related to average pore
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