BuffermetryFundamentals of moisture buffering Properties of hygroscopic materials Diffusion enhanced materials and structures Experimental: Sorption experiments Experimental: Diffusion experiments Incorporating the buffer in the construction Whole room simulations and experiments Experiment in the Passys environmental room Appendices - instruments and procedures Wiki howto |
\documentclass[a4paper]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \setcounter{secnumdepth}{-1} \setcounter{tocdepth}{-1} \usepackage{subfigure} \usepackage{textcomp} \usepackage{amsmath} \usepackage{graphicx} \usepackage{cclicenses} \usepackage{rotating} %\usepackage{gensymb} \pagestyle{headings} \newcommand{\degree}{\ensuremath{^\circ}} \newcommand{\superscript}[1]{\ensuremath{^{\textrm{#1}}}} \newcommand{\subscript}[1]{\ensuremath{_{\textrm{#1}}}} \addtolength{\topmargin}{-10mm} \addtolength{\textheight}{+15mm} \widowpenalty=2000 \clubpenalty=2000 %\makeatletter %\makeatother \begin{document} \markboth{Padfield and Jensen -- humidity buffering}{Padfield and Jensen -- humidity buffer capacity} \title{\vspace{-2cm}Humidity buffering by absorbent materials} \author{Tim Padfield and Lars Aasbjerg Jensen} \vspace{-3cm} \maketitle \begin{abstract} Unfired clay brick, wood, and cellular concrete have been evaluated as relative humidity (RH) buffers for indoor spaces. Their response to a cyclic variation of RH has been measured and expressed in a novel unit for describing the buffer capacity, the `buf' with symbol B. This is defined as the quantity of water vapour exchanged through unit area of surface expressed as the volume of space which will experience the same change in amount of water vapour when exposed to the same relative humidity (RH) cycle. This number is approximately equal to the number of air changes needed to exhaust the buffer moisture reserve in a typical room lined with the material. Unfired perforated brick, 5 cm thick, has a buffer capacity of 27 for a daily RH cycle, providing significant resistance to RH change caused by an air exchange rate of once per hour. Wood cut across the grain was next with a value of 15, just ahead of massive unfired brick at 10. Cellular concrete was an unimpressive buffer at 7 but worst of all was fired perforated brick with a buffer value of 3 even for a long RH cycle. However, even the perforated unfired brick reacted slowly to changing RH, having a buffer capacity nearly doubling from a one-day to a four-day humidity cycle then doubling again for a very long cycle. For a long cycle, represented by a week at a steady RH, the performance approached that predicted from sorption measurements made on finely granular samples of the brick. The steepness of the water vapour sorption curve is only an approximate, and optimistic, indicator of moisture buffer performance on a daily cycle. For practically useful performance, a wall needs to have a moisture-active surface considerably larger than its area facing the room. The buffer capacity can be considerably increased if deeper layers of the wall are brought into use by convecting, or forcing, air through internal channels. A wall, 106 mm thick, of unfired perforated brick with the channels arranged parallel to the surface and ventilated mechanically, has a B-value of 61. The B-value concept can be extended to irregular objects within the room, giving them a total equivalent air volume, regardless of surface area. \end{abstract} \subsection*{Introduction} Building physicists have long been concerned with moisture exchange with absorbent materials in the walls and roofs of buildings. Water vapour is generally regarded as a nuisance, causing condensation within walls, with consequent mould growth and corrosion of construction materials. However, the stabilisation of the interior climate by moisture-active building materials and furnishing is of great value in the world of museums and archives. Humidity buffering by absorbent materials has long been used to stabilise the microclimate in showcases and transport boxes. These have a very low air exchange rate, so the exact rate of moisture exchange between the buffer material and the air in the case is not important. In this article we explore the potential for extending the benefits of humidity buffering to better ventilated enclosures: stores, archives and even museum galleries. For these large spaces, the buffer material must be cheap and available through large scale production. There are no building materials explicitly formulated to buffer indoor relative humidity (RH) so we have investigated the few materials which have a fairly large water sorption as a function of RH. These are unfired brick, wood and cellular concrete. All these materials are inherently variable in their sorption properties. Brick clays have different sorption according to their mineralogy - kaolin having very little sorption while sodium montmorillonite (bentonite) has such extreme sorption that unfired brick would crack with even a moderate change in RH. Wood species vary somewhat in sorption and cellular concrete is a generic term for many different porous mineral blocks. The one tested here, `Celcon', is a fibrous aluminosilicate containing no cement. The computer simulation programs developed for modelling moisture movement in buildings have concentrated on the diffusive movement of water molecules through the outer walls and roof. Even slow water movement through the wall can cause serious damage to the building structure but diffusive movement through the solid components of outer walls, particularly the interior paint layer, is a negligible influence on the interior climate, compared with the effect of air exchange through openings and moisture injected through human activities. We know that buildings which are heavily loaded with water absorbent materials keep their internal RH remarkably stable, even over a whole year. Figure \ref{ipswicharchive} shows the Suffolk County Record Office in Ipswich UK. Its climate has been measured over several years. Figure \ref{ispwichclimate} shows the microclimate within. The RH varies between 52\% and 58\% with a gentle annual cycle. The RH is controlled to this moderate range by winter heating alone. This drives the RH down a little in winter, because of the low moisture content of cold air. During the summer, the infiltrating air would raise the RH but for the buffer effect from the paper. This is shown clearly in the lowest trace, which is the difference between the outside and inside water vapour concentration. In summer, the concentration is consistently higher outside, but the paper holds the inside concentration down. % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.6\textwidth]{ipswicharchive.jpg}% \caption{\small{The Suffolk County Record Office in Ipswich, UK. Opened in 1990, Architect Henk Pieksma}} \label{ipswicharchive} \end{figure} % ------------------- % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.6\textwidth]{ipswich4.png}% \caption{\small{The annual cycle of temperature and relative humidity in the Suffolk County Record Office. The lowest trace indicates the difference between the concentration of water vapour inside and outside. During the winter the inside RH is driven down by air exchange, during the summer the outside air has more water vapour but the buffering by the archived documents prevents the RH from rising to equivalence with the outside water vapour concentration.}} \label{ispwichclimate} \end{figure} % ------------------- Other museum stores, and particularly museum galleries, have the same need for RH stability, but do not have the buffer capacity provided by densely packed paper records. Can this lack of buffer material be compensated by building, or lining the walls, with moisture absorbent materials? \subsection*{The experimental evaluation of buffer performance of building materials} The candidate materials have been exposed to a cyclic RH variation between 50\% and 60\% RH. The consequent exchange of water vapour with the surrounding space has been measured. The experimental technique is described in detail by Padfield \cite{padfield2002}. The apparatus, with the perforated brick specimen, is shown in figure \ref{unfiredbrickinchamber}. Briefly, the material is exposed in a sealed chamber while the RH is set to follow a cyclic variation, controlled by the temperature of water in a weighed reservoir. The temperature is adjusted by a thermoelectric heat pump in the bottom of the reservoir. It is assumed that water lost from the reservoir is mostly absorbed in the test material, with a small correction for the sorption by the chamber equipment and for the change in water vapour content of the space. By weighing the water rather than the specimen, specimens of widely different geometry and dry weight can be tested conveniently. % ----------------------------- \begin{figure}[hbt] \centering \includegraphics[width=0.4\textwidth]{unfired_perf_brick_corr.jpg}% \caption{\small{Eight perforated unfired bricks, exposed in the climate chamber. The apparatus controlling the RH and measuring the weight of water moving into the specimen is at the bottom of the picture. The exposed area of the brick wall is 0.2 m\superscript{2}, its depth is 53 mm. The sides and back are sealed with aluminium foil so the perforations are exposed to the chamber air as blind tubes.}} \label{unfiredbrickinchamber} \end{figure} % ------------------- \subsubsection*{The quantitative description of the buffer performance} The experimental apparatus yields a weight of water transferred between the test object and the reservoir as a consequence of a change of ambient RH applied over a defined cycle time. For materials destined to be used for walling, or for cladding a wall, this weight change can be normalised to one square metre of exposed surface. For irregular moisture active specimens which might be found inside a room, such as a leather sofa stuffed with kapok, the weight change for the whole specimen is a more sensible measure of performance. For books in a library, a typical weight change per linear metre of shelving would be appropriate. Given the diversity of materials and forms which combine to influence the microclimate of the room, we need to find a way of expressing their performance which can be summed conveniently to predict how the room will react to the exchange of water vapour with outside air and the generation of water vapour by human activity within the room. We transform the measured water exchange of our specimens to the equivalent volume of air (strictly speaking the volume of space) which will experience the same cyclic change in RH with the same water vapour transfer. This concept is illustrated in figure \ref{aircolumn}. This equivalent volume is labelled the B--value for the material. For building materials, as tested, the volume is calculated per square metre of exposed surface. For irregular shaped buffering objects, such as a sofa, the B--value can be defined as the equivalent air volume for the entire object. The sum of the B--values for all wall surfaces and all sorptive components within a room gives a larger, virtual volume for the room (figure \ref{virtualbath}. To calculate the effect of moisture generation and air exchange, one uses the actual air exchange, and the actual moisture production, but calculates the resulting change of RH for these fluxes dispersing into the larger virtual volume. Put simply, if the total of B--values is 100, the change of RH in the room will be that calculated for the dispersion of infiltrated air and generated moisture into a moisture-inert room which is a hundred times as big. % ----------------------------- \begin{figure}[!htb] \centering \includegraphics[width=0.3\textwidth]{equivaircolumn.png}% \caption{{\small A visual display of the `equivalent air column' principle for defining a figure of merit for a buffer material or construction. The horizontal area of the buffer is one square metre. Suppose that the RH is increased by 1\%. The buffer material will absorb water vapour through its surface as it moves towards achieving equilibrium at this higher RH. The volume of the column is defined as that volume which will also increase by 1\% RH when injected with exactly the same amount of water which enters the buffer. A highly buffering material will absorb a lot of water, so its equivalent air column will be high. This unit of buffer capacity is called the `buf' (B) with dimension length.}} \label{aircolumn} \end{figure} % ------------------- % ----------------------------- \begin{figure}[!hbt] \centering \includegraphics[width=0.6\textwidth]{virtualbathroom_m.png}% \caption{\small{The B-values for all surfaces and furniture, and the actual room volume, are added up to give a larger, virtual room volume. All water vapour fluxes are led into this volume and then the RH is calculated.}} \label{virtualbath} \end{figure} % ------------------- /subsubsection*{The effect of cycle time on the exchangeable water supply} The B--value increases with the RH cycle time. because deeper layers of the material become involved in the diffusion process. A 24 hour cycle matches the pattern of human activity, but a longer cycle time would be appropriate for designing an archive, which has a much slower air exchange and very little human generated water vapour. The B--values were measured for a 24 hour and a 96 hour sinusoidal RH variation. The longer term performance is approximated by a longer square wave cycle. The ultimate performance, given infinite time for equilibration, can be calculated from the sorption curve, which has also been measured for the test materials. /subsubsection*{The effect of air movement on the water exchange through the surface} Most of the experiments have been conducted with a high air speed, by indoor standards, between 0.2 and 1.2 m/s. This was fast enough to make diffusion through the specimen the rate determining step but not too fast to be totally unrealistic. Some experiments were conducted at low air velocity - less than 0.1 m/s, and some experiments were made with a permeable surface coating over the specimen. /subsection*{Experimental results} Table \ref{buffervalues} show the B--values for a one day sinusoidal cycle, then a four day sinusoidal cycle and finally a long cycle represented by holding the RH steady at each of the extreme values, 50\% and 60\%, for long enough for the specimen to reach equilibrium, but not longer than two weeks. The last column shows the theoretical B-value on the assumption that all the exchangeable water is available for movement between the material and its surroundings. This value is derived from the equilibrium sorption curves between 40\% which is shown in figure \ref{sorption40-60b}. \begin{sidewaystable}[htb]
\centering
\begin{tabular}{l c c c c c}
\hline
Specimen description & Depth (mm) & B--24 hour & B--96 hour & B--long & B--static sorption % ----------------------------- \begin{figure}[t] \centering \includegraphics[width=0.6\textwidth]{sorption40-60b.png}% \caption{\small{Sorption of water vapour over a limited RH range. The plots show the response to cyclic step changes of RH between 40, 50 and 60\%. The hysteresis loops are insignificant over this moderate RH range. The sorption cycles for each material are offset vertically for clarity. `Moler' is a clay rich diatomaceous earth quarried in western Denmark. `Hemcrete' is lime mortar mixed with hemp residues. `Celcon' is a porous calcium-aluminium silicate block. The clay products are from Wienerberger brickworks in Helsinge, Denmark.}} \label{sorption40-60b} \end{figure} % ------------------- The measurement precision is such that for the poorly absorbent materials B--values less than 5 are omitted from the table. For more absorbent materials the variation between specimens of different wood species, or different clay pits, would be greater than the experimental error. The values given here are therefore indicative rather than exact, For the perforated specimens, the B--value depends greatly on the air turbulence at the surface. The effect of ventilation vigour on the performance of the perforated brick was checked by exposing the brick in a larger chamber with a much gentler air circulation system, more typical of a dwelling. The B--24 value sank from 39 to 10, illustrating the importance of air circulation around highly absorbent materials. This dependence on air speed was confirmed by adapting the smaller experimental chamber to provide a slow air movement. \subsection*{Discussion} The clear winner in buffer performance is unfired perforated brick. This is a material in large scale production as an intermediate stage in the making of fired perforated brick. The energy used to dry the unfired brick is derived from the waste heat from the firing process, but a small proportion of unfired brick can be removed from the production line before firing without disturbing the normal production process. The unfired brick was exposed in several variations: a single thickness of brick with perforations exposed at only one end, a double thickness with perforations aligned, and the double thickness with the surface covered by a single layer of Whatman no. 1 filter paper (88g/m\superscript{2}) to prevent air flow within the perforations. The bricks were also set in a line of eight with all perforations aligned and air was forcibly blown through the assembly. In this case, all except the perforated sides of the bricks were sealed. This ventilated system, with a B\subscript{24} of 61 should be compared with the value 39 for the 100 mm deep perforated brick exposed passively to the general movement of the chamber air. The single depth brick (50 mm) had a B--value 27. It is not surprising that the deeper recesses of the perforations are not so active in the daily cycle but the effect of closing the perforations to forced air circulations by putting filter paper over the surface is dramatic: the B--value falls to 10. When the air velocity across the face of the uncovered perforated brick was reduced to less than 0.1 m/s, the B--value dropped to 10. Even the long period performance with good ventilation is notably impaired by the addition of filter paper, which is itself a good humidity buffer (Figure \ref{papercover}). These large changes in buffer performance emphasise the importance of access of circulating air to an intricately perforated or grooved surface. They also show that increasing the surface area by perforating the material is only advantageous in a strong air flow, typical of an office fan at about 2 m distance. One must conclude that buffering by absorbent materials in the walls and furnishing of houses is a slow process. Plain surfaces, even of strongly absorbent materials such as wood cut across the fibre direction (B = 15), have poor buffer capacity against a 24 hour RH cycle. % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.6\textwidth]{papercoveredunfiredbrick_s.png}% \caption{\small{The effect of covering unfired perforated brick with a single layer of filter paper. The response curves to a four week square wave RH cycle are plotted superimposed. The top and bottom boundary lines indicate the ultimate buffer capacity derived from the static sorption measurement.}} \label{papercover} \end{figure} % ------------------- The effectiveness of humidity buffering of the indoor climate can be estimated by considering a typical room, with walls lined with perforated unfired brick. A room, 5 x 4 m, has a wall surface to volume ratio of 0.9, but corridors and small rooms bring the ratio to about one for a typical dwelling. Assuming a typical air exchange rate of 1 per hour, a room with internal wall cladding of unfired brick, with a B-value 27 for the 24 hour RH cycle will have an effective air change rate of 1/27 per hour, so it will take about a day to equilibrate with the outside water vapour concentration. If there is little convective air circulation however, it takes only about 10 hours for the RH to approach equilibrium with the outside water vapour concentration. Over a longer period the B-value increases, roughly doubling for a four day cycle, and doubling again for a two week cycle, but the influence of the air exchange rate comes to dominate the indoor water vapour concentration, since the B--value does not increase proportionately with the number of air exchanges. Nevertheless, the Suffolk County Record Office needs only a B--value around 200, assuming an air exchange rate about once per day. To provide this degree of stability to a store for non-absorbent objects, such as railway engines is certainly within range but would demand cladding all outer walls and also intermediate partition walls. with unfired brick. The degree of buffering required can be reduced by semi-active climate control through pumping air into the building during periods when, by chance of the weather, the outside vapour concentration is suitable for driving the inside RH to the set point. For museum exhibitions, there is no inherent buffering, because most exhibits are in showcases and exposed exhibits are often varnished. The flux from internal water vapour sources cannot be calculated, without good data for visitor numbers and length of stay. There is growing use of carbon dioxide sensors in museums, from which the likely water vapour production can be deduced if the air exchange rate is measured. which is difficult. At present therefore, it seems that exhibition buffering for annual stability is not practical, but buffering of small galleries with relatively few visitors against the moisture flux during opening hours is likely to be effective. \subsubsection{The B--value concept} The buffer capacity test described here issimilar to the method defined in the Japanese standard \cite{jis} and the proposed Nordtest \cite{nordtest}. These methods used a set series of step RH changes and express the result as the weight of water exchanged through one square metre per percent RH change. All these measuring protocols give a single number for the buffer performance. This number is not directly usable in heat and moisture diffusion models, which are based on finite element calculations dependent on two material properties, water sorption and diffusion. The B--value can be considered a lumped vapour capacity which is always in equilibrium with water vapour in the space in the room. The element of delay caused by diffusion within the material is only approximately compensated by choosing a B--value matching the typical cycle of water vapour production. This will be the daily cycle for measuring buffering in a bedroom, to see if the sleepers can keep the windows closed without causing condensation on the glass. For kitchens, a lower B-value should be chosen to match the short but more frequent periods of vapour generation. Janssen and Roels \cite{janssen-roels2008} suggest a procedure for combining data from different cycle times into a capacity, an equivalent thickness and a diffusion rate which can be integrated into a finite element program. They demonstrate this by modifying the proposed Nordtest procedure, using the water transferred at an early state of the cycle to represent the performance on a shorter cycle. We present the B--value as useful in simpler calculations to estimate the environment in a room, dependent on moisture movement through gaps in the envelope and internal production but ignoring as relatively negligible the moisture diffusing through the outer wall. The reverse influence of the room RH on diffusion through the wall is another matter, not considered here. The B--value is strongly influenced by temperature, compared with the exchange measured in kg, because the sorption curves of materials are largely independent of temperature, while the moisture content of space for a given RH varies greatly with temperature. The B--value can be calculated approximately at different temperatures, roughly doubling for a ten degree cooling. This makes buffering of cold stores very effective. It also enhances the resistance to drying of stores which are only slightly warmed in winter to keep the annual average RH lower than that outside, as illustrated by the Suffolk County Archive. The B--values resulting from these experiments are optimal, requiring an air velocity past the surface which is only attained in rooms with fans. The short cycle performance will be worse in rooms with merely natural convective air movement but the long period performance will be less sensitive to air movement. This study was designed to improve the performance of museum stores and archives, which have both a low air exchange and little internal moisture generation, but they also have a slow air movement. In an ordinary dwelling, the best material in this study, the perforated unfired brick, will, if used on all walls, give a B--value for the room of around 10, representing a significant buffering of the internal climate on the scale of a day. Notice that these tests refer to buffering within the moderate RH range. Bathrooms are subject to high moisture flux which will cause condensation on non-absorbent surfaces. The unfired brick will absorb the condensate, preventing dripping. The moisture will move rapidly by capillary processes which are insignificant at the moderate RH of these tests. The performance of unfired brick in kitchens and bathrooms, where transient high RH is inevitable, will be much better. \subsection*{Conclusion} The moisture buffer capacity of clay is sufficient to moderate the course of the RH in a house built in unfired brick, as it is influenced by infiltrating outside air and by water vapour released by humans breathing, cooking and washing. The resistance to RH change caused by infiltration can be calculated from the exchange rate and the buffer value of the moisture-reactive components of the room walls and furnishing. For specialised buildings such as archives, there is already evidence from existing buildings that humidity buffering by the stored paper is capable of ensuring a steady RH through the year, provided the air exchange rate is held to about once per day. The usefulness of buffers against moisture production by human activity has to be confirmed by full scale experiment. \subsection{Acknowledgements} This work was financed by a Danish Government scheme (UMTS project 9528) supporting the conservation of cultural relics. The construction of the climate chamber was financed by a Danish Energy Agency grant for developing alternative thermal insulation for buildings. We thank the technical staff of the Department of Civil Engineering of the Technical University of Denmark for help in building the apparatus, particularly Klaus Myndal and Keld Plougmann. We thank Associate Professor Kurt Kielsgaard Hansen and Professor Carsten Rode for their support. We thank Carl-Otto Nielsen and Finn Christensen of Wienerberger brickworks in Helsinge, Denmark, for their generosity in providing materials and for their interest in our work. Dominic Wall supplied the climate measurements from the Suffolk Record Office. This research is part of a continuing program of the Research, Analysis and Consulting group in the Conservation Department of the National Museum of Denmark. We thank our colleagues in the group, Poul Klenz Larsen, Morten Ryhl-Svendsen and Benny B\oslash hm. \begin{thebibliography}{9} \bibitem{padfield2007} Tim Padfield, Poul Klenz Larsen, Lars Aasbjerg Jensen and Morten Ryhl-Svendsen, `The potential and limits for passive air conditioning of museums, stores and archives'. in `Museum Microclimates', T. Padfield and K. Borchersen (eds.) National Museum of Denmark, 2007, pp 191--198. ISBN 978-87-7602-080-4 \bibitem{ryhl-svendsen2009} Morten Ryhl-Svendsen, Lars Aasbjerg Jensen, Poul Klenz Larsen and Tim Padfield, 2009. `Does a standard temperature need to be constant?' Submitted for publication, Going Green conference, British Museum, April 2009. Preprint at: \bibitem{bs} British Standard, BS5454-2000. \bibitem{padfield2002} Tim Padfield, Ruut Peuhkuri, Carsten Rode, Kurt Kielsgaard Hansen, `Non-Isothermal Water Vapour Transmission through Porous Insulation. Part 1: The Climate Chamber'. Proceedings of the 6th Symposium on Building Physics in the Nordic Countries, Trondheim, Norway, June 17-19, 2002, 413-420 ISBN: 82-91412-02-2 \bibitem{nordtest}Carsten Rode, `Moisture buffering of building materials'. Report BYG-DTU (Department of Civil Engineering, Technical University of Denmark) R-126 2005, ISSN 1601-2917, ISBN 87-7877-195-1, Appendix A1, page 51 -- 55. \bibitem{fullversion}The experimental data are available on the authors' website: \bibitem{jis}JIS A 1470--1:2002. Test method of adsorption/desorption efficiency for building materials to regulate an indoor humidity -- Part 1: Response method of humidity. \bibitem{roels-janssen2006} Staf Roels and Hans Janssen, `A comparison of the Nordtest and Japanese test methods for the moisture buffering performance of building materials'. \textit{Journal of Building Physics} (ISSN: 1744-2591) (DOI: 10.1177/1744259106068101), 2006, vol: 30, issue: 2, pages: 137-161. Complete preprint available through: \bibitem{stehno}Viktor Stehno, `Praktische Berechnung der instationären Luftzustandsänderungen in Aufenthaltsräumen zur Beurteilung der Feuchtigkeitsbelastung der raumbegrenzenden Bauteile.' \textit{Bauphysik} 4 (1982) 128 -- 134. \bibitem{cunningham}M.J.Cunningham, `The building volume with hygroscopic materials -- an analytical study of a classical building physics problem' \textit{Building and Environment} 38 (2003) 329--337. \bibitem{janssen-roels2008} Hans Janssen and Staf Roels, `Qualitative and quantitative assessment of interior moisture buffering by enclosures' \textit{Energy and Buildings} 41 (2008) 382--394. \bibitem{morton2005} Tom Morton, Fionn Stevenson, Bruce Taylor, Nicholas Charlton Smith, `Low Cost Earth Brick Construction'. Arc Architects, 2005 ISBN 0-9550580-0-7 \end{thebibliography} \end{document} \subsection*{Appendix A: The experimental evaluation of buffer performance} The chosen building materials -- unfired brick, fired brick, wood and cellular concrete -- were sealed in turn in an airtight chamber and subjected to a sinusoidal variation in RH. The RH variation was caused by evaporation from, and condensation into, a weighed reservoir. The water vapour flux was controlled by varying the temperature of the water in the reservoir with a Peltier heat pump. The free space in the chamber was so small that its change in water content with RH variation was negligible in comparison with the water exchanged with the test specimens. The change in weight of the reservoir was therefore equal but opposite to the change in weight of the specimen. This indirect measurement allows much greater precision of measurement than would be obtained by directly weighing specimens of varying weight, shape and water sorption. The apparatus is shown in figure \ref{unfiredbrickinchamber}. It is described in detail in \cite{padfield2002}. % ----------------------------- \begin{figure}[hbt] \centering \includegraphics[width=0.4\textwidth]{unfired_perf_brick_corr.jpg}% \caption{\small{Eight perforated unfired bricks, exposed in the climate chamber. The apparatus controlling the RH and measuring the weight of water moving into the specimen is at the bottom of the picture. The exposed area of the brick wall is 0.2 m\superscript{2}, its depth is 53 mm. The sides and back are sealed with aluminium foil so the perforations are exposed to the chamber air as blind tubes.}} \label{unfiredbrickinchamber} \end{figure} % ------------------- The weighing precision is better than one gram but the overal precision of repeated cycles was two grams. The RH precision was +/- 0.2\% but there were periods of fluctuations within these limits which consistently added to the indicated weight, one to three grams. This appears to be a subtle electrical interference which defied all efforts to identify and eliminate it. The practical consequence of this imperfection is that the data for the short cycles of weakly absorbent materials, brick and cellular concrete, is subject to significant measurement error while the measurement uncertainty for the more absorbent materials, clay and wood, is insignificant compared to the natural variability in the properties of these materials. The experimental method is similar to that proposed in the Nordtest procedure \cite{nordtest}. The specimen performance is defined only by the vapour exchange through its surface. The specimen may be of any thickness, laminated or perforated. Nordtest requires only one rectangular cycle of 8 hours at high RH followed by 16 hours at low RH, repeated until a stable pattern emerges. Our specimens were subjected to three RH cycles: 24 and 96 hour sinusoidal cycles and 2 week square wave. The RH cycled between 50\% and 60\%. Cycling at each frequency continued until a reliable repetition was achieved, though there was usually a steady drift in weight caused by imperfect pre-equilibration of the specimens to the mean 55\% RH. There was also a small drift in weight caused by leakage of air into the chamber. A typical measurement sequence is shown in figure \ref{unfiredbrickgraph}. Data for all the materials, as well as details of the experimental apparatus, are given in the web version of this article. \cite{fullversion} % ----------------------------- \begin{figure}[hbt] \centering \includegraphics[width=1\textwidth]{perf_unfired_brick_graph.png}% \caption{\small{The perforated unfired brick, exposed successively to three 96 hour RH cycles, then 24 hour cycles and finally to steady chamber RH. Parallel lines mark the envelope of the cycles. The numbers indicate the weight of water in grams absorbed through the 0.2 m\superscript{2} exposed area of the bricks.}} \label{unfiredbrickgraph} \end{figure} % ------------------- \subsubsubsection*{The sorption curves of the materials} The dynamic performance of the materials does not match the total exchangeable water as defined by the sorption curve of the material, in which the specimen is weighed after coming to equilibrium with a step change in RH. It is useful to see how close the dynamic water exchange comes to the value measured at equilibrium. The sorption curves were measured in a separate climate chamber which could hold and weigh all the specimen materials as they were subjected to step changes in RH. The full sorption curves were measured, but the behaviour during slow cycling in the RH range 50\% to 60\% was also measured to define the hysteresis loop over this modest range. This behaviour is shown in figure \ref{sorption40-60b}. % ----------------------------- \begin{figure}[t] \centering \includegraphics[width=0.6\textwidth]{sorption40-60b.png}% \caption{\small{Sorption of water vapour by materials over a limited RH range. The plots show the response to cyclic step changes of RH between 40, 50 and 60\%. The hysteresis loops are insignificant over this moderate RH range. The sorption cycles for each material are offset vertically for clarity. `Moler' is a clay rich diatomaceous earth quarried in western Denmark. `Hemcrete' is lime mortar mixed with hemp residues. `Celcon' is a porous calcium-aluminium silicate block. The clay products are from Wienerberger brickworks in Helsinge, Denmark.}} \label{sorption40-60b} \end{figure} % ------------------- \subsection*{Presentation of the experimental results} The Nordtest method, and the similar Japanese standard \cite{jis} quote the moisture exchange as kilos of water passing in a given time through a square metre of surface per percent RH change as a consequence of a step changes in RH. We go a stage further in abstraction: we express the exchanged water as the volume of space which will experience the same change of RH when injected with that amount of water vapour. At a constant temperature, this value is proportional to the kg/(m\superscript{2}.\%RH) of the Nordtest proposal and the Japanese standard. The dimension of this unit is metres. This choice of an indirect unit of buffer performance will be explained in detail in a later section. In table \ref{buffervalues} the materials and variations tested are listed with a brief description of their nature. The next column is the thickness. The subsequent columns list the buffer performance, expressed as equivalent space column height, in metres, for the three cycle times. The final column lists the maximum possible buffer performance, based on the static tests of sorption capacity. \begin{table}[htb]
\centering
\begin{tabular}{l|r|r|r|r|r}
\hline
Specimen description & Thickness & B-24 & B-96 & B-long & B-sorp All specimens were wrapped in aluminium foil so that they presented only one plane surface to the chamber air, which was circulated by small fans which gave an approximately 1 m/s air flow over the surface. The best peforming specimen was unfired perforated brick. It was exposed in several variations: a single thickness of brick with perforations exposed at one end, a double thickness with perforations aligned, and the double thickness with the surface covered by a single layer of Whatman no. 1 filter paper (88g/m\superscript{2}) to prevent air flow within the perforations. The bricks were also set in a line of eight with all perforations aligned and air forcibly blown through the assembly. In this case, all except the perforated sides of the bricks were sealed. This ventilated system, with a B\subscript{24} of 61 should be compared with the value 27 for the same weight of brick material in the single thickness perforated brick exposed passively, with one end covered, to the general movement of the chamber air. The paper covered double thickness, value 10, should be compared with the uncovered value 39. These two comparisons emphasise the importance of access of circulating air to the buffer surface. Plain surfaces, even of strongly absorbent materials such as wood cut across the fibre direction (15), have poor buffer capacity against a 24 hour cycle in ambient moisture flux. For practically useful buffering \subsection*{The quantitative description of buffer performance} The deliberate use of humidity buffers, both as interior wall cladding and in freestanding indoor structures, is of great interest to museums in particular, which are currently debating the necessity of expensive fine control of RH by mechanical means. The quantitative analysis of humidity buffering in these interior spaces can be done without regard to moisture diffusion through the outer walls. This is because diffusion, though significant to the development of moisture damage in the small spaces within the structure of a wall, has a negligible influence on the room microclimate, which is dominated by air infiltration and internal moisture sources such as people and their cooking pots. The RH resulting from these processes can then, if one wishes, be fed back into a more detailed finite element analysis of the outer wall. To quantify how a buffered room reacts to infiltration and moisture production it is convenient to express the moisture buffer capacity as equivalent to a virtual room considerably larger than the real room. Infiltrating air will spread its influence over this virtual volume, reducing the RH change that would occur in a room of the real dimensions but with no absorbent materials within it. Likewise, the steam from a cooking pot will disperse into this virtual volume, causing a smaller rise in RH. Analysis of thermal processes menwhile remains firmly locked to the actual room dimensions. The first step is to recalculate the exchanged moisture measured by weight in the experimental chamber into an equivalent air volume. Figure \ref{aircolumn} explains the `equivalent air column' concept. % ----------------------------- \begin{figure}[!hbt] \centering \includegraphics[width=0.3\textwidth]{equivaircolumn.png}% \caption{{\small A visual display of the `equivalent air column' principle for defining a figure of merit for a buffer material or construction. The horizontal area of the buffer is one square metre. Suppose that the RH is increased by 1\%. The buffer material will absorb water vapour through its surface as it moves towards achieving equilibrium at this higher RH. The volume of the column is defined as that volume which will also increase by 1\% RH when injected with exactly the same amount of water which enters the buffer. A highly buffering material will absorb a lot of water, so its equivalent air column will be high. This unit of buffer capacity is called the `buf' (B) with dimension length.}} \label{aircolumn} \end{figure} % ------------------- We propose as a useful measure of buffer performance the equivalent air volume per square metre of apparent surface. Imagine a square metre of wall surface, laid horizontal, which is the base for a column of air (strictly speaking a column of space). The height of the column is such that when the air space is subjected to a change of RH, from 50\% to 60\% for example, the material supporting the air column will react to this new RH by absorbing exactly the same amount of water vapour as must be added to the air column alone to give the air this same increase in RH. This unit we call the `buf', with symbol B. The surface used in this calculation is the surface area of the wall as seen by an observer in the room. The wall may be highly perforated or ridged to increase the active surface area but this extended surface is not used to derive the B-value. The concept can even be applied to walls which are impermeable on the surface but have, for example, concealed tubes of absorbent cardboard convecting air through louvres at the base and top of the wall. The B-value can be extended to complicated geometries such as shelves of books, by giving an equivalent air volume per metre of shelving, for example. Irregular objects can be given a B-value that is not related to surface area, it is just a property of that object, with dimension cubic metre. The B-value will approximately double with every 10\degree{}C drop in temperature. This is because the amount of water vapour required to cause a certain change of RH in space diminishes with temperature, while the equilibrium moisture content of materials is dependent mainly on RH, only slightly influenced by temperature. The buffer capacity of absorbent materials in a cold store will therefore be significantly larger than at human comfort temperature. However, the diffusion rate also diminishes with temperature, so the observed B-value for short RH cycles will not increase as much as this naive view would indicate. The influence of the diminished diffusion rate becomes less important at longer cycle times when the buffer value approaches the theoretical capacity of the buffer. For a full description of the buffer capacity, the equivalent air column height B must be accompanied by a statement of the temperature, the RH cycle time and waveform, as well as the nature of the specimen, which can be a complicated laminate or a mechanically ventilated labyrinthine construction. Note that the column height is independent of the amplitude of the RH cycle, assuming linear sorption by the material, which is approximately true between 10\% and 65\% RH. \subsection*{Using the B--value in calculations} The merit of the B-value becomes apparent when one limits the scope of the calculation to predicting the influence on the interior RH of air leakage and of moisture release within the room, as sketched in figure \ref{virtualbath}. To calculate the consequent change of RH, one divides the leakage in actual room volumes per day by the imaginary room volume calculated from the sum of the B-values of all the participating components. For internal vapour sources likewise, the rise in RH is calculated from the injected water vapour quantity dispersed into the volume represented by the summed B-values plus the actual room volume. Generation of moisture in a room tends to have a daily cycle, so the 24 hour B value is appropriate for calculation in occupied rooms. For uninhabited spaces such as stores, both air exchange rate and internal moisture generation are minimal, so the long period B value is appropriate. For cold stores, the long B value at 18\degree C can be recalculated to the lower temperature equivalent air volume. The B-value is more intuitive as a unit than the kg/(m\superscript{2}.\%RH) of the Nordest proposal and the Japanese standard. A room, 5 x 4 m, has a wall surface to volume ratio of 0.9, but corridors and small rooms bring the ratio to about one for a typical dwelling. For a public building such as a museum the ratio will be smaller. Assuming a typical air exchange rate of 1 per hour, a room with internal wall cladding of unfired brick, with a B-value 27 for the 24 hour RH cycle, will take about a day to equilibrate with the outside water vapour concentration. \subsection{Comparison of the materials and their geometries} There is a striking contrast between the good performance of unfired brick and the scarcely measurable buffer capacity of brick from the same source after firing. The sorption is mainly due to the clay component, which is destroyed by firing. Clay minerals vary in their sorptive power, with sodium montmorillonite showing high sorption and kaolinite low sorption. Most brick clays have a mixture of clay species. These unfired bricks are from a calcareous clay deposit in northern Denmark. The table shows different B-values for identical unfired bricks in different orientations and thickness. This underlines the point that the B-value is not a material property but a property of the structure under test. The reduction in B-value caused by a surface coating is dramatically shown by the unfired perforated brick coated with a single thickness of Whatman no.1 filter paper. The delay in vapour transmission is large even for the long period test. The performance reduction is largely due to the prevention of forced or convective air circulation into the perforations of the brick. Clearly, effective moderation of the RH in a house can only be achieved by labyrinthine structures, not necessarily attached to the walls. \subsection{Discussion} This paper presents the measured moisture buffer performance of selected materials and structures. It also presents a novel way of presenting these data, designed to facilitate calculations of the interior microclimate in buildings, and also to give an intuitive impression of the amount of material needed to make a significant impact on the microclimate. Current standards, and proposed standards, for defining the moisture buffering capacity of materials provide information that cannot directly be used in simulation studies % toA suitable way of defining the merit of a buffer material as wall cladding, or a buffer item of intricate geometry, is to express its moisture exchange capacity in terms of air exchange At present, there are three ways of estimating moisture exchange between the air in the room and the outside air and the walls. The most fundamental method is to use two material properties to calculate moisture movement through materials: the sorption curve and the diffusion coefficient. The sorption curve is a measure of the total amount of exchangeable water in the material, the diffusion coefficient is a measure of how quickly water molecules can move through the material. The transfer of water vapour from the surface to the room air is relatively fast. It's exact rate becomes significant in calculations of rapid changes of atmospheric moisture but becomes less significant as the time scale of the process lengthens. The diffusion coefficient for materials of useful moisture capacity is so small that no building material performs well as a humidity buffer. Analogous concepts of capacity and diffusion apply to heat transfer through structures but the process is generally an order of magnitude faster. For effective moisture buffering on the scale of a day, we have to design labyrinthine structures with a large surface area, perhaps even forcing air movement over the surface. For such constructions the diffusion process becomes intricate to calculate, so some other, simpler way of describing buffer performance is needed. \subsubsection{Single number performance indicators} There are currently two commonly cited ways of describing the buffer performance as a single number: the proposed, but not yet ratified, Nordtest standard \cite{nordtest} and the Japanese standard \cite{jis}. These two standards are summarised and compared by Roels and Janssen \cite{roels-janssen2006}. Both standards impose a cycle of step changes of RH and report the amount of water passing through the surface of the specimen in kg/m\superscript{2}·\%RH. These buffer perfomance indicators have some limitations as intuitively understandable numbers. Expressing the performance in kg/m\superscript{2} masks the better buffering at lower temperature, where much less water transfer is required to alter the RH in a room. This makes RH buffers much more effective in cold stores, as used for film, seeds and other perishable items. The progress towards equilibrium slows down at lower temperature but the ultimate capacity for moisture exchange hardly changes. The buffer performance defined in these single numbers can be converted into the `Equivalent Capacity Model' developed by Stehno. \cite{stehno} In this model, the buffering by all materials within a room, or applied to walls, is combined into a single layer with a defined water capacity which is always in equilibrium with the room air. Such a layer can conveniently be coupled into a calculation of the diffusion process through the wall. However, it is unrealistic in that there is no resistance to vapour movement between buffer and room air. This model has therefore faded in competition with the alternative described below. \subsubsection*{Two-constant descriptions of buffer performance} The `Effective Moisture Penetration Depth' method \cite{cunningham} lumps the moisture-active room content and the moisture action in the wall into an effective depth, a capacitance and a surface resistance to vapour exchange with the room air. It can be likened to the single active layer of the Equivalent Capacitance Model separated from the room by a membrane with a diffusion rate which is a combination of the surface resistance and the resistance of half the effective depth. Finally there is the full finite element method where the wall is divided into thin layers each with a capacity and a diffusion rate. This method was derived from heat flow calculations which have been adapted to vapour movement. However, vapour diffusion is so much slower in most wall constructions that one must question the usefulness of such calculations in the real world, where water vapour movement is dominated by water molecules entrained in the flow of air through cracks and defects in the construction. \subsubsection*{Two constant descriptions derived from single value protocols} Janssen and Roels \cite{janssen-roels2008} have used points on the approach to equilibrium curve of the Nordtest protocol to derive a buffer value weighted according to the length of the vapour production cycle. In real life, there is not always an easily definable vapour production cycle, so Janssen and Roels further develop the weighted buffer value concept into an equivalent effective moisture penetration depth. \subsubsection*{The equivalent air volume concept} The concepts and methods described above are rooted in the history of the development of the study of water movement through buildings. The research began as a consequence of damage to buildings caused by condensation and consequent biological growth and corrosion within the outer walls of buildings, the so-called building envelope. The extension to human comfort indoors and the influence of interior furnishings, such as books and bedsheets, came much later and is not yet fully integrated in the elaborate mathematical tools developed first for predicting heat flow and then adapted to describe water movement. In this article we concentrate on the indoor environment, and in particular on the indoor environment of archives and museum stores, with the aim to simplify climate control without risk to the durability of the stored objects. Seen from this viewpoint, the important influence on the indoor RH is humidity buffering by the room contents and air leakage over the annual climatic cycle. The elaboration of current mathematical treatments is not necessary or useful. Air tightness is so essential to the climate control that diffusion of vapour through the walls becomes a negligible influence on the room RH, though the reverse influence, of the room RH on moisture accumulation within the outer wall, is strong and can be applied to the standard models for behaviour of outer walls. That is the background for our research and it leads us to a new concept in defining the merits of building materials, and interior furnishing materials, as humidity buffers. \subsection*{Experimental method} The test materials were subjected to a 10\% sinusoidal variation in RH around the average value 55\%. Over this range most materials have a nearly linear sorption curve and a narrow hysteresis loop. The diffusion rate over this range is also nearly constant. The apparatus is described in detail in an appendix. Its essential innovation is that the amount of water moving through the specimen surface is measured indirectly, by measuring the water flux moving into or out of the confined, airtight space containing the specimen. In this way it is possible to measure accurately the water exchange in heavy assemblies which would be difficult to weight directly with sufficient precision. The RH around the specimen is changed by alternately heating and cooling a water reservoir within the container. The water vapour exchanged between the chamber space and the specimen is found by weighing the water in the reservoir. The variation in water vapour content of the chamber volume, which is about 0.25 m\superscript{3}, is negligible, so one can assume that what is lost from the water reservoir is gained by the specimen. \subsection*{Experimental results for perforated unfired clay brick} The concept of buffer value will be illustrated using experimental results for the unfired perforated brick specimen shown in figure \ref{unfiredbrickinchamber}. The weight changes following the imposed RH cycles are shown in figure \ref{unfiredbrickgraph} for sinusoidal cycles lasting one day and four days and for a long period imposed by step changes of RH. The numbers on the graph are the actual weight of water in grams transferred back and forth through the specimen surface in reaction to the cycling relative humidity in the chamber. For the 24 hour, 96 hour and `infinite' cycles, the weights are 8.2, 17.7 and 33 g respectively. These numbers are first recalculated to one square metre of wall, giving 41, 88.5 and 165 grams respectively. This is in response to a 10\% RH cycle amplitude but the cycle amplitude is arbitrary and it is eliminated from the calculation when the water sorption is converted into the air column equivalent. Turning now to the air column calculation, the saturation water vapour content for one cubic metre of space at 18\degree{}C is 15.29 g, so a 10\% RH change will cause a 1.53 g change in water content per cubic metre. Using data from the 24 hour cycle, 41 g water will raise the RH by 10\% in 26.8 cubic metres of air. Rounding to a whole number, B = 27 m is the figure of merit of the material, at the defined temperature and cycle time. In this case an air exchange rate of over twice per hour will be necessary to exhaust the buffer. Another way of looking at the matter is that the humidity buffering effect will be just noticeable even in a house subjected to this quite large air exchange rate. In a store room with an exchange rate of once per day, the buffering will be the main influence on the interior RH. It is interesting to note that the four day cycle gives about twice the buffer capacity and the `infinite' cycle gives about four times the 24 hour capacity. The theoretical maximum B-value, calculated from sorption measurement on finely powdered material is even greater. This shows that even with perforated clay brick presenting a very large active surface area, slow diffusion within the material limits the buffer performance. If the surface area of the brick were to be increased by making more perforations, the density per unit of wall area would decrease, so there is an optimal degree of perforation, depending on whether speed of response or buffer capacity is more important for the intended purpose. A double depth of brick, with the perforations 10 cm deep, gave less than double the response to both the daily (B = 39) and the four day (B = 95) cycle. Massive unfired brick, made from the same clay mix, has a notably inferior performance, showing a B-value 10 for the 24 hour cycle, less than half that of the perforated version though it has more mass per unit of wall area, both test walls being 53 mm thick. In contrast, thermal buffering of the daily temperature cycle by solid earth brick involves about a half metre depth within the wall, giving an amelioration of indoor temperature which has been exploited and appreciated for millenia by the inhabitants of hot countries. If a 500 mm thick unfired earth wall were to be perforated to allow convective air circulation in depth, one could add a humidity buffering performance which would provide a stable indoor climate throughout the day. \subsection*{The performance of a mechanically ventilated structure} % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.4\textwidth]{blownbricks.jpg}% \caption{\small{The eight perforated unfired bricks are here assembled with their perforations in line, ventilated by a fan. The outside surfaces were sealed before exposure in the chamber. The wall surface area was 0.1 m\superscript{2}, the thickness 108 mm.}} \label{blownbricks} \end{figure} % ------------------- % ----------------------------- %\begin{figure}[htbp] %\centering %\includegraphics[width=1\textwidth]{perf_unfired_ventilated_annot.png}% %\caption{\small{The buffer performance of the perforated unfired bricks with internal ventilation through the perforations. The wall area is 0.1 m\superscript{2}.}} %\label{perf_ventilated_unfired_annot} %\end{figure} % ------------------- The solution to the limit set by diffusion rate is to perforate the wall and force air through the narrow passages. We have measured an alternative arrangement of the same unfired perforated bricks stacked so that their perforations were aligned within the wall. A small fan moved air through the earth tubes at about 1 m/s. The surface of such a wall can be entirely non-absorbent, which allows a much greater choice of decorative surface treatment. The arrangement is shown in figure \ref{blownbricks}. The figures of merit are B = 61, 108 and 243 respectively for 24 hour, 96 hour and `infinite' periods. This is only a little more than the B-value for the 4 day cycle for the same thickness of brick with blind perforations exposed directly to the container air but is 50\% greater than the B-value for the daily cycle. The advantage of forced circulation diminishes as the cycle time increases. One can conceive of labyrinthine walls like this being ventilated by thermal convection, without mechanical aid. \subsection*{Other buffer materials} % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.6\textwidth]{endgrainwood.jpg}% \caption{\small{Wooden blocks cut from a beam with the end grain exposed on one face. The wall area is 0.2 m\superscript{2}.}} \label{endgrainwood} \end{figure} % ------------------- Soft wood cut across the grain is shown in figure \ref{endgrainwood}. The diffusion rate of water vapour in the length direction of wood is about four times the rate across the fibre direction. Nevertheless, on the 24 hour cycle, wood is a mediocre humidity buffer. Its figure of merit is 15 and 34 for the 24 and 96 hour cycles respectively. Aerated concrete is an imprecise name covering a range of lightweight inorganic building blocks. Our specimen is the variety known as `gasbeton'. It is a calcium aluminium silicate made by reacting water, sand, lime and aluminium powder. The structure is a finely porous mass of silicate needles interspersed with larger spherical spaces, originally hydrogen gas bubbles. The buffer performance of this specimen is quite poor. B is 7 for the 24 hour cycle and the scarcely better 9 for the 96 hour cycle. \subsection*{Discussion} The revelation of the good moisture absorption of unfired clay brick will not come as a surprise to the large fraction of mankind which lives in earthen houses, but this article will remind engineers and architects in rich nations of a hidden merit of a cheap and unfashionable building material. Substantial moderation of the variation in room RH cannot in practice be achieved by a plain wall surface. Modern interiors are invariably finished with paint or wallpaper. Even a layer of Whatman no 1 filter paper (88 g/m\superscript{2}), without glue or paint, reduces by three quarters the 24 hour response of the perforated unfired brick, which was the most moisture responsive of the tested materials. The room furnishings contribute substantial RH buffering; in paper-filled archives the buffering is so powerful that rapid-response air conditioning is unnecessary \cite{padfield2007}. A satisfactory description of the total buffer capacity is achievable by considering only the interior surface of the absorptive wall and the materials enclosed within the room. In a room with useful buffer capacity, diffusion through the outer walls will be a negligible influence. This is why we do not try to reconcile our method with heat and moisture modelling programs. We regard the walls as effectively inert and impermeable structures, for calculation of the interior RH. The buffer capacity of a veneer of perforated unfired brick, for example, is regarded as a component of the room interior, rather than as part of the outer wall. We offer a simple measure of the buffer potential of these interior moisture-active materials used as a wall lining: the volume of space which has the same water exchange capacity as unit area of the surface under test. For materials within the room, such as rows of books, the equivalent space can be cited without specifying the surface area. This measure of performance is simple and independent of the amplitude of RH variation (within the limits of the normal indoor environment). The RH calculated in this way can be used in finite element models of moisture transfer through walls. Compared with the Nordtest method, the B-value method is similar in its emphasis on performance per unit of surface area, disregarding the materials, the thickness or the intricacy of the wall behind. The B-value is less stringent about experimental conditions. It allows any reasonable cyclic RH variation within the linear range for sorption, which is about 10\% to 65\%. For the irregular variation in moisture ingress from outside and generation within the room, one could develop an effective depth model with diffusion coefficient as presented by Janssen and Roels \cite{janssen-roels2008}. Validation of such a model by measurement is well beyond the scope of this article. The few materials we have measured are the commonest immediately available, but they are not the only promising candidates. Cement bonded earth bricks, usually made on site, should perform well, since the cement gel has a high water vapour sorption. Hemcrete is a lime-sand mixture filled with hemp (\textit{Cannabis sativa}) fragments left over from processing for fibre. This material also is usually mixed and applied immediately on site. Among wood-based materials found in building suppliers there are cement bonded wood chip boards and compressed wood chip boards with similar properties to plywood but with more cut fibres exposed at the surface. We would not expect these to perform better than end grain wood. An immediate use for buffer materials is in bathrooms subjected to intermittent bursts of water vapour which are currently exhausted through ducts by fans. A test in an unfired brick house built by Tom Morton \cite{morton2005} showed that walls of unfired brick worked as well as mechanical ventilation in reducing condensation. Bedrooms benefit from humidity buffering, since asthmatics sensitive to dust mites need to keep the RH below 60\%. Ventilation during the day will equilibrate the wall to a low RH, during the night the ventilation can be much reduced, with buffering maintaining the low RH even as the room cools. \subsection{Acknowledgements} This work was financed by a Danish Government scheme (UMTS project 9528) supporting the conservation of cultural relics. The construction of the climate chamber was financed by a Danish Energy Agency grant for developing alternative thermal insulation for buildings. We thank the technical staff of the Department of Civil Engineering of the Technical University of Denmark for help in building the apparatus, particularly Klaus Myndal and Keld Plougmann. We thank Associate Professor Kurt Kielsgaard Hansen and Professor Carsten Rode for their support. We thank Carl-Otto Nielsen and Finn Christensen of Wienerberger brickworks in Helsinge, Denmark, for their generosity in providing materials and for their interest in our work. This research is part of a continuing program of the Research, Analysis and Consulting group in the Conservation Department of the National Museum of Denmark. \newpage \subsection*{Appendix A: measured values} The entire sequence of measurements is shown, unedited, in figure \ref{rawdata}. Note that the weight is here shown as diminishing with increasing RH. This is because the weight change recorded is that of the water in the reservoir rather than in the specimen. % ----------------------------- \begin{figure}[!hbp] \centering \includegraphics[width=0.9\textwidth]{tinman200912complete.png}% \caption{\small{Unedited climate data from the experiment.}} \label{rawdata} \end{figure} % ------------------- \newpage % ----------------------------- \begin{figure}[!b] \centering \includegraphics[width=0.7\textwidth]{sorp_bothways.png}% \caption{\small{Sorption of water vapour by the tested materials over a large RH range, in both directions of RH change. Although the pine sorption curve is much steeper than that for unfired brick, the brick is 2.5 times as dense, bringing its sorption per unit volume much closer to that of pine.}} \label{sorp0-100} \end{figure} % ------------------- %\clearpage \subsection*{Appendix B: the climate chamber} The climate chamber is shown in figure \ref{chamberperspective}. The annular temperature control system is shown in cutaway in figure \ref{annulus}. The flux control device is shown in figure \ref{fluxmachine} and explained in figure \ref{fluxgen}. Normally, the top is closed with an airtight stainless steel lid and covered with 200 mm of wool insulation. % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.5\textwidth]{chamberperspective.jpg}% \caption{\small{The buffer measurement chamber with lid removed, showing the ventilated brick test specimen and the top of the flux generating apparatus. The inner cylindrical space is 793 mm diameter, 500 mm deep.}} \label{chamberperspective} \end{figure} % ------------------- % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.5\textwidth]{chambercutaway.png}% \caption{\small{The chamber temperature is controlled by air blowing around the annular space. The electric heating element is marked \textbf{H}, the water cooling is marked \textbf{C}. Both heating and cooling are switched by the computer program. The flux generator within the inner chamber, \textbf{F}, is also supplied with cooling water to its heat exchanger. }} \label{annulus} \end{figure} % ------------------- % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.7\textwidth]{fluxmachine_2009.jpg}% \caption{\small{The flux generator. See figure \ref{fluxgen} for the explanation.}} \label{fluxmachine} \end{figure} % ------------------- % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.8\textwidth]{fluxgen2009.png}% \caption{\small{The flux generator heats or cools the water reservoir on the left, alternately evaporating and condensing water. The weight of the full reservoir is just overbalanced by the counterweight at the other end of the beam, which is pivoted in the middle. In normal operation, the raised cam tilts the beam so the reservoir rests on the heat exchanger, which is held at 2 degrees above the chamber dewpoint. At one minute intervals, the chamber fans are stopped and the cam rotates to release the beam to rotate freely up against the load cell which is placed close to the knife edge holding the reservoir. Flexible stainless steel strips supply current to the Peltier elements which control the water temperature in the reservoir. These strips are under slight tension which keeps the reservoir level during weighing. Various adjustments to the bearing points and to the counterweight blocks allow the beam to be balanced so that the exact tilt has no influence on the weighing process.}} \label{fluxgen} \end{figure} % ------------------- The chamber climate is managed and measured through a computer program written in Python, running on a PC with Debian Linux operating system. This program controls a Hewlett Packard programmable data control and acquisition unit which in turns operates various valves and relays to govern the operation of the chamber. For this experiment the chamber had a controlled RH, with feedback from a dew point sensor. The chamber can also operate by controlling the water vapour flux, measuring the RH as a consequential value. It is clear from figure \ref{rawdata} that there was intermittent instability in the RH control. This is a slightly modified version of the apparatus described in detail by Padfield et al. \cite{padfield2002}. The sorption experiments were made in an apparatus which mixes a wet and a dry air stream within a chamber held at constant temperature. The specimens are suspended within the chamber on an automatic carousel which drops each specimen in turn onto a hook suspended from an external balance. The chamber need not be opened during the process, so cyclic RH steps can be applied with complete assurance that there is not a moment of exposure to an unregulated RH. The instrument is shown in figure \ref{sorpmachine}. % ----------------------------- \begin{figure}[htbp] \centering \includegraphics[width=0.5\textwidth]{sorpmachine.jpg}% \caption{\small{The sorption measuring device. Finely divided specimens are loosely packed in polyester mesh bags which are suspended from a carousel which rotates them in turn to be hooked to a rod, connected via a briefly open tube to a balance mounted out of sight above the picture. The climate is controlled by mixing two air streams, one saturated, the other dry. The entire assembly is held at a constant temperature in a double enclosure.}} \label{sorpmachine} \end{figure} % ------------------- \subsection{The authors} Tim Padfield, MA(Oxon) PhD(Technical University of Denmark), is an independent consultant on microclimate in historic structures and museums. He lives in Devon, SW England. \textit{tim@padfield.dk; www.conservationphysics.org} \vspace{2mm} \noindent Lars Aasbjerg Jensen, Cand. scient., is a conservator specialising in museum climate, in the Conservation Department of the National Museum of Denmark. \textit{lars.aasbjerg.jensen@natmus.dk} \vspace{10mm} %\noindent \copyright \textit{Tim Padfield and Lars Aasbjerg Jensen} \noindent \cc \textit{Creative Commons licence: attribution -- non-commercial -- no derivative works.} \end{document} %parking place for bits and pieces We propose changing the way of expressing buffer capacity to an indirect unit: the volume of air which has equal response to the specimen. This provides automatic inclusion of the changing buffer capacity at different temperatures. Furthermore, this way of expressing buffer capacity has descriptive power: since most rooms have a very approximate numerical equality between wall area and volume, the equivalent air volume indicates how many air changes are necessary to bring the buffer to equilibrium with the RH of the invading air. assumes a thickness of material equal to the penetration depth based on the effusivity. This thickness is uniformly active in moisture exchange through an equally fictitious surface membrane with a defined resistance to vapour penetration. |