Ion concentration profiles in sandwich-brick specimens have been determined experimentally at different degrees of water saturation. Based on the experimental data, ion diffusion coefficients were determined by inverse analysis. The diffusion equation served as a basis for an optimization technique. It has been shown that the ion diffusivity in bricks decreases markedly as the moisture content decreases. The interface between two adjacent bricks slows down the ion migration at low water content in particular. It is planed to investigate the interface between mortar and bricks in further experimental and numerical studie

Buchwald, A.

Kaps, Ch

Sadouki, H.

Wittmann, F.H.

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Internationale Zeitschrift für Bauinstandsetzen und Baudenkmalpflege 5. Jahrgang, Aedificatio Publishers, Heft 1, 3 - 1 4 (1999) Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments H. Sadouki \ A. Buchwald 2 , F.H. Wi t tmann 1 and Ch. K a p s 2 ' inst i tute of Building Materials Swiss Federal Institute of Technology, Zurich, Switzerland Professur Bauchemie Fakultät Bauingenieurwesen, Bauhaus-Universität Weimar, Germany Abstract Ion concentration profiles in sandwich-brick specimens have been determined experimentally at different degrees of water saturation. Based on the experimental data, ion diffusion coefficients were determined by inverse analysis. The diffusion equation served as a basis for an optimization technique. It has been shown that the ion diffusivity in bricks decreases markedly as the moisture content decreases. The interface between two adjacent bricks slows down the ion migration at low water content in particular. It is planed to investigate the interface between mortar and bricks in further experimental and numerical studies. Keywords: Ion diffusivity, brick, interface, water content, inverse analysis Rechnerische Bestimmung der lonenbeweglichkeit in Ziegelstein unter Zuhilfenahme von Ergebnissen aus nichtstationären Diffusions-versuchen Zusammenfassung An zusammengesetzten Elementen aus Ziegelproben unterschiedlicher Wassersät-tigungsgrade wurden Profile der Ionenkonzentration experimentell bestimmt. Mit Hilfe der inversen Analyse wurden die lonendiffusionskoejfizienten in feuchtem Ziegelstein unter Verwendung der experimentell bestimmten Daten ermittelt. 3 H. Sadouki, A. Buch wald, F.H. Wittmann and Ch. Kaps Der Auswertung wurde die nichtlineare Diffusionstheorie zugrunde gelegt. Es konnte nachgewiesen werden, daß der Diffusionskoeffizient empfindlich vom Was-sersättigungsgrad abhängt. Er sinkt rasch mit abnehmendem Wassergehalt. Die Grenzfläche zwischen zwei aneinander grenzenden Steinen wirkt insbesondere bei niedrigem Feuchtigkeitsgehalt als deutliche Diffusionsbremse. Es ist vorgesehen, bei weiteren Untersuchungen die Grenzfläche zwischen Mörtel und Ziegelstein näher zu analysieren. Stichwörter: lonendiffusion, Ziegelstein, Grenzfläche, Wassergehalt, inverse Analyse 4 Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments 1 Introduction Water and water movement are at the origin of numerous types of damage obser-ved in masonry. Water movement in most porous building materials can be numeri-cally simulated in a realistic way. A quantitative description of salt migration, however, is much more complex [1], Salt migration can be subdivided at least into two processes based totally on different mechanisms. Dissolved ions can be trans-ported with the migrating water. But in micro-porous materials such as concrete a strong filter effect has to be taken into consideration. The second transport mecha-nism is ion concentration gradient driven diffusion. This mechanism is used in practice to remove dissolved ions from salt containing masonry by application of a compress . In this contribution the ion diffusivity in brick masonry shall be determined. Based on experimental results, a numerical model is validated. The ion diffusion coefficient can then be calculated by inverse analysis. The influence of water con-tent on the observed diffusivity has been studied in particular. Results provide us with a solid basis for the prediction of time-dependent redis-tribution of ions in moist masonry. Results may also help to optimize desalination by the compress method. 2 Preparation of samples In order to measure the diffusivity of ions such as N a + in bricks at different moi-sture levels, sandwich-brick specimens have been prepared. Usual masonry brick with a pore volume of 3 4 % determined by mercury high pressure porosimetry were used. Cylindrical specimens were drilled out parallel to the extruding direc-tion and cut into discs . These layered specimens consist of three brick plates com-posed as shown in Figure 1. The central brick layer was impregnated by a salt solu-tion ( N a 2 S 0 4 ) . The three brick plates are equilibrated with the s ame moisture con-I 1 Brick-1 j Brick-2 j Brick-3 (water) • (water+Na2S04) j {water) ^ i — — I > (diffusion of ions) | | (diffusion of ions) - I J 16 in 16 ma ^ 4 16 ma Figure 1: Schematic representation of the three layers of the test block 5 H. Sadouki, A. Buchwald, F.H. Wittmann and Ch. Kaps tent. Four different moisture contents have been chosen, i.e. 25, 55, 78 and 100% of the maximum moisture capacity of the brick, Wm a x . Paper filters have been inserted between two adjacent plates in order to ensure a better contact at the inter-facial zones. This sandwich construction is mechanically compressed in order to enhance the contact between the three layers. Immediately all the faces of the sandwich specimens are sealed in order to prevent any moisture exchange between specimens and the surrounding atmosphere. Both free sodium and sulfate ions will then gradually migrate towards the adjacent untreated layers, untill the entire composite system reaches its final ionic equili-brium. This ionic transfer is predominantly governed by diffusion. Diffusion indu-ced by ionic concentration gradients in the porewater. As all layers have the same moisture content, no moisture motion may take place. That means the ions cannot be transfered by an advection process. Initially some water movement may take place in the opposite direction of ion diffusion due to osmosis. It must be also outlined that, at the chosen moisture contents (25, 55, 78 and 100% of the maxi-mum moisture capacity of the brick, Wm a x) , water held in pores is mainly in liquid phase. A typical desorption isotherm of a clean brick is given in Figure 2 [2], The equilibrium moisture content in salt containing bricks is much more higher. At selected durations of diffusion, the three plates were disconnected and milled down step by step up to defined depths. The brick powder was used to analyse the water-soluble sodium content. c a> C . 8 O 0 a) i- . 6 (0 1 4 TJ a) N . 2 I i_ O. o C O 20 40 60 80 100 r el a t i v e hurri di t v r % Figure 2: Typical desorption isotherm of an untreated brick at 20 °C [2] • — I I i | I I ' i i i i f r 7 * ! | • i i i i i i | [ i | < i i | i i i ' 1 i ttt~ 6 Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments 3 Transport model By assuming that no advection phenomenon and no chemical reaction can take place during the test, the transient transfer of the ions held in porewater of the porous system can be described by a diffusion equation given by the second Fick's law which is mathematically expressed by the following partial differential equa-tion : ^ = d i v ( D ( C ) - g r a d C ) (1) in which t is the diffusion time and C is the ion concentration D(C) is the ion diffusion coefficient. The diffusion coefficient D(C) may depend on the actual ion concentration C. As it will be shown in the following numerical analyses, however, a constant ion diffusion coefficient can describe the diffusion process with sufficient accuracy for a given moisture content. In accordance with the experiments, the following initial conditions are assu-med: C{x ,) = o = CQ for x within the impregnated midd le brick (2a) /) = o = 0 f ° r x within the left or right br ick (2b) No boundary conditions are fixed because the system is closed (no interaction with its surrounding). 4 Numerical analysis In the numerical analysis, equation (1) is used in its integral formulation [3]. We can integrate equation (1) in space over a conveniently small finite volume V of the diffusion region and write: d ¡Cdv = jdiv(D-gradC) dv (3) d t y y By means of the divergence theorem, the right-hand term of equation (3) is conver-ted to a surface integral, and assuming an average value C over the volume V, equa-tion (3) can be written as follows: V — = \D gradC dA (4) dt p In our case, the diffusion problem is simplified to a one-dimensional. The integra-ted finite difference method [3] is used to solve the problem. The diffusion domain is discretized into n small subdomains. The discretization is refined in the two 7 H. Sadouki, A. Buchwald, F.H. Wittmann and Ch. Kaps interfacial zones, this allows us to take into account eventually the presence of the filters, as it will be shown later. For the j-th element, the exchange of ion species with its neighbouring elements (j'-l) and (i+l), can be approximated by the mass balance as follows: AC. C -C , C -C V r - ; = D t . u - - ' - ^ - - W W ' 4,,, (5) In equation (5) A¡k is the area between adjacent elements I and k, and Dik is the harmonic mean diffusion coefficient of the elements, this later term is constant in our case. In inhomogeneous materials or if the diffusivity depends on the concen-tration this assumption is not valid any more. The set of equations (5) can then be solved numerically by an adequate method for the unknown C,. 5 Determination of the ion diffusivity Ion diffusivity is a priori the unknown material parameter. The measured ion con-centration profiles will be used in order to find the best ion diffusion coefficient. This can be realized by minimizing the functional quadratic error E(Db,Dj)\ E(Db,Df) = Jj\ccalixi,x,Db,Df)-Ccxpixi,x)]2 (6) I In this functional, Cca/ and Cexp are the calculated and the measured ion concen-tration respectively at position x{ and at diffusion time T. and Dj are the ion dif-fusivities of the brick and the interface respectively. As it will be seen in the next section, the interfacial zone has not to be modelled specifically if the bricks are moisture saturated because the contact between adjacent brick layers is ideal with regard to the ion transfer. On the contrary, at lower moisture content, the interface with the inserted paper filter slows down the ion diffusion process. 6 Results 6.1 Ion concentration profiles Figure 3 shows the spatial distribution of the sodium ion concentration in the sand-wich brick specimen, represented as relative ion content per dry mass of brick. Because of complete symmetry of the system one half is shown only. In this case, the specimen is moisture saturated (W = Wmaj[). The dashed line represents the ion concentration at the beginning of the diffusion process. The measured ion concen-tration at different positions, as indicated as distance from the symmetry axis of the 8 Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments Figure 3: Measured (symbols) and simulated (solid line) Na+-concentration profiles after a diffusion time of 78 h if the system is moisture saturated (W = VVmar ). The dashed line represents the ion concentration profile at the beginning. O 5 1 0 1 5 2 0 o o s i t i o n x r m m l specimen after a diffusion time of 78 h is given in Figure 3 by two symbols (x stands for one side of the specimen and A for the other). The continuous line repre-sents the simulated profile for the fitted ion coefficient of diffusion as obtained by the above described optimization technique (equations 4 and 6). In the case of Figure 4, the measured and simulated ion concentration profiles are plotted for a diffusion duration of 77 h and if the moisture content of the specimen is 78 % of the maximum moisture capacity of the brick (W = Wmax). As it can be seen from Figure 4, the ion concentration gradient at the interface between the initially Na2S04-impregnated brick (the centre) and its adjacent brick plates (initi-ally free from Na 2S0 4 ) is steeper as in the rest of the specimen. This effect can be explained by the action of the interface which plays a role of an additional resi-stance with respect to ion migration. Consequently the ion transfer in the interfa-cial zones is slowed down. As has been mentioned above already, this effect is taken into account in the numerical model by introducing a thin layer at the interfa-cial regions. This layer is characterized by its thickness and its own ion diffusion coefficient (Dj). The simulated ion concentration profile shown in Figure 4 by a solid line represents the best fit of diffusion equation (4) and equation (6) for the diffusivity of the brick (Db) and the diffusivity of the interface {Dp. Figure 5 shows the experimental and simulated ion concentration profiles after a duration of diffusion of 51 h and if the moisture content is 55% of Wmax. Here again, the interface is taken into consideration in the modelling. In this case the resi-9 H. Sadouki, A. Buchwald, F.H. Wittmann and Ch. Kaps Figure 4: Measured (symbols) and simulated (solid line) Na+-concentration profiles after a diffusion time of 77 h and if the moisture content is W = 78%-Wtruu. The dashed line represents the ion concentration profile at the beginning. . 4 0 IT Figure 5: Experimental and simulated ion concentration profiles after a diffusion time of 51 h and if the moisture content is 55% of Wmnr. 10 Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments stance of the interface with respect to the ion diffusion is much more pronounced as in the case shown in Figure 4. In Figure 6 the diffusion after 146 h at a water saturation of W = 25%-Wmax is shown. By comparing this case with the case shown in Figure 5, the resistance of the interface with respect to the ion migration seems to be less pronounced. This can probably be explained by the influence of the adaptation of moisture between brick and interfacial paper. In the case shown in Figure 6, the exposure time is nearly three times longer than in the case shown in Figure 5, the interface may gradually lose its resistance when exposed to ions for a long time. 6.2 Ion diffusion coefficient The optimal ion diffusivities obtained by combining the measured ion concentra-tion profiles with the diffusion equation by means of an inverse analysis are given in the Table 1. As can be expected the ion diffusivity decreases significantly with the degree of water saturation. If the brick is moisture saturated the ion diffusivity is roughly 7.5 times lower than the diffusivity in pure water. It should be mentioned that the cal-culated values of diffusivity of the moisture saturated brick are in agreement with results obtained with different experimental arrangement [5]. These values reflect Figure 6: Measured (symbols) and simulated (solid line) Na+ concentration profiles after a diffusion time of 146 h and if the moisture content is . The dashed line represents the ion concentration profile at the beginning. 11 H. Sadouki, A. Buchwald, F.H. Wittmann and Ch. Kaps Table 1: Ion diffusivity of the brick and the interface between brick plates at different Ide-grees of water saturation and at different durations of diffusion. For comparison the value in bulk water for infinite concentration [4] is given Degree of water Duration of diffu- Ion diffusivity [10"6 cm2/s] saturation [%]S sion [h] Brick Interface 100 78 1,67 1,67 78 77 1,54 0,07 55 51 1,02 0,00 25 146 0,70 0,02 Pure water - 12,5 the inf luence of ion interaction in the pore solution and of the tor tuous pore sys tem of the brick material . T h e role of the interface be tween the brick samples can be neglected in the mois ture saturated state but it b e c o m e s important at lower water content . In fur ther exper imenta l s tudies, the ion concentra t ion must be measured more accurately in the vinicity of the transit ional zone in order to get m o r e detai led infor-mat ion on the shape of the concentra t ion gradient in this critical region. In addit ion, the interface between mor ta r and brick shall be investigated in the fu ture . 7 Conclusions By means of a special sandwich-br ick spec imen, ion concentrat ion profi les can be measured for different degrees of water saturat ion. Based on the exper imenta l ly de te rmined ion concentra t ion prof i les and by app-lying an appropriate inverse analysis the ionic di f fus ivi ty in br icks can be determi-ned. T h e interface be tween two ad jacent bricks has been model led in detail . This transit ional region is character ized by its th ickness and its own ion diffusivity. At low mois ture content , the interfacial zone has a high resis tance with respect to ion migrat ion. T h e diffusivi ty of N a + ions in brick increases wi th the water content . Acknowledgement T h e authors thank M r H. Wagne r for assis tance in chemical analysis and the foun-dat ion „Deutsche Bundes t i f tung U m w e l t " for financial support . 12 Numerical Determination of Ion Diffusivity in Bricks Based on Non-Stationary Diffusion Experiments References [ 1 ] Mayer G. und F.H. Wittmann: Ein Modell zur Beschreibung des Wasser- und Salztransports in Mauerwerk, Int. Journal for Restoration of Buildings and Monuments, Vol.2, No.l , pp.67-82, (1996) [2] Weimann M.: Private communication (1998) [3] Narasimhan T.N. and P.A. Witherspoon: An integrated finite difference method for analyzing fluid flow in porous media, Water Resources Research, pp. 57-64,(1989) [4] Frick U.: Beurteilung der Diffusion im Grundwasser von Kristallingestei-nen, NAGRA Interner Bericht, NIB 92-92, (1993) [5] Buchwald A. und Ch. Kaps: Zur Diffusion des lonenpaares Na+ und S042' in wassergesättigtem Ziegelmaterial - Modellexperimente zur Mauerwerk-entsalzung, (in preparation) A. Buchwald received her diploma in Building Materials Engineering from the Bauhaus-Universität Weimar. She is currently doing a doctorate at the chair of Building Chemistry in Weimar dealing with desalination and ion diffusion in masonry materials. Prof. Dr. rer. nat. habil. Ch. Kaps, graduated in Chemistry in 1971 at the Friedrich-Schiller-Universitat Jena. From 1973 working as Research Assis-tant in Solid State Chemistry, he was involved in projects for Electronic and Glass Industry. In 1978 he obtained his doctorate in chemistry of thin amor-phous films. The thesis for habilitation is dealing with ion exchange reac-tions in oxide glass 1989. In 1992 he was appointed Professor of inorganic and glass chemistry at Fachhochschule Jena. In 1998 he has been nomi-nated professor and head of the chair of Building Chemistry at the Bau-haus-Universitat Weimar. 13 H. Sadouki, A. Buchwald, F.H. Wittmann andCh. Kaps Prof. Dr. F.H. Wittmann, Member of WTA, first studied physics at the universities of Karlsruhe and Munich, Germany, and in 1969 habilitated in civil engineering at University of Technology in Munich. Since 1976, he has been holding the position of professor for building materials, first at Delft, Netherlands, subsequently at EPF Lausanne, Switzerland, and pres-ently at Swiss Federal Institute of Technology (ETH) Zurich, Switzerland. His main interest and experience arc in the fields of cement-based materials and application of fracture mechanics. Dr. Hamid Sadouki, Diploma in Physics in 1977 and PhD in Materials Science in 1987 from the Swiss Federal Institute of Technology in Lau-sanne. Since 1988 research scientist at the Institute of Building Materials of the Swiss Federal Institute of Technology in Zurich. Research of main inter-est: numerical modeling of moisture and heat transfer and fracture mechan-ics in porous composite materials. 14 

Rechnerische Bestimmung der lonenbeweglichkeit in Ziegelstein unter Zuhilfenahme von Ergebnissen aus nichtstationären Diffusionsversuchen

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