Measuring water vapour permeability using remote-reading humidity sensors

The water vapour permeability is a material property used in calculations of the hygrothermal performance of buildings. The standard test method (the ‘cup test’), little changed for decades and based on measuring weight changes, has been shown repeatedly in round-robin comparisons to have poor accuracy and little consistency between laboratories. Here we describe a new approach in which the primary measurement is of the humidity difference across the test sample, which is monitored continuously using sensors that are remotely readable. The box-in-box (BiB) apparatus described is smaller and simpler than that of the standard cup test. The BiB test is of shorter duration and is carried out without disturbance to the sample. New results on calcium silicate sheet, brick ceramic and autoclaved aerated concrete are compared with published vapour permeability values obtained by the standard test (considered to be of lower accuracy).


Introduction
The water vapour permeability D v is the property of a porous material that defines the rate of transport of water vapour in a gradient of vapour pressure p w (or relative humidity RH) at a fixed temperature T. This property is used widely in building physics [1,2], particularly in models of the hygrothermal behaviour of building structures. Values of D v are required in * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. associated design methods, for example for the moisture buffering of internal spaces [3]. This is the context of the work reported here. Water vapour transmission is also important in textile, paper and packaging technologies, in biological, environmental and biomedical transpiration physics [4,5].
In the widely used method of measuring D v , little changed from that described by Joy and Wilson in 1963 [6], a cup containing a saturated salt solution is capped with a specimen of the test material and placed in an environmental chamber. Inside the cup the saturated salt solution establishes a fixed RH, which by the phase rule remains constant so long as both solid salt and saturated solution are present together, irrespective of the amount of water. Thus the solution acts as a humidistat and a source or sink of water at constant vapour pressure p w . The environmental chamber is maintained at a different constant RH, either by using a different saturated salt solution or more commonly by using a dynamically controlled water injection system. By this arrangement a gradient of water vapour pressure is established across the test specimen, and water vapour then diffuses through the test specimen from the higher RH to the lower RH. The rate of transfer is determined by weighing the cup from time to time, and from such data the vapour permeability is estimated. This arrangement, generally known as the 'cup test', is described in several standards [7,8].
Despite its long history of use, the cup test has been shown repeatedly in round-robin studies to be of poor reproducibility [9][10][11][12]. While numerous sources of error have been identified, notably in [6,[13][14][15], the most intractable is that of controlling (or of knowing) the RH at each face of the specimen. Without constant and precisely known boundary conditions on the specimen surfaces, the test procedure fails to match the underlying theory of its operation. This difficulty is inherent in the experimental arrangement: since there is a finite water flux through the specimen, there must necessarily be gradients of water vapour pressure (or RH) not only across the specimen but also between the specimen and the surface of the salt solution in the cup, and across the boundary layer adjacent to the specimen in the environmental chamber. But in the standard cup test, the water vapour pressures at or near the surfaces of the test specimen are not measured, and the accuracy of the estimate of D v is immediately compromised. The poor reproducibility then arises because the true boundary condition at the specimen surface depends in an uncontrolled manner on the internal circulation of water vapour in both cup and environmental chamber, neither of which is adequately specified in standard tests.
In the new test described here, we circumvent this difficulty by making continuous RH measurements close to the two surfaces of the specimen.

Theory
In the simple schematic of figure 1, we show a mass flux of water j m through a porous barrier separating two compartments A and B in which the water vapour pressure is maintained at different constant values p wA , p wB . The total pressure P 0 is the same on both sides of the barrier, and the system is isothermal with temperature T. By Fick's law, we have where c w is the gas phase water concentration and D w is a diffusivity with dimension L 2 T −1 . Provided that water transport in the barrier occurs solely by molecular diffusion in the gas phase we can regard D w as the water vapour diffusivity of the barrier. Now we note that the mass concentration c w is equal to the vapour density of water ρ v . Assuming ideal behaviour we have ρ v = p w M/(RT) where M is the molar mass of water, and T the absolute (kelvin) temperature, so that where the lumped quantity D v = D w M/(RT) is called the water vapour permeability, with dimension T. In building physics, D v is often denoted δ p , but here we follow the notation of [16]. The vapour transport resistance factor µ = D w0 /D w , where D w0 is the water vapour diffusivity in still air at the same temperature T and pressure P 0 .
Remark. As noted elsewhere [16], the flux is purely diffusive and there is no advection in the barrier. Therefore D v is not a permeability in the Darcian sense, but is a quantity proportional to the binary molecular diffusivity D w . However the terminology is long established and we follow it here. In the case of water vapour in air at normal environmental temperatures and pressures, the partial pressure of water vapour p w rarely exceeds 0.04 atm and is often much less. Water is therefore a dilute component of the gas phase and D w may be regarded as the tracer diffusivity of water vapour in air within the barrier material.

Concept and design
In the standard test [7,8,17], the primary data are the weights of the cup measured from time to time to monitor the progressive transfer of water through the sample. As we have noted, among several practical difficulties, the most intractable is the  absence of any satisfactory control of the humidity gradient across the sample.
In the box-in-box (BiB) device we describe here and shown in figure 2, the inner box is also a humidistat, with the test material set into the lid of the box. The outer box is a second humidistat providing a different RH. To that extent only the BiB test resembles the standard cup test, with the environmental chamber replaced by a second saturated salt solution humidistat. In all other respects the BiB test and the cup test are markedly different. In the BiB test, the primary data are not weights but are the humidities in the two boxes, measured continuously with remote-reading sensors. The sensors measure both RH and temperature at preset intervals, say every 5 min. Each RH sensor is located close to the sample surface, so that the difference in RH across the sample ∆(RH) IB/OB is measured directly throughout the course of the test. In addition, each box is fitted with a micro-fan to circulate air across the sample surface. The boxes are placed in a temperaturecontrolled enclosure for the duration of the test. The primary data are the RH measurements at each side of the test sample, as shown in figure 3. At the start of a test a precisely measured mass of water (typically 0.5-1 g) is added to the large excess of solid salt in the Inner Box before it is closed. The test runs until all the water is completely transferred from the Inner Box to the Outer Box, as indicated by the RH sensors. We note that at a given temperature T the solid salt + saturated solution + vapour is thermodynamically invariant, and has constant water vapour pressure at the solution surface so long as there is any water present.
The use of remote-reading RH sensors brings great advantages, which we have exploited previously in a device for measuring rates of evaporation [18]. A remote-reading sensor has been recently used to measure the RH inside the cup of a standard vapour permeability test [19,20], showing the existence of an RH gradient inside the cup. This contributes to the poor control of the RH at the sample surface, the troublesome defect of the standard cup test.
The BiB test of figure 2 is compact, with the OuterBox only 190 × 130 × 90 mm, much smaller than standard cup test apparatus. The reduction in size, and the use of micro-fans, tends to increase the diffusive flux through the specimen and to shorten the duration of the test. The test runs described here were complete in 40-80 h.

Materials
Three materials have been used: a calcium silicate board denoted HCS, an autoclaved aerated concrete AAC; and a fired-clay ceramic brick HBC. All three are commercial materials, and to allow comparison with prior published data they are the same materials that were used in the Hamstad roundrobin study of 2001-2003 [11]. The HCS and HBC materials used are from the same stock of materials that was distributed for the Hamstad project. In the case of AAC, measurements were made on newly acquired material from the same manufacturer, and having similar density and porosity as the original Hamstad material. The three materials have diverse compositions and physical properties. HCS, widely used as a thermal insulant, consists mainly of fibres of the hydrothermal mineral xonotlite, with small amounts of calcite and cellulose [21,22]. Its open fibrous microstructure has an unusually low packing density and high volume-fraction porosity [16]. In AAC, a structural masonry material, the binding component is the hydrothermal mineral tobermorite-11 Å [23], which is combined with sand and small quantities of other minerals [24]. The material has a bimodal pore structure in which large bubbles are dispersed in a fine-grained matrix [25]. Although the porosity is high the coarse pores are only weakly interconnected, mainly through the fine pores. The HBC brick ceramic is typical of machine-made clay bricks: the complex mineralogy reflects noncalcareous raw materials [26], and the porosity and bulk density are roughly mid-range for modern commercial bricks [27]. HBC is non-hygroscopic, and HCS and AAC are only weakly hygroscopic, with less than 1.5 % mass fraction water content at 50 % RH (25 • C). The contribution to the total flux from capillary transport is considered negligible. Data on physical properties are collected in table 1.

Test procedures
In the tests reported here the Inner Box humidistat (figure 2) was established with a saturated solution of sodium chloride NaCl (RH 75.3 ± 0.1 %) made by adding water to a large excess of solid salt. In the Outer Box magnesium chloride hexahydrate MgCl 2 .6H 2 O (RH 32.8 ± 0.2 %) was used. Reference data on the equilibrium RH values of these and other saturated salt humidistats are provided by Greenspan [28]. Values from other sources of data [29,30] are similar. The relative humidities in the Inner and Outer boxes give an RH difference across the sample of about 40 % with a mean RH of about 50 %. These values are typical of conditions within construction elements and adjacent spaces. Other humidistats can be selected to suit the needs of the user [31]. All tests were run at 25 ± 0.2 • C. Test samples were conditioned at the Outer Box RH in order that the sorbed water content should be the same at the beginning and the end of a test run. In any case, as shown in table 1 the mass-fraction water content of all the materials used is extremely small. The RH/T sensors were calibrated individually. They were found to be stable; calibration corrections were in the range ±0.7 % RH. Sensors were conditioned before tests in the appropriate humidistat. The microfans delivered a circulatory airflow of 1.2 L min −1 (IB) and 6.0 L min −1 (OB) at maximum speed but were operated at about one-quarter speed by means of DC buck converters on the 3 V input voltage. The Inner Box had a volume of about 180 ml, the Outer Box 470 ml.

Data analysis
From the primary RH data shown in figure 3, we calculate the RH difference ∆(RH) IB/OB across the sample, as shown in figure 4. This is roughly constant for most of the test, and then reduces rapidly as the quantity of water in the Inner Box approaches zero. This roll-off is not caused by a change in the water vapour pressure at the surface of the solution but rather by a reduction in the area of solution surface supplying water vapour. However, we continue to measure ∆(RH) IB/OB throughout the test, and then make a numerical estimate of the integral where t 1 , t 2 are the start and end times of the test run. The water vapour permeability D v is then:  where p w0 is the saturated vapour pressure of water at temperature T, m w is the mass of water used, L is the sample thickness and A the sample area. It is good practice to report the permeability at the standard atmospheric pressure at sea level of 1 atm, P a0 = 101 325 Pa. We record also the atmospheric pressure P a throughout the test, most conveniently using a Tempo sensor disc which like the RH/T sensors is remotely readable. If the mean atmospheric pressure measured in the test run isP a , then the adjusted value of the permeability is D v,atm = D vPa /P a0 . The value ofP a is weighted by ∆(RH) IB/OB . The diffusivity D w = D v (RT)/M is likewise adjusted to standard atmospheric pressure, D w,atm = D wPa /P a0 . The resistance factor µ is independent of pressure (and also of temperature).
We note that the variation of atmospheric pressure over the duration of a test run is usually small, typically less than 2 %. However, larger deviations from the standard atmosphere may occur for reasons of geographical elevation.
A small correction to the initial mass of water is sometimes made to allow for leakage from the box. In our tests this was very small, about 2 ×10 −5 g (h % RH) −1 , and can be reduced to a value close to zero by using an additional silicone rubber gasket (cut from 0.2 mm thick sheet, Silex Ltd UK) between the seals of the lid.

Performance
Results of a series of tests are compiled in table 2. The values of D w and D v are derived from datasets such as are shown in  . A notable feature of the data is the clear dependence of ∆(RH) IB/OB on the resistance factor µ of the material. The IB RH of HBC is some 7 % higher than that of HCS, indicating a marked difference in the RH gradient between the sample and the surface of the saturated salt solution. In the standard test it is necessary to estimate that gradient (and the associated mass transfer resistance) by means of supplementary tests [7]. In the BiB test, this is no longer required since the RH at each sample surface is measured directly. In figure 5 the measured values of resistance factor µ for HCS, AAC and HBC are shown, together with published values. The values from the Hamstad round-robin [11] show great scatter. Indications are that the BiB test delivers values that are consistent with earlier measurements, and that replicate values have much smaller scatter.

Conclusions
The new test for determining the water vapour permeability that we describe has five advantages over the standard cup test. These are that • the raw RH data are logged continuously, providing much greater data density than manual weighings; • acquiring RH data at or close to the sample surface largely circumvents the problems of estimating resistances within the chamber and cup; • the incorporation of micro-fans in both boxes reduces gradients of RH; • the duration of the test is reduced from several weeks to several days; • the test runs unattended, and there is no disturbance to the sample during the test.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.