1. Introduction

Presence of moisture in a material usually leads to itsdegradation. It is also one of the main problems in preservationof ancient buildings and in deterioration of properties of ther-mal insulations. Most damages in buildings, particularly inold buildings, are a direct or indirect consequence of moisture[1,2,3,6].

The water content in a porous material is defined as theratio of the mass of moisture inside the sample to the mass ofthe dry sample. As density of water vapour is almost threeorders of magnitude smaller than density of the liquid phasethe water content in the sample practically corresponds to itsliquid water content. The standard measurement of the mois-ture content is accomplished by means of the gravimetricmethod which is a destructive method. Some attempts werealready undertaken in the past to use IR thermography fornon-destructive evaluation of moisture presence in materials.These attempts were of mainly qualititative nature with nosound mathematical basis. They use dependence of eitherthermal or radiative properties on the moisture content [1,4].

At low water contents the liquid water occurs in a pendularstate and does not form a continuous phase. The limitingvalue when the liquid water starts to form the continuousphase is known as the critical water content Wcr. Above Wcrthe liquid transfer happens in capillaries with the highest eva-

poration rate; while below it moisture transfer occurs only byvapour transfer, with a sharp decrease in the evaporation rate.Determination of the critical water content can be performedif the sudden increase in evaporation rate is observed [6]. Theweathering conditions, such as the cycles of freezing-thawing,wetting-drying and salt crystallization, are more damaging forporous building materials in the presence of water above thecritical moisture content.

The main objective of this paper is to carry out prelimi-nary experiments on variation in temperature of the moist,porous medium and propose a mathematical model of theenergy and moisture transport phenomena in porous samplein a direct contact with the ambient humid air. The model is tobe subsequently used to analyze IR assisted non-destructiveexperimental determination of moisture content in the buildingmaterial and is aimed to in-situ measurements.

2. Experimental stand and results

For the preliminary measurements a simple experimentalstand was designed - Figure 1. The sample of common, redbrick, with dimensions of the sample: 100 mmx100 mm x40mm, was surrounded by thermal insulation made from polys-tyrene. Two thermocouples (chromium-aluminium type) werefixed to the sample. One was located underneath the sampleand the other one at its surface exposed to the ambient air -see Figure 1.

71

Abstract

Liquid water is one of theagents responsible for

damage of building materials.Therefore determination of itscontent in porous materials isof primer importance. A newquantitative method, based onIR observation of variation inthe surface temperature of amoist sample in the humidenvironment, is proposed. Themathematical model, on whichthe method is based, uses thefundamental assumption thatthe liquid phase appears in

thermodynamic equilibriumwith the water vapour inpores of the material. Pre-liminary measurements onthe moist material are car-ried out on a specially de-signed experimental standusing infrared camera. Itseems that the transient partof the surface temperatureresponse is the most suitablefor determination of thewater content in the porousmaterial.

Keywords: Moisture content,infra-red method.

Determination of MoistureContent in a Porous Building

Material Using Infra-redBased MethodPiotr FURMANSKI1,

Tomasz S. WIÂNIEWSKI2

Institute of Heat Engineering, Warsaw Universityof Technology, Warsaw, Poland

1)e-mail: pfurm@itc.pw.edu.pl,2)e-mail: tswis@itc.pw.edu.pl

Vo l u m e 5 - N u m b e r 7 - M a y 2 0 0 9 ( 7 1 - 7 5 )

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The samples were dried for long time in anair dryer to remove moisture and subsequentlyfilled with the known amount of liquid waterwith the water content corresponding to 5, 10and 15%, respectively. The samples were thenwrapped in a foil and kept in the dryer for threedays until its moisture distribution in the sam-ples was uniform. Then each sample was placedin a box compartment filled with the thermalinsulation and the upper surface of the sample also covered bya thermal insulation.

Subsequently, the cover was removed and the upper sur-face of the sample exposed to the ambient air. As temperatureT∞ and humidity φ∞ of the ambient air, were different than inthe sample heat and moisture transfer with the surroundingoccurred. The exposed surface of the samples was observedwith the infrared camera Thermocam SC2000 (Flir IRSystems, INC.) operating in the wavelength range from 6 to12 µm and the radiation temperature of the sample surfacerecorded. The recorded temperatures of the sample surfaceare presented in Figure 2a.

Variation of temperature versus time was also recorded bythe thermocouples. They showed the similar change of thesurface temperature as measured by the infrared camera. Theambient temperature do not change more than of 0.5° duringthe whole measurement time and contributed to the slightincrease of the sample temperature in the longer period oftime - see Figure 2b.

After some cooling time, temperature of the sample sur-face approached the steady value corresponding to Ts,min. Thisperiod approximately lasted about 10000 seconds and seemedto not appreciably vary with the water content. A small tem-perature difference between the sample surface and its interiorwas also observed - Figure 2b. The recorded temporal varia-tions in the surface temperature were used to calculate the rateof temperature drop. The results are collected in Table 1.

They show a trend that with the increase of water content therate of the surface temperature drop decreases. It was alsofound that the maximum surface temperature drop To –Ts,min

increases with the water content.

3. Mathematical model

In formulating the mathematical model it was assumedthat a sample of the moist material is in contact with a humidambient air at a different temperature. The sample is partiallyfilled with liquid water and partially by water vapour mixedwith the air. The vapour and the liquid phase are in thermody-namic equilibrium, i.e., they are in a saturated state. Inside thematerial conjugated processes of heat transfer by conductionand moisture transfer by diffusion occur [2]. They are accom-panied by the condensation or evaporation processes of themoisture, which contribute to heat transfer.

The heat and mass transfer in the sample is assumed to beone-dimensional with the lateral surfaces thermally insulatedand impermeable for moisture flow. At the front surface, thatis in contact with the ambient humid air at temperature T∞ andhumidity φ∞, liquid water evaporates and carries off someheat. The surface also exchanges energy with the surroundingby convection. Due to relatively low rate of vaporization eitherinside the sample or on its external surface no significantvariation of water content across the sample is assumed.Using the above-cited assumptions the energy equation canbe written as:

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Figure 1. Scheme of the experimental stand and view of the moistsample.

Figure 2. Variation of temperature in the centre of the samplesurface versus time for the sample of moist brick with moisture

content W = 15%:–a) IR –thermogram, –b) thermocouple measu-rements Note: n - environmental (air) temperature, u- temperatureat the bottom of the sample, s - surface temperature of the sample.

Water content

Characteristic time

of temperature

drop

Maximum tempe-

rature drop

τ

To –Ts,min

[s]

[°C]

TABLE 1. Experimental results

W [%] 5

603

2

10

879

2,7

1375

3,2

15

(1)

(a) (b)

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with the corresponding balance of the water vapour:

where ρg stands for density of air and water vapour mixture inthe pores and denotes the mass condensation rate.

For the case of saturation the mass fraction of vapour in thegaseous phase is equal to its saturation value, i.e. yv = yv,sat, andbecomes a unique function of temperature. Then eq.(2) maybe multiplied by the latent heat of condensation and added toeq.(1). In this way the heat source in eq.(1) is eliminated:

The new symbols introduced in eq.(3) are defined as:

with a derivative of the mass fraction of water vapour yv versustemperature

where Rv - particular gas constant of the water.

In a similar manner, for the case of saturation at the exter-nal surface facing the ambient air the boundary condition canbe expressed as

where ρv is density of vapour at its partial pressure.

Noting that

where φ is the relative humidity and expanding of the satura-tion pressure at the surface pv,sat(Ts) in series of the vapoursaturation pressure in the ambient air, i.e., pv,sat(T∞), allows foreq.(5) to be cast in the form:

where the new symbols are defined as:

and

At the depth of the porous material no heat transfer occurred:

at x Û ∞,

while at the initial moment of time the uniform temperaturedistribution was assumed:

T(x,t = 0) = To (9)

A set of equations, i.e., eq.(3), (6), (8) and (9) was analy-tically solved to give the following expression for tempera-ture of the sample surface:

Ts(t) = Ts,min + (T0 –Ts,min)exp(η2) erfc(η) (10)

where ,

- characteristic time of temperature drop, (11)

The surface temperature tends to the minimum value atthe long times as observed in experiments - see. Figure 2.

In eq.(12), the relative humidity at the surface φs appears.This relative humidity generally depends on the water contentin the material and surface temperature and is known as thesorption/desorption isotherm. The sorption isotherm repre-sents the amount of vapour adsorbed at thermodynamic equi-librium conditions as a function of the relative humidity of themoist air. The sorption isotherm strongly depends on tempe-rature, composition and microstructure of the porous mate-rial, specific volume area of the porous material and its bulkdensity.

The water content in a porous material can be found fromthe sorption isotherm for the material φs (T∞,W) when theexperimentally determined minimum value of the surfacetemperature, the temperature and relative humidity of theambient air, as well as the ratio are known –eq. (12).

A plot of the temporal variation in the surface temperaturecan also be used in determining W. It then suffices to find thecharacteristic time τ for

and with the known evaluate the thermal effusivity of theporous material. Subsequently, from the known relation bet-ween eef and W the water content can be calculated.

4. Dependence of thermo-physical propertiesand characteristic time on water content

Thermal properties of the moist, porous medium depend,to a significant extent, on water content. Accounting for muchgreater density and specific heat of the liquid water than air aswell as the relation between sg and the water content W, themodified volumetric specific heat of the moist porous materialcan be expressed as:

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73

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(11)

(13)

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In the last, right hand side expression influence of thewater content on the specific heat is explicitly separated withthe following symbols introduced:

,

The effective thermal conductivity of moist, porous mate-rial accounts not only for composition and thermal propertiesof the constituents of the sample but is also dependent on theinternal structure of the medium. The simplest formula for theeffective thermal conductivity of the porous material corres-ponds to constituents located parallel to heat flow. Noting thatthe thermal conductivity of air is circa twenty times smallerthan that of liquid water the modified effective thermalconductivity, defined by eq.(4), can be cast in the followingform:

where

,

In the preliminary experiments a moist sample made ofthe common, red brick with certain water content was consi-dered. The thermo-physical properties of the dry sample wereassumed as follows: ρd = 1800 kg/m3, kef,d = 0,84 W/(m.K),(ρc)ef,d = 1,582 MJ/m3, ε = 0,3. The liquid water and watervapour properties were adopted as: ρl = 1000 kg/m3, kl = 0,63W/(m.K), (ρc)l = 4,2 MJ/m3, Dv = 2,49.10–5 m2/s, kv = 0.027W/m.K) while the air properties to be: ka = 0,0259 W/(m.K),(ρc)a = 1,206 MJ/m3, respectively. The temperature, relativehumidity and pressure of the ambient air followed from theexperiment with T∞ = 24 °C, φ∞ = 0.43 and p = 0.101325 Mpa.The convective heat transfer coefficient on the external sur-face of the sample was assumed to be hT = 13 W/(m2.K) andrelated to the convective mass transfer coefficient by the for-mula hm = (Dv/kv)hT. A simplified formula for the saturationpressure of water vapour as a function of temperature, as citedin [2], was used in the calculations.

Due to small variation in temperature across the samplethermo physical properties of the moist material were assumedconstant and evaluated at temperature T∞. Dependence of thecharacteristic time τ of temperature drop as defined in eq.(11)has been calculated using the presented formulae and shownin Figure 3. The respective experimental data were includedin Table 1. Despite simplifying assumptions introduced in thetheoretical analysis and small variation in the ambient airtemperature during experiments comparison of the experi-mental data with theoretical results seems promising.

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(1)

(14)

Figure 3. Approximate relation between thecharacteristic time τ and water content W for the considered experimental sample.

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Conclusions

Presence of liquid water is one of the agents responsible for deterioration of materials such as building materials and thermalinsulations. A study on determination of the liquid water content in porous materials was carried out in the paper. Preliminarymeasurements on the moist material, in the form of common red brick, were also performed on a specially designed experi-mental stand using infrared camera. A mathematical model of the heat and mass transfer processes in the moist sample wasproposed in the paper.

The model was used to propose two new methods for determination of the water content in the porous material. One isbased on the experimentally found minimum temperature of the material surface while the other on the characteristic time ofthe drop in this surface temperature. Approximate evaluation of dependence of the characteristic time on the water contentfor the studied material was carried out and reasonable agreement with the experimental results was found. The adsorptionisotherm for the studied material was not known and should be determined in order to verify another method in determiningW. Further theoretical and experimental studies will be here valuable especially these, which will allow to carry out the sen-sitivity analysis of different parameters on a value the water content determined.

Dv

e

hT

hm

k

L

Mv, Ma

p

Sg

T

W

ερ(ρc)

φ

Subscripts:

a

diffusion coefficient of water vapour, m2/s

thermal effusivity, , J/Km2s1/2

convective heat transfer coefficient, W/(m2.K)

convective mass transfer coefficient, m/s

thermal conductivity, W/(m.K)

latent heat of condensation, L = 2500 kJ/kg

molar masses of water and air, Mv = 18,015,

Ma = 28,967 kg/kmol

total pressure, pv,sat - saturation pressure of water

vapour, Pa

volume fraction of gaseous (liquid) phase in

pores, kg/m3

temperature, K (°C)

water content, kg of moisture /kg of dry material

porosity of material

density of porous material, kg/m3

volumetric specific heat of porous material,

J/(m3.K)

relative humidity

air

NomenclatureReferences[1] Avdelis N.P., Moropoulou A., Theoulakis P.: Detection of water deposits and

movement on porous materials by infrared imaging. Infrared Physics &Technology, Vol. 44 (2003), pp.183-190.

[2] Furmanski P., Wisniewski T.S., Elzbieta Wyszynska: Detection of moisture inporous materials through infrared methods. Archives of Thermodynamics,Vol. 29 (2008), No.1, pp.19-40.

[3] Gayo E., Frutos de J.: Interference filters as an enhancement tool for infraredthermography in humidity studies of building elements, Infrared Physics &Technology, Vol. 38 (1997), pp.251-258.

[4] Hüttner R., Schollmeyer E.: The on-line detection of moisture and moistcoatings by means of thermal waves, QIRT, Proceedings of EurothermSeminar, Vol. 37 (1996), pp.215-219.

[5] Milazzo M., Ludwig N., Poldi G.: Moisture detection in walls through measu-rement of temperature, QIRT, Proceedings of Eurotherm Seminar, Vol. 39(1998), pp.91-96.

[6] Tavukcuoglu A., Grinzato E.: Determination of critical moisture content inporous materials by IR Thermography, QIRT Journal, Vol. 3 (2006), pp.231-245.

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