The surface uptake of an air pollutant happens through a so-called quasi-laminar sublayer of more or less stationary air of thickness on the order of millimetres [34]. The slowest of the air transport, of the PM2.5 to the surface by convection and diffusion through the sublayer, and the surface reactivity, will limit the deposition. With increasing airflow velocity up to the surface dry deposition velocity, the sublayer becomes narrower, the concentration gradient through it steeper, and the pollution transport to the surface increases, as more (a higher concentration of) pollution comes closer to the surface. At even higher airflow velocity above the surface dry deposition velocity, and constant room concentration, the surface uptake will be constant. Smooth and little reactive surfaces can quickly be saturated even at low airflows. However, indoor concentrations are usually below those outdoors, and increasing ventilation, and airflows, will increase the indoor concentrations, and the deposition to the surfaces (by Eq. (1)). Thus, to limit deteriorating surface reactions, it is essential to reduce the air pollution concentrations, their ventilation to the indoors, the pollution transport flow to below the (maximum) surface reaction rate, and to reduce this rate, as represented by the surface deposition velocity (vs).
Concentrations
The outdoor concentrations estimated from fuel consumption before 1960 were reported to be considerably more uncertain than those from the dispersion modelling or measurements after 1960 [11]. There is then considerable additional uncertainty in the indoor concentrations due to estimation by the I/O ratios (see Additional file 1). Annual pollution measurement of, especially, O3 and PM2.5 in the Oslo University Aula are needed to validate the present (2020) concentrations (Appendix Table 3).
Mechanical filtration and air pollution sinks
The mechanical air filtration in the Aula from 1975 reduced the I/O particle concentrations. The effect of the filtration depended on the fraction of the total ventilation air that passed the filters and the filtration efficiency. The natural and remaining mechanical particle ventilation (after filtration) subtracted the particle deposition in natural infiltration paths and to indoor surfaces, will have determined the I/O ratio due to ventilation (when not then considering other transport ways such as with visitors). It should be considered how the range of possible I/O PM2.5 ratios with filtration (the I/O values after 1975 in Table 2) depend on the suggested natural (unfiltered) I/O ratio (the I/O values before 1975 in Table 2) and the filtration efficiency. The typical higher outdoor than indoor PM10/PM2.5 ratio indicates overestimation of the PM2.5 filter efficiency by the ions I/O ratio measured in the Aula. On the other hand, the origin of some of the indoor particles, and ions, trapped in the filter, from indoor sources and/or natural particle transport and infiltration into the Aula indicates underestimation of the filter efficiency by the ions I/O ratio. Considering the opposing influences and the reported ePM1-60% (see Experimental) of the filters, a PM2.5 filter efficiency of 80% (0.8) was used in the illustrating estimates below, based on the measured ions I/O ratio of 0.2 (Fig. 5), but keeping the uncertainty in mind. Equations (2) to (5) give the indoor sink fractions of an outdoor pollutant that is ventilated and infiltrating into a building, depending on the filtration efficiency. The equations were derived from the simple mass balance of the sink fractions of the particles in the ventilation air (F, d) depending on the efficiency of the mechanical ventilation filters, in the steady state. More detailed derivations of a similar purpose can be found in for example [64, 65]
$${F}_{n}={I}_{o}-{F}_{m},$$
(2)
$${F}_{m}=\frac{\left(1-{I}_{o}-d\right)\times \left(1-f\right) }{f},$$
(3)
$${F}_{d}= \left({F}_{n}+{F}_{m}\right)\times \left(d/\left(1-d\right)\right),$$
(4)
$${F}_{f}= 1-{F}_{n}-{F}_{m}-{F}_{d},$$
(5)
where Io is the I/O ratio, Fn and Fm are the indoor fractions of the pollution transported in with the natural and mechanical ventilation, Fd is that deposited on the indoor surfaces, Ff is that captured by the filters in the ventilation system, d is the constant fraction of deposition to surfaces from the indoor air (in the steady state) and f is the constant filter efficiency. One should note here that the I/O ratio and fractions of pollution in the air will be larger on infiltration than exfiltration, the difference being the indoor deposition. Thus, the deposition happens from a concentration varying between that in the infiltration and exfiltration air, and the concentration and deposition calculated from the overall I/O ratio represents an average. Figure 8 gives the indoor sink fractions of PM2.5, for the suggested I/O ratio scenarios in the Aula and a filter efficiency of 0.8, calculated from Eqs. (2) to (5).
Figure 8 shows the fractions of PM2.5 that will have infiltrated naturally, still have been introduced through the mechanical ventilation system, that will have deposited on indoor surfaces, and the remaining part that will have been removed by the filters with a PM2.5 removal efficiency of 0.8 installed in the mechanical ventilation system. The PM2.5 fractions are shown for different possible I/O ratios below the lower (a, I/O ratio = 0.5) and upper (b, I/O ratio = 0.8) limits of the I/O ratio suggested for the situations without filtration before 1975. The amount of naturally infiltrated air (the “leakage”) determines the position along the horizontal axis. It is seen in Fig. 8 that at the suggested filter efficiency (f) of 0.8, and I/O ratio of 0.8 before filtration, the lowest I/O ratio that could be reached with the filtration is 0.16 in a situation with no natural infiltration (the unfiltered I/O ratio × (1 − f) = 0.8 × 0.2). Figure 8 shows that the filtration in the Aula from 1975 (at f = 0.8) probably reduced the fraction of outdoor PM2.5 that was ventilated indoors with between 10 and 64% depending on what the I/O ratio was without filtration (between 0.5 or 0.8) and became with filtration (between 0.1 or 0.16 and 0.4). The smaller PM2.5 reduction of 10%, obtained by a change from the lower pre-filtering I/O ratio limit (of 0.5) to the upper filtering I/O ratio limit (of 0.4) seems however unrealistic. If assuming that the change was between the limits of the I/O ratio without filtration (0.8 or 0.5) to the lower limits with filtration (0.16 or 0.1) the reduction was between 64 and 40%. This is 80% (0.64/0.8 and 0.4/0.5) of the particles in the total ventilation air, rather than the 87.5% reduction shown in Fig. 7 for a change from an I/O ratio of 0.8 to one of 0.1. Thus, to obtain this reduction from the higher (possible) I/O ratio without filtration (of 0.8) to the lower suggested limit for the I/O ratio after filtration (of 0.1) a higher filter efficiency than 0.8 would be needed. The average probable reduction, of 62% (Fig. 7), is not affected by this consideration as this was calculated between the change from the high I/O limits from before to after filtration (0.8–0.4) and the change from the low I/O limits from before to after filtration (0.5–0.1).
Air pollution transport to the paintings
The deposition of air pollution ventilated into the Aula will be influenced by the air movements. If the transport of air pollution to indoors surfaces, such as the Aula paintings, is less than the surface reactivity (given by the deposition velocities in Table 2) the deposition could be less than estimated in this work. The average non-disturbed laminar airflow velocity along Aula room surfaces was estimated to be about 0.3 – 0.4 cm s−1 (see Sect. “Ventilation and air pollution transport to the paintings in the Oslo University Aula”). These airflow velocities are about four to more than one magnitude higher, depending on pollutant, than the surface deposition velocities (Table 2). The low ventilation regime in the Aula thus probably reduces the deposition of pollution gases and PM2.5 to the room and paintings, mainly by reducing the indoor concentrations, rather than the airflow transport to the surfaces.
There will however be variations from the average air velocity in the Aula, due to variations in the airflow path lengths along the room surfaces and residence time of the air, which can influence the deposition on the paintings. Variations can occur towards higher values due to mixing of compartment air and air circulation, and where there is disturbed air due to for example turbulence from air outlets, the room features and geometry, heat sources and gradients, and natural infiltration paths and visitors. Variations can occur towards lower airflow in possible pockets and zones of more stagnant air. There will be some, here undetermined, mixing of the inlet to outlet air between the three compartments, the scene, hall, and gallery. Little such mixed air probably flows along the paintings. The longer flow paths from the inlets to the outlets of such air could potentially result in somewhat higher (average) flow velocities. The airflow velocity is, generally, high(er) and often turbulent in the outlet ducts from ventilation systems, which can also induce turbulence along walls [66]. At low Reynolds numbers (Re) from the outlets, less than approximately 500, it has been found experimentally that the flow along the walls from outlet jets is probably transitional (turbulent to laminar) or laminar [67, 68]. Other reports [69] are of transition to turbulent flow along surfaces generally between Re = 105 and 3 × 106. The needed airflow rates at the outlets and their location can, potentially, increase the air mixing along and pollution transport to surfaces in the Aula even if the overall air exchange is low and, probably, usually mainly laminar. More detailed convection and turbulence measurements than was possible in this work would be of interest.
Deposition
Indoor dry deposition velocities vary much depending on the indoor air and surface characteristics. The uncertainty in the assessment for the Munch paintings (Table 2) is difficult to suggest. The surface deposition velocities could be considerably higher, than given in Table 2, to for example rough or soiled parts of the paintings. The surface deposition velocity may increase as the paintings get more soiled and deteriorated. New soiling particles might adsorb more easily and strongly to the established soiling than to the original painting surface. The soiling can enhance further soiling at an increasing rate. Thus, the regular cleaning and especially a tailor-made maintenance is important to reduce the accelerating damage [40]. What the temporal variation in the soiling rate may have been depending on the cleaning status of the paintings, is clearly an issue of interest.
Although the small and dark particles is the most critical, it is not the only concern. The total particle deposition will be larger than that of PM2.5. Some amount of the PM10–2.5 fraction will penetrate to the indoors by natural ventilation paths and deposit. A partial correlation between the outdoor an indoor PM10–2.5 has been observed [60] that was stronger in the summer and for higher concentrations. This was explained by higher ventilation in the summer, and relatively more transport of coarser particles with visitors in the winter (which is not related to outdoor air concentrations). The larger extent of impaction and settling by gravitation of particles in the PM10–2.5 range and above can lead to increased localized deposition [7].
In the National Gallery of Oslo, the indoor fraction of PM10/PM2.5 was measured to 1.5 [59]. This would imply, for the typical double deposition velocity of PM10 to PM2.5 [70]), a three times higher mass deposition of PM10, than PM2.5 to the paintings in the Aula (ignoring in this case the different deposition of PM10 and PM2.5 to different surface orientations). This however probably better describes the historical situation before the installation of mechanical filtration in ~ 1975. The present (2020) deposition of PM10 is probably less than three times that of PM2.5, estimated to 0.011 ± 0.006 g m−2 a−1, but will also depend on the transport of particles into the Aula outside of the mechanical ventilation system. In three British museums the soiling rate and fraction of fibrous dust on the walls, was reported to be significantly higher up to about 150 cm on the wall, due to dust from the floor and visitors [71]. On the higher (than 3 m from the floor) mounted Munch paintings in the Aula (Fig. 1) deposited large particles from visitors and indoor activities, often of organic origin, are still observed [33, 35]. Thus, the total soiling rate is expected to be higher than that estimated for the PM2.5, or even PM10, fraction in this work. Still, the visual nuisance and deteriorating effect of the soiling by the smaller and expected darker PM2.5 particles from combustion, are larger due to the particle’s stronger adherence, deeper penetration into surface topography and pores, and more difficult cleaning [7, 35, 72, 73]. From values of the particle densities (and characteristics) and/or the soiling density, the expected developing surface coverage [74, 75] or soiling thickness could be suggested from the deposition rates.
The estimated effect of the particle filtration indoors in the Aula, of 62% (50–80%) reduction in the mass deposition of PM2.5, constitutes only a small fraction of the probable deposition before 1975 (Fig. 6a), but it will have resulted in a significant reduction in the development of the soiling since 1975 (Fig. 7). The renovation of the filtration system in 2009–2011 will have further improved the situation. If the present filter efficiency were known, or could again be measured, and PM measurements could be performed for a period including some (short) time without the particle filters installed, but otherwise under normal operating conditions, the fraction of the particles which still infiltrates naturally and the effect of the filtration in reducing the deposition could be determined.
The indoor deposition of O3 may today be much higher than of other air pollutants (Fig. 6a). This result should be interpreted with caution as a risk indication and warning rather than a definitive risk. How much of the O3 surface loss that will be due to its decomposition and how much due to chemical reactions, will clearly depend on the oxidizability of the surface material and to some extent on the indoor temperature, relative humidity (RH) and amount of surface adsorbed water [16, 76]. Homogeneous reactions are, in the situation with low, or no, expected indoor NO probably a small sink for the O3 [57]. Although, some indoor loss of O3 indoors by reaction with NO and formation of NO2 is typical in cities in the summer [77, 78]. With the low ventilation in the Aula the residence time of any emitted VOCs (volatile organic compounds) and amount of their reaction products with O3 could be higher than is common indoors. It seems important to further evaluate, including experimentally, the rates of and deterioration risks due to, O3 deposition on the paintings, besides those of particles and NOx. With access to annual values of the indoor concentration of O3 and PM2.5 and more information about possible reactions, of especially O3, with the paintings, the indoor deposition, and present risk, due to these pollutants could be better assessed. For validation and comparison with the deposition estimates, experimental measurements of the soiling rate in the Aula are ongoing on canvas samples with white grounds [5] and Teflon filters [79] mounted on the wall close to two of the Munch paintings. It might also be possible to assess the present soiling amount on locations on the paintings or other surfaces in the Aula. Although, due to the past renovation campaigns, the frequent cleaning and maintenance, and many sensitive conservation concerns, this is challenging.
The models presented in this work are in the form generally and commonly used to describe indoor air pollution deposition. Their explanatory power depends on the correctness of the assessed historical values of the I/O concentration and the deposition velocities. Clearly, there is considerable uncertainty in these values and thus the estimated historical trends of the air pollution deposition to the Munch paintings. The estimates should, however, be regarded also as an example of a comparison case with the outdoors. We think this assessment provides useful values of the historical amounts and trends of the indoor sink fractions and mass deposition of air pollution to the paintings, that could be practically compared with site measurements.