Antonin Fabbri

Teddy Fen-Chong

Comptes Rendus Mécanique (CRM)

/media sub-bstrate ins an esti-ount ofieexploite leslle permetdes taillesdans unC. R. Mecanique 333 (2005) 425–430http://france.elsevier.com/direct/CRAS2BFreezing and thawing porous media:experimental study with a dielectric capacitive methodTeddy Fen-Chong∗, Antonin FabbriInstitut Navier, LMSGC, 2 allée Kepler, 77420 Champs-sur-Marne, FranceReceived 5 October 2004; accepted 18 January 2005Available online 23 March 2005Presented by Michel CombarnousAbstractA capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porousjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral suthe radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly providemation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amliquid water in frozen porous media by combining drying and freezing tests.To cite this article: T. Fen-Chong, A. Fabbri, C. R.Mecanique 333 (2005). 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.RésuméÉtude du gel et dégel des milieux poreux par un capteur capacitif. À l’aide d’un dispositif de sonde capacitive, on étudle changement de phase eau/glace dans des milieux poreux consolidés soumis au gel et dégel. Cette techniquepropriétés diélectriques de l’eau, de la glace, de l’air, et du substrat minéral dans la gamme des fréquences radio. Ed’obtenir directement les abaissements des températures de solidification et de fusion et indirectement la distributionde pores via la relation de Gibbs–Thomson. Elle devrait aussi fournir un moyen d’évaluer la teneur en eau liquidemilieu poreux en combinant un test en séchage et en gel.Pour citer cet article : T. Fen-Chong, A. Fabbri, C. R. Mecanique 333(2005). 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.Keywords: Porous media; Freezing; Thawing; Unfrozen water; Supercooling; Capacitive sensor; Dielectric; CementMots-clés : Milieux poreux ; Gel ; Dégel ; Eau non-gelée ; Surfusion ; Capteur capacitif ; Diélectrique ; Ciment* Corresponding author.E-mail addresses: teddy.fen-chong@lcpc.fr (T. Fen-Chong), antonin.fabbri@lcpc.fr (A. Fabbri).1631-0721/$ – see front matter 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.doi:10.1016/j.crme.2005.01.007426 T. Fen-Chong, A. Fabbri / C. R. Mecanique 333 (2005) 425–430ommonlyseriouswatercanningia likeaterialse/waterThe experi-ve beency range.. 1. Theseentalacitance iser, ice,n of eachacitanceto reach aT200 from1. IntroductionWater freezing temperature depression in porous media is a well-known and established phenomenon cattributed to intermolecular surface forces, pore water impurity, or supercooling [1–3]. This can result in acivil engineering or geotechnical durability problem, as reviewed in [3]. That is why the amount of liquidin (partially) frozen porous media has been investigated by nuclear magnetic resonance [4], differential scalorimetry [5], acoustic approach [6], or time domain reflectometry [7], on loosely bonded porous medsilty, clayey soils, or silica glass powders. Low temperature calorimetry was also applied to cementitious min [8–11]. This Note presents the use of a spectroscopic-like dielectric capacitive method for studying the icphase change in cohesive porous media such as stones, cement pastes, concrete, or fused glass beads.mental set-up, calibration, and use for studying the drying (air/water phase change) of similar materials hadescribed in [12].2. Dielectric capacitive method2.1. Basic measurement principleThe capacitive method consists in measuring the electric capacitance of a sample in the radio-frequenThe sample is inserted between two plane and circular stainless steel electrodes as sketched out in Figare connected in parallel to a 30–50 MHz oscillator circuit, which forms an oscillating circuit. The experimapparatus delivers a reduced resonant frequency that depends on the sample capacitance. A plane capproportional to its real dielectric constant. As a partially frozen porous material is composed of liquid watand the solid mineral substrate, its dielectric constant depends on the dielectric constant and volume fractiophase. Accordingly, any variation of the liquid water content by ice/water phase change gives rise to capchange, as explained below.Fig. 1. Schematic diagram of the capacitive sensor-based apparatus. The oscillator was implementing a frequency divider in orderlow frequency range (in the order of several kHz) before outputting the resonant frequency to the data logger device. Galden PFPE HSolvay Solexis company is used as cryogenic fluid for its low static dielectric constant (about 2 at 20◦C).T. Fen-Chong, A. Fabbri / C. R. Mecanique 333 (2005) 425–430 427electricdegreew thet ice and16]. Inter downt of icetice/waternts arehe samesamplesed withhesive andsignificantsheatinge rangeearerature,Fig. 2. Frequency dispersion of water and ice real dielectric constants at different temperatures.2.2. Dielectric properties and ice/water phase changeThe use of the capacitive method for freezing conditions relies on the different relaxation times of thedipole moments of water molecules in liquid water and in ice Ih. These relaxation times characterize theof electric polarisability of liquid water and ice, and thus their real dielectric constants. Fig. 2 shows howater and ice real dielectric constants vary with frequency and temperature. These curves assume thaliquid water dielectric behaviour are well-described by the single relaxation time-based Debye model [13–particular, our numerical calculation extrapolates the experimental relaxation time data for supercooled wato −40◦C. Under these hypotheses, Fig. 2 reveals that from 1 MHz to 1 GHz the real dielectric constanis equal to its optical value (electronic polarisation) of 3.2 whereas that of liquid water is still equal to its stavalue (orientation polarisation) between 80 and 105 depending on temperature. In addition to this high icpermittivity contrast, experimental tests on dry mineral samples indicate that their real dielectric constaindependent of temperature (between−40◦C and 20◦C) and close to the optical permittivity of ice: 3.8 for silicaconstituting home-made fused glass beads, which is in good agreement with data handbook of [17]. Ttemperature-independence has been obtained without any sample (air between the electrodes).3. Experimental testsCylindrical cement samples were cored and sawed from their benches. Cylindrical fused silica beadscome from home-made female moulds that are placed into an oven at 630◦C. All were then cleaned up fromscraps, dried at 50◦C in an oven until their mass becomes constant. Water saturation was always performdegassed house distilled water at 3 kPa air pressure. For each test, the sample was wrapped in plastic adweighed just before and after each capacitive test to evaluate the water mass content and to check that nowater evaporation happened. Freezing and thawing tests were realized between 20 and−40◦C by constant stepof between (generally) 1 and 5◦C for 20 min.3.1. Freezing and thawing point depression of cement pastesFig. 3 shows the variation of the reduced resonant frequency with temperature during the cooling andstages of a CPA-CEM I cement paste. The frequency varies almost linearly with temperature, except in thof two particular temperatures, around −6◦C and −43◦C, where the slope changes significantly. The linfrequency variation is related to the continuous variation of the real dielectric constant of water with temp428 T. Fen-Chong, A. Fabbri / C. R. Mecanique 333 (2005) 425–430is work is[9]ezing be-gphysical-micaltering ofneousFig. 3. Freezing and thawing of a water-saturated cement paste.Table 1Review of some cement paste freezing temperature as obtained by low-temperature calorimetry. The left-hand side column of threlated to Fig. 3Reference This work Bager and Sellevold [8] Béjaoui et al. [10] KaufmannCement Ordinary Portland Cement (CPA CEM I)W/C Ratio 0.5 0.4 0.5 0.5Cure HR 100% until drying or testingDrying before testing 70◦C (1 week) none HR 11% none none noneTf 1 [◦C] −6 none −9 none −10 −4Tf 2 [◦C] none −25 none −25 −25 noneTf 3 [◦C] −43 T (t)  −37 −43 −43 −43 −40as shown in Fig. 2. The frequency slope change is due to the progressive water/ice phase change: a first freginning at −6◦C and ending at −15◦C, a second freezing at −43◦C on cooling, and ice melting beginninat −13◦C and ending at 0◦C on heating.3.2. DiscussionTable 1 indicates that our freezing temperatures are in good agreement with some other works. Theorigin of these freezing temperatures can be explained as follows.The transition temperatureT ∗ at which an ice crystal of mean curvatureκ∗ is in stable equilibrium with neighbouring liquid water, both mechanically (Young–Laplace’s law) and thermodynamically (equality of chepotentials) is approximated by the Gibbs–Thomson equation [2]:T ∗ = Tf − γ κ∗Sf(1)whereγ  0.0409 J/m2 is the water/ice interface energy andSf  1.2 MJ/(m3 × K) is the entropy of fusionper unit of crystal volume [16]. Sinceκ∗ = 1r∗1+ 1r∗2wherer∗i=1,2 are the principal curvature radii of the ice/wainterface, we classically haveκ∗ = 2r∗for spherical ice crystal; κ∗ = 1r∗for cylindrical ice crystal (2)wherer∗ is the radius of the spherical or cylindrical crystal. It remains now to specify the physical meanradiusr∗ in the context of partially frozen porous media. In-pore ice formation can result from: (i) heterogeT. Fen-Chong, A. Fabbri / C. R. Mecanique 333 (2005) 425–430 429ucleationleadingIn the firstuldM Igeneousosannelstl so thatreng radiical poregraphelop ane liquidare doney and therelationpendenceanalysisein-poreadequaten degreenucleation where dispersed nucleating agents in water act as catalyst sites [18,10]; (ii) homogeneous n(although less probable than the previous one); (iii) ice percolation through nanoscopic channel-like poresto the sample free surface where heterogeneous nucleation is easier or to already frozen pores [2,10,11].two mechanismsr∗ corresponds to the critical ice spherical embryo radius while in the latterr∗ is related to thechannel-like pores radii.If we assume that the initial freezing temperature ofT ∗  −6◦C is due to ice nucleation, then freezing shobe initiated from ice spherical germs of radiir∗  11.4 nm, according to (1) and (2). This is possible in CPA-CEcement pastes since these are full of micrometric pores in which water is thus supercooled down to −6◦C. Oncethese large pores are frozen, ice can then propagate through cylindrical channels of radiir∗  5.7 nm to otherwater-filled pores. This picture is most probable for heterogeneous nucleation (as compared with homonucleation). According to [10], the second freezing atT ∗  −43◦C is due to ice nucleation from spherical embryof r∗  1.6 nm since the other mechanism would give ice propagation through too much thin cylindrical chof radii r∗  0.8 nm. Consider now the thawing temperature. Melting begins atT ∗  −13◦C and is the greatest aT ∗  −3◦C: assuming that all channel-like pores are frozen, this means that the ice crystal is also cylindricathe corresponding radii of melting are respectivelyr∗  2.6 nm andr∗  11.4 nm. As the transition temperatugiven by (1) is the temperature above which ice crystal cannot exist with neighbouring water, these meltican provide an estimation of the cement paste pore size distribution. To do so, we calculate the cylindriradiusR = r∗ by inverting (1) with the thawing temperature as input data [1]: this is illustrated in the insetof the right-hand side of Fig. 3.3.3. Amount of liquid waterSince the ice/water phase transformation cannot be directly quantified by weighing, one has to devindirect way for evaluating the relation between the spectroscopic dielectric answer of a sample and thwater mass contained in the pores. To do so, the following procedure is adopted. First, capacitive testson progressively dried samples, as described in [12]. This gives a relation between the resonant frequencliquid water amount. Then freezing tests are conducted on the same initially saturated sample, thus giving abetween the resonant frequency and the temperature. Both drying and freezing tests then provide the deof the liquid water amount on the temperature by eliminating the resonant frequency parameter. Such datasurmises that both the slight difference between the dielectric constants of air (1) and ice (3.2), and the temperaturdependence of the water dielectric constant, are of no importance.This elementary procedure is certainly not suited for complex materials like cement pastes for which thewater contains ions and chemically interacts with the mineral substrate. On the other hand, this may befor simple porous media such as fused glass beads. Fig. 4 shows the variation of the liquid water saturatioFig. 4. Freezing and thawing of fused glass beads.430 T. Fen-Chong, A. Fabbri / C. R. Mecanique 333 (2005) 425–430e curvesetures, thes whichistribu-biningsimetryn Gaulardores: the5–167.hnol. 34n, Cold1, pp. 83–1 (1995)ed pastes,e solutionPhD thesisue Françaiseal, Québecia by the(ratio of liquid water volume over the sample porosity) with temperature for fused glass beads. On cooling thslope changes abruptly at−6 ◦C while on heating this happens at 0◦C. This indicates that the water-to-ice phachange corresponds to the end of supercooling in deca-micrometric pores. Below these transition temperaliquid water amount changes slightly with temperature, which may be due to residual phase change.4. ConclusionThe capacitive method is well-suited for determining the freezing and thawing temperature depressionare of primarily concern for cementitious materials use in civil engineering, and for estimating pore size dtion. It also holds good promise for evaluating the amount of liquid water in frozen porous media by comdrying and freezing tests. Further work is now undertaken to improve this determination.AcknowledgementsWe are grateful to François Martineau for samples machining, Philippe Vié and Sabrina Bichon for poromeasurement and fused glass beads fabrication, Benoît Crescini for cement paste fabrication, and Fabiefor technical assistance.References[1] M. Brun, A. Lallemand, J.F. Quinson, C. Eyraud, A new method for the simultaneous determination of the size and shape of pthermoporometry, Thermochim. Acta 21 (1977) 59–88.[2] G.W. Scherer, Freezing gels, J. Non-Crystalline Solids 155 (1993) 1–25.[3] J.G. Dash, H.-Y. Fu, J.S. Wettlaufer, The premelting of ice and its environmental consequences, Rep. Prog. Phys. 58 (1995) 11[4] K. Watanabe, M. Mizogucchi, Amount of unfrozen water in frozen porous media saturated with solution, Cold Reg. Sci. Tec(2002) 103–110.[5] T. Kozlowski, A comprehensive method of determining the soil unfrozen water curves, 1. Application of the term of convolutioReg. Sci. Technol. 36 (2003) 71–79.[6] J.F. Thimus, J. Aguirre-Puente, F. Cohen-Tenoudji, Determination of unfrozen water content of an overconsolidated clay down to−160◦Cby sonic approaches – comparison with classical methods, in: Yu, Wang (Eds.), Ground Freezing 91, Balkema, Rotterdam, 19988.[7] E.J.A. Spaans, J.M. Baker, Examining the use of TDR for measuring liquid water content in frozen soils, Water Resour. Res. 32917–2925.[8] D.H. Bager, E.J. Sellevold, Ice formation in hardened cement paste, part II: drying and resaturation on room temperature curCement Concrete Res. 16 (1986) 835–844.[9] J. Kaufmann, Experimental identification of damage mechanisms in cementitious porous materials on phase transition of porunder frost deicing salt attack, PhD thesis, École Polytechnique Fédérale de Lausanne, Ecublens, CH-1015 Lausanne, 1999,no 2037.[10] S. Béjaoui, E. Revertégat, J.P. Bournazel, Mécanismes de formation de la glace au sein des pâtes de ciment et des bétons, Revde Génie Civil 6 (2002) 1309–1332.[11] B. Zuber, Vers une modélisation du comportement des matériaux cimentaires exposés au gel, PhD thesis, Université de Lav(Canada) & École Normale Supérieure de Cachan (France), 17 December 2002.[12] T. Fen-Chong, A. Fabbri, J.P. Guilbaud, O. Coussy, Détermination of liquid water content and dielectric constant in porous medcapacitive method, C. R. Mecanique 332 (2004) 639–645.[13] R.P. Auty, R.H. Cole, Dielectric properties of ice and solid D20, J. Chem. Phys. 20 (8) (1952) 1309–1314.[14] G.P. Johari, E. Whalley, The dielectric properties of ice Ih in the range 272–133 K, J. Chem. Phys. 75 (3) (1981) 1333–1340.[15] U. Kaatze, The dielectric properties of water in its different states of interaction, J. Solution Chem. 26 (11) (1997) 1049–1112.[16] V.F. Petrenko, R.W. Whitworth, Physics of Ice, Oxford University Press, 1999.[17] D.R. Lide (Ed.), Handbook of Chemistry and Physics 2001–2002, 82nd ed., CRC Press, 2001.[18] G.W. Scherer, Crystallization in pores, Cement Concrete Res. 29 (1999) 1347–1358.

Freezing and thawing porous media: experimental study with a dielectric capacitive method

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Freezing and thawing porous media: experimental study with a dielectric capacitive method

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