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Wet and Dry Surface Deposition of Air Pollutants and Their Modeling BRUCE B. HICKS The net rate of delivery of trace gases to receptor surfaces is largely determined by the chemical affinity of surface materials for the gas in question. If molecules of the gas are captured efficiently or react quickly upon contact with the surface, then high surface flux densities can be expected. Large particles are deposited by gravitational settling and by inertial impaction; the efficiency of their capture depends on their shape and the structure of the surface at the point of impact. Small, submicron particles have difficulty penetrating the quasilaminar air layer adjacent to smooth surfaces, but once they contact the surface they are efficiently retained by van der Waals forces. All particles are susceptible to electrostatic forces that will encourage deposition if either the particles or the receptor surfaces carry an electrical charge. The presence of temperature and humidity gradients near the surface can also promote or hinder the deposition of particles. Most of these matters have been investigated in studies of deposition to relatively uniform surfaces of pipes or plates in wind tunnels. Extrapolation to the real-world case of complicated surface shapes is sufficiently uncertain that quantitative statements cannot be made. The role of rainfall and other kinds of atmospheric precipitation is equally com- plicated. Current ecological concern about the acidity of rain has focused attention on adverse effects associated with precipitation chemistry, but it must be recognized that rainfall provides a natural cleansing mechanism in many instances. In highly polluted areas, it is possible that the major effect of rainfall will be to remove some previously deposited pollutants from exposed surfaces and promote the subsequent deposition of soluble gases and small particles to those areas j such as crevices) that remain moist. Bruce B. Hicks is Director, NOAA Atmospheric Turbulence and Diffusion Laboratory, Oak Ridge, Tend. This work was supported in part by the Multistate Atmospheric Power Production Pollution Study and sponsored by the U.S. Environmental Protection Agency. 183

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84 CONSERVATION OF HISTORIC STONE BUILDINGS There has been considerable recent work on the transfer of air pollu- tants to receptor surfaces. Much of this work has been associated with concern about potential ecological effects of the increases in atmo- spheric sulfur loading expected to accompany an increase in the use of coal as an energy source. Current fears about acid rain have con- centrated attention on chemical deposition by precipitation, but there is a continuing awareness that dry deposition processes are capable of delivering similar quantities of material even to areas fairly distant from pollution sources. With near sources, such as within cities where pollution levels are high, we must expect dry mechanisms to deliver at least as much material to exposed surfaces as wet, especially when the surfaces in question are sloping or are somehow protected from the direct impact of precipitation. The results of modern research on ecological factors associated with chemical deposition are not usually transferable to the case of stone weathering because the ecological work places strong emphasis on matters related to biology. However, a small component of these stud- ies seeks to identify and formulate the mechanisms that control the rates of deposition of airborne pollutants. This work combines theo- retical and laboratory research with field investigations of pollutant fluxes to provide a comprehensive understanding of the processes that determine the dry fluxes of many trace gases and small particles to uniform, natural surfaces. In the present context of deposition to stone- work, the recent ecologically oriented work allows us to reconsider some of the formulations developed in earlier chemical engineering studies of the deposition to flat plates and to the surfaces of pipes. Likewise, recent work on the chemistry of rainfall has tended to concentrate on its acidic properties and their possible changes with both time and space, since these factors are of definite ecological im- portance. These studies have provided greatly improved understanding of the processes that combine to produce polluted rain and have given workers a much better fee] for the natural variability of precipitation chemistry. But before discussing details of the wet and dry deposition processes that are capable of delivering pollutants to exposed stone- work, it is useful to consider the mechanisms that contribute to de- terioration and hence to identify the specific deposition phenomena that are likely to be most important. The mechanisms are: . Physical Mechanisms The presence of water at the surface is known to be a key factor in promoting the fracturing and erosion of stone. Water penetrates pores and cracks and causes mechanical stresses

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Surface Deposition of Air Pollutants Affecting Decay both by freezing and by the hydration and subsequent crystallization of salts.~.23.4 Chemical Mechamsms Some deposited chemical agents wiD react with stone surfaces. Sulfur compounds have been indicted as the most critical factors in this regard, 5 mainly because they are often acidic and can have high concentrations in city and suburban air; but nitrogen compounds should be considered as well. Fluxes of trace gases (e.g., sulfur dioxideJ can be high, especially when promoted by biological activity like that mentioned below. Dissolution by chemical reaction with contaminants contained in precipitation is one of the most fa- miliar eroding processes, particularly in the case of carbonaceous stone. Details of the chemical reactions involved are well documented.6 Biological Mechanisms Many different biological factors have been shown to be important. Growths of lichens, mosses, algae, mold, fungi, and bacteria are capable of promoting at least surface deterio- ration.7 Some bacteria can synthesize sulfuric for nitric) acid from airborne sulfur dioxide (or nitrogen oxides). Guano contains phosphoric acid, which can also cause considerable damage.3 185 In light of the above comments, it appears desirable to focus present attention on the deposition of sulfur dioxide and small (potentially acidic) particles, on the condensation of water at the surface and at already deposited particles, and on the characteristics of pollutants . . . . . c .e. 1verec . in prec1p1tat1on. DRY DEPOSITION A pollutant in air near a surface will be transported to the immediate vicinity of the surface by average winds and turbulence. This process is usually rapid; only at night, when conditions become very calm, can pollutant uptake rates be limited by Tow turbulence. As a pollutant approaches the surface, molecular (or Brownian, in the case of particles) diffusion becomes increasingly important. Brownian diffusivity can be so low, however, that aerosol particles have difficulty penetrating the quasilaminar layer adjacent to the surface. Once a pollutant particle or molecule contacts the surface, it is not necessarily captured (al- though van der Waals forces are usually considered sufficient to capture particles).8 Thus, there is a surface resistance that quantifies the ab- sorption of trace gases or the retention of particles at the surface. Once material is deposited, chemical reactions can impose further variability on the overall uptake characteristics and are likely to be especially

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186 CONSERVATION OF HISTORIC STONE BUILDINGS important if the surface is wet. The entire process of particle deposition will be modified if-particles carry an electrostatic charge. Much of what we know about nongravitational deposition of gases and small particles to surfaces follows from studies of transfer to the walls of pipes from fluids flowing through them. These studies have shown, for example, that the transfer coefficient associated with dif- fusion through the quasilaminar layer in contact with smooth surfaces can be conveniently formulated in tenets of the diffusivity of the quan- tity in question {in most literature, nondimensionalized as the Schmidt number, Sc = v/D, where v is viscosity and D is the pollutant diffu- sivity) and the friction velocity, u*. The conductance, or transfer ve- locity across the quasilaminar layer is proportional to u*; the constant of proportionality is usually written as a quantity B that is then directly dependent on Sc. Figure 1 shows the results of several experiments which indicate that B ~Sc-2'3. The similanty between deposition to flat smooth surfaces in con- 10-3 m ~` 10-4 \ ~ O ~0 \ O 10-5~ 1 1 1 1 1 1 111 1 1 1 1 1o2 o 103 104 Sc 105 FIGURE 1 Variation of the surface boundary layer property B (see equation 1J with Schmidt number for transfer to smooth flat surfaces {after Lewellen and Sheng, 19801. Data are derived from Harriot and Hamilton {1965; open circlesI, Hubbard and Lightfoot {1966; triangles), and Mizushina et al. {1971; solid circlesI.

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Surface Deposition of Air Pollutants Affecting Decay 187 trolled circumstances and to stone surfaces in natural conditions may be somewhat limited. However, in wind tunnel studies they appear to be in general agreement. Moller and Schumann, for example, find close to a SC-2/3 dependence in the case of small-particle transfer to water surfaces in wind tunnels.9 Figure 2 presents a familiar set of wind tunnel observations of the deposition velocity Ivy = F/C, where F is the flux density and C is the airborne concentration of the pollutant) to horizontal, flat surfaces, as a function of particle size. For particles sufficiently small that gravitational settling is insignificant, these-re- sults are dominated by near-surface, quasilaminar behavior such as that seen in Figure 1. Indeed, the line drawn on the left in Figure 2 has a slope compatible with that in Figure 1. The corresponding expres- SlOn IS: Vd = u*B = A u*Sc-2'3, (1) where A is a constant. There are, however, inconsistencies between the sets of results that cause some loss of confidence in generalizing expressions of this kind. First, it appears that the precise value of the exponent is not known. While studies of trace gas transferal and particles) ~ agree in the relevance of a - 2/3 power law relationship, a survey by Brutsaert indicates exponents ranging between -0.4 and -o.8.~2 Second, the value of the numerical constant A in equation 1 appears quite uncertain. The line drawn through the data of Figure 1 corre- sponds to A ~ 0.06, yet agreement with the small-particle data of Figure 2 seems to require A ~ 0.6. These values span the result rec- ommended by Wesely and Hicks for the case of sup dioxide fluxes to fibrous, vegetated surfaces.~3 They suggest relations equivalent to A ~ 0.2, as was indicated by earlier experiments conducted by Shep- herd. 14 Regardless of the uncertainties about the detailed formulation of deposition through the quasflaminar layer, it is clear that large particles will penetrate it less easily than smaller ones, unless influenced by gravity or some other process (such as inertial impaction. Figure 2 refers to the special case of smooth horizontal surfaces. At the right hand side of the diagram, observations conform with the predictions of Stokes-law settling, although with some enhancement because of inertial impaction.8 Generalization of these results to sloping surfaces is not a trivial exercise, although calculations based on horizontally projected areas might provide acceptable estimates of gravitational settling rates in some situations. The contribution by inertial impac-

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188 C,, C: o it o CL LL CONSERVATION OF HISTORIC STONE BUILDINGS 10 0.1 0.01 0.001 100 _ O X:/ A_ 0! i. ~ ~X++~! - ~~: _ +/X 1 1 1 1 1 1 1 1 1 1 1 1 0.01 0.1 1 10 100 PARTICLE DIAMETER (,um) FIGURE 2 Particle-size dependence of the deposition velocity to relatively smooth horizontal- surfaces. The line at the left represents a Schmidt-number relationship like that of Figure 1. At the right is the expected Stokes-law relationship, with a curve drawn by eye to draw attention to the enhancement due to inertial impaction. Crosses indicate results concerning aerodynamically smooth surfaces: vertical crosses to filter paper {slough, 1973J and diagonal crosses to glass {Liu and Agarwal, 1974J. Dots apply to artificially roughened surfaces (slough, 1973J. The remaining data refer to water surfaces, for friction velocities of 40 cm/s {Moller and Schumann, 1970; inverted triangles J and 11, 44, and 117 cm/s {Sehmel and Sutter, 1974; triangles, squares and circlesJ.

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Surface Deposition of Air Pollutants Affecting Decay tion also cannot be easily calculated, since it will be influenced greatly by local flow distortion and microscale roughness characteristics. Recent work has shown that most aerosol acidity is associated with small particles of the "accumulation" size range, mostly between 0.2 and 1.0 ,um diameter. In the context of the dry deposition of acidic particles to smooth surfaces, therefore, gravitational settling and in- ertial impaction become less important concerns than diffusive trans- port and surface retention. Diffusion has been considered above; near- surface transport is conveniently formulated in terms of the Schmidt number. If particles are efficiently captured on contact with the sur- faces, then available information indicates that equation 1 provides a way to evaluate how deposition will vary with particle size. The above arguments concerning larninar layers and their effect on the transfer of particulate pollutants are relevant when the surface involved is homogeneous and smooth. However, when it is roughened, the barrier presented by the quasilaminar layer is likely to be pene- trated, and transfer rates might be considerably enhanced. In particular, large values of vat might be expected when surface discontinuities and sharp irregularities occur with characteristic scales greater than the scale thickness of the diffusive layer. The depth of this layer is usually assumed to be determined by viscosity and the friction velocity; cias- sical studies of flow over sand in wind tunnels indicate layer thick- nesses of the order of 50 Am in moderate velocities twind speed of a few m sod. Surface roughness elements of this characteristic size should therefore be suspected as sites for preferred deposition, especially if they are sharp and irregular. 189 PHORETIC EFFECTS Transfer of both gases and particles can be influenced by evaporation from a wetted surface or by condensation. The role of condensation is of special interest, since as moisture is deposited at the surface, there is a mean flow of air to replace the condensed vapor, and net deposition velocities of all pollutants are increased accordingly. The magnitude of this Stefan flow, Its' is readily calculable as: VS = (ma/mW) (`E/p), 1,2) where E is the evaporation rate {in kg m-2s-~), p is air density, ma is the molecular weight of air, and mw is that of water. At standard temperature and pressure, the overall deposition velocity is increased

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190 CONSERVATION OF HISTORIC STONE BUILDINGS by about 0.005 cm s-i for every 100 W m-2 of latent heat transferred by condensation. The maximum rate of dewfall to vegetated surfaces is known to be about 45 W m-2 Equivalent to about 0.07 mm h- i j2i, so that the increase in vet is unlikely to exceed 0.003 cm so-. Even lower values should apply in the case of statues and monuments, but these might stfl] be of similar magnitude to the values predicted for the transfer of small particles to smooth surfaces, as considered in Figure 2. In daytime, evaporation from wet surfaces will tend to protect them from pollutant deposition. When liquid water is present at the surface, evaporation rates are controlled by the availability of heat, primarily from insolation, and can easily be more than an order of magnitude greater then the condensation rates considered above. When evapo- ration is proceeding strongly, Stefan flow might provide a barrier against the deposition of those pollutants {especially small particles) having deposition velocities normally less than about 0.03 cm s- i. Such strong evaporation rates are not infrequent, but wet stone surfaces will be rapidly dried and the effect cannot persist for Tong periods. Stefan flow affects particles and gases alike; however, there are re- lated mechanisms that act primarily on particles. These phoretic forces result from the response of particles to the impaction of air and water molecules in the presence of temperature and humidity gradients. The effect is to drive particles toward cold or evaporating surfaces. Frie~ander shows that the thermophoretic velocity increment can be expressed as: v~~ -0.3 (v/~ VT, (3) where T is absolute temperature. The negative sign indicates the coun- terflux direction of the imposed motion (away from warm surfaces), and the constant 0.3 is actually a slight function of particle size (0.33 for 0.1 ,um, 0.28 for 0.3 ~m, and 0.16 for 1.0 ~m). It is informative to introduce the sensible-heat flux H and to rewrite equation (3) as via ~ - 0.3 Pr H/(p cpT) {4) where Pr is the Prandt! number, v/DT, analogous to the Schmidt num- ber in equation 1; DT is thermal diffusivity, p is air density, and cp is the specific heat of air at constant pressure. Equation 4 indicates an additional velocity increment amounting to about 0.0065 cm s- ~ for every 100 W m-2 of sensible-heat flux. At night, H rarely exceeds this value and is typically - 10 to - 20 W m-2, so that even though dep-

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Surface Deposition of Air Pollutants Affecting Decay 191 osition is enhanced, it is only by a small amount. In daytime, however, heat fluxes con exceed 500 W m-2, imposing a considerable barrier against particle deposition. A similar phoretic force is exerted on particles by water molecules Effusing past them. Whereas the Steen velocity considered above was a consequence of a mean displacement of the gas by evaporating water molecules, ~ffusiophoresis is a result of a net flux of water molecules past the particle in question and of a flux of heavier air molecules to replace them. The resulting velocity is sometimes combined with and often confused with the Stefan flow described earlier. The detailed investigation presented by Goldsmith and May shows ~ffusiophoresis to be far less important than either Stefan flow or thermophoresis in the circumstances of interest here.22 A word of caution seems appropriate at this stage. Many of the equations given above assume the existence of a laminar layer in con- tact with the surface, a situation that appears highly unlikely undess the surface under consideration is remarkably smooth and uniform Which may well be so when a stone surfaceiis new and polished). Thus, we should avoid the use of these relations to quantify deposition with precision, but instead should employ them to identify critical properties and to determine the circumstances in which deposition will be greatest. WET DEPOSITION Recent interest in the quality of precipitation {especially its acidity) has resulted in a wealth of data on the chemical composition of rain and snow. Rain fall itself is a highly variable quantity that is known to conform quite closely to a Tog-normal frequency distribution. Its chemical characteristics are even more varied, but analyses of data obtained by the Multistate Atmospheric Power Production Pollution Study (MAP3S) show that pollutant concentrations in precipitation events also tend to follow the expected log-normal distribution.23 Table 1 summarizes some of the results of the MAP3S survey, and combines them with data derived from sampling conducted by the Department of Energy Environmental Measurements Laboratory (DoE/EMt).24 The intent is to extend the MAP3S conclusions to suburban and city areas; the MAP3S sites are carefully selected to be well away from such areas and are intended to be indicative of regional-scale characteristics rather than the local variations that are likely to be mainly of interest here. Hydrogen, sulfate, and nitrate ion concentrations are selected for consideration in Table 1. The rural sites in the northeastern United

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192 CONSERVATION OF HISTORIC STONE BUILDINGS TABLE 1 Long-Term Mean Concentrations of Hydrogen, Sulfate, and Nitrate Ions in Precipitation Collected at Selected Sites H + SO4- NO3 pH C . SC C SC C SC Rural sites Chester, N.Ja 4.1 75 73 36 Ithaca, N.y.b 4.1 81 1.9 60 2.2 32 2.0 State College, pate 4.1 79 2.2 62 2.4 39 2.2 Charlottesville, Va.b 4.1 72 2.1 61 2.2 28 2.3 Miami, Ohiob 4.2 65 1.9 65 1.8 29 1.9 Urbana, [lib 4.4 43 3.5 71 1.8 30 1.8 Beaverton, Oreg.a 5.5 3 20 7 Urban and city sites Argonne, Hl.a 4.6 25 105 32 New York, N.y.a 3.9 130 150 40 NOTE: Concentrations are in microeqliivalents per liter. C is the mean concentration, and sc is the appropriate standard deviation. A log-normal distribution is assumed, so that Sc applies to the normal distribution of a variable x = in C. a Data from Feely and Larsen t1979~. b Data from the MAPLES network {MAPLES, 1981~. States appear to yield similar results: Hydrogen and sulfate ion con- centrations are in the range 60 to 80 microequivalents per liter, End nitrate is 30 to 40. The Chester site of the DOE/EML network is well away from upwind sources and does indeed provide results that agree with the MAP3S data in the Northeast; hence the two data sets appear to be compatible, even though DOE/EML provides monthly averages only, whereas MAP3S concentrates on events. The Urbana data show evidence that midwestern rural precipitation chemistry is somewhat different from that farther east; while sulfate and nitrate concentrations appear much the same, hydrogen ion concentrations seem to be sub- stantially lower. The Beaverton, Oregon, data extend this trend to the West Coast, where the precipitation is cleaner in all aspects. The New York City data were obtained at a central rooftop location. Hydrogen ion and sulfate concentrations are about `double the values typical of the Northeast as a whole, but nitrate concentrations are relatively unaffected. The Argonne, Illinois, data were obtained at a suburban site about 40 km upwind of downtown Chicago, but in an area influenced by considerable industrial activity. The Argonne nitrate values seem unaffected, but the sulfate concentrations are intermediate between regionally characteristic values and the New York City max-

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Surface Deposition of Air Pollutants Affecting Decay 193 imum. Hydrogen ion concentrations at Argonne seem strangely low, but are suspected of being influenced by soil-derived material capable of neutralizing the more acidic constituents. The Urbana data are thought to be similarly affected, but clearly to a lesser extent. The MAPaS data provide excellent evidence that the Tog-normal fre- quency distribution usually associated with the precipitation process itself also provides a good representation of the chemical concentration data. The standard deviations listed in Table 1 show remarkable uni- formity. With the sole exception of the Urbana hydrogen ion data, values range between 1.8 and 2.4, and the average is 2.0. Thus the shape of the frequency distribution is fairly constant and can therefore be extended with some confidence to the case of cities. In this way it is possible to estimate the probability of encountering exceedingly acidic ra~nfaD when only its long-term average characteristics are known, and it is similarly possible to estimate the frequency distributions of concentrations of different chemical species. For central New York City, for example, Table 1 indicates that the probability of any single rainfall event producing a pH less than 3.0 is about 15 percent. It might be noted that the standard deviations in Table 1 indicate a fairly constant spread of pH values at every site except Urbana. In general the standard deviation of the pH of event precipitation is about 0.9 (1.5 at Urbanal. Since pH depends on the logarithm of the hydrogen ion concentration, the frequency distribution of event pH values will be close to Gaussian. It is evident in Table 1 that even polluted rain has very low ionic strengths. A complication that is not evident in the table is that the greatest ionic strengths tend to be associated with the smallest rain- falis, so that high concentrations need not necessarily suggest large doses of chemical contaminants. Moreover, the probability of an ex- tremely acidic event appears to be quite low, even in city and suburban environments. These considerations combine to suggest that deteri- oration by the action of chemicals in precipitation might not be as important as that caused by the hydration and mobilization of surface materials already deposited. In some situations the net washing effect might even be beneficial. It is certainly clear that local variations of precipitation chemistry can be large and that generalizing is bound to be dangerous. AIR CONCENTRATIONS The mechanisms that deposit pollutants constitute only the final step in a chain of events that transport and transform them between sources

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94 CONSERVATION OF HISTORIC STONE BUILDINGS and receptors. The mechanisms that combine to result in the dry deposition of gaseous pollutants are likely to be most effective when the air is turbulent (i.e., mainly in daytime) and when the surface is moist and therefore acting as a good sink for soluble gases. For particles, dry deposition is mainly limited by transport very near the surface and may well be greatest when water is condensing. But none of these mechanisms will result in a large flux of pollutants unless sufficient concentrations of the pollutant are accessible in air near the surface. Many variables contribute to the diurnal cycle in concentration of any air pollutant. The highest concentrations can occur at night in some cases and during the daytime in others. Variability of this kind is greatly influenced by the spatial distribution and height of emission sources. It is also greatly influenced by whether relatively undiluted pollutant plumes can be carried near the surface by atmospheric mixing (fumigation) or by some local interference with flow patterns, such as might be caused by a large building, a hill, or rows of trees. Thus there is no general consensus that sulfur dioxide, for example, will peak in the daytime, although an early morning peak associated with fumi- gation is frequently observed. Superimposed on any regular cycle of this kind will be a random variability whose magnitude and frequency distribution will vary greatly with time and location. The temporal variability in air pollution con- centrations is a well-known feature that emphasizes the need to obtain relevant data by experiment whenever specific areas of interest can be identified. The need is amplified by the additional uncertainty asso- ciated with spatial (differences, especially within cities or in areas af- fected by local traffic. Furthermore, it is evident that more detail is required than is obtained in most pollution monitoring programs, since the deposition processes vary with the time of day. It would be difficult to interpret daily averaged concentration data, whereas averaged daily cycles and frequency distributions would be quite informative. CONCLUSIONS Both wet and dry deposition of polluters can cause significant dete- rioration of exposed stonework. Wet deposition imposes sudden but infrequent doses of pollutants, most of which will be in dilute solution. Concentrations will vary widely both in time and in space, but as a rule of thumb the pH will be roughly normally distributed, with a standard deviation of about 1.~. It is obviously possible to protect exposed surfaces from the direct effect of precipitation, but it is not immediately clear that the use of shelters will generally be beneficial.

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Surface Deposition of Air Po11u tan ts Affecting Decay 195 Dry deposition is a slower but more continuous process than wet deposition, and it is always possible that incident precipitation will wash off material previously deposited by dry processes. However, in cold weather the mechanical effects associated with repeated freezing and thawing of water are likely to overwhelm all other factors. Both dry and wet fluxes will be greatest when air concentrations of pollutants are high. Although the relationship between air concentra- tions snot the chemical composition of precipitation is exceedingly complicated, rates of deposition by dry mechanisms are intimately related to air quality in the immediate vicinity of receptor surfaces. Regarding dry deposition to exposed stonework, the following addi- tional points seem clear: In daytime, particle fluxes will be greatest to the coolest parts of exposed surfaces. Both particle and gas fluxes will be increased when condensation is taking place at the surface and decreased when evaporation occurs. If the surface is wet, impinging particles will have a better chance of adhering, and soluble trace gases wfl] be more readily captured. The chemical nature of the surface is important; if rates of reaction with deposited pollutants are rapid, then surfaces can act as nearly perfect sinks. Biological factors can influence uptake rates by modifying the ability of the surface to capture and bind pollutants. The texture of the surface is important. Rough surfaces will pro- vide better deposition substrates than smoother surfaces and will per- rnit easier transport of pollutants across the near-surface quasflaminar layer. Finally, it should be emphasized that the present state of knowledge regarding pollutant uptake by surfaces of any kind is rather rudimen- tary. Nevertheless, important processes can be identified with some confidence. While the rates of uptake cannot be predicted at all closely, the circumstances under which the greatest fluxes occur can be de- tem~ined. In particular, some surface properties that are likely to cause locally enhanced deposition can be identified, and hence areas that are potentially at risk can be singled out. REFERENCES 1. Winkler, E.M., and E.J. Wilhelm. 1970. Saltburst by hydration pressures in archi- tectural stone in urban atmosphere, Geol. Soc. Am Bull. 81:57~572.

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196 CONSERVATION OF HISTORIC STONE BUILDINGS 2. Winkler, E.M., and P.C. Singer. 1972. Crystallization pressure of salts in stone and concrete, Geol. Soc. Am. Bull. 83: 3509-3514. 3. Fassina, V. 1978. A survey of air pollution and deterioration of stonework in Venice, Atmos. Environ . 12:220~221 1. 4. Gauri, K.L. 1978. The preservation of stone, Sci. Am. 238: 196-202. 5. Yocom, J.E., and R.O. McCaldin. 1968. Effects of air pollution on materials and the economy. In Air Pollution (A.C. Stern, ea.) Academic Press: New York. 6. Keller, W.D. 1977. Progress and problems in rock weathering related to stone decay In Engineenng Geology Case Histories Number 11. Geological Society of America. 7. Torraca, G. 1977. Brick, adobe, stone, and architectural ceramics: Deterioration process and conservation practices, reprinted in Papers in Atmosphenc Science {A. Mestitz and O. Vittori, eds.) Consiglio Nazionale delle Richereche: Italy. 8. Friedlander, S.K. 1977. Smoke, Dust and Haze Fundamentals of Aerosol Behavior. John Wiley: New York. 9. Moller, U. and G. Schumann. 1970: Mechanisms of transport from the atmosphere to the Earth's surface, J. Geophys. Res. 75: 3013~019. 10. Deacon, E.L. 1977. Gas transfer to and across an air-water interface, Tellus 29: 363-374. 11. Lewellen, W.S., and Y.P. Sheng. 1980. Modeling of Dry Deposition of SO2 and Sulfate Aerosols. Electric Power Research Institute Report EA-1452. 12. Brutsaert, W. 1975. The Roughness length for water vapor, sensible heat, and other scalars, I. Atmos. Sci. 32: 202~2031. 13. Wesely, M.L., and B.B. Hicks. 1977. Some factors that affect the deposition rates of sulfur dioxide and similar gases on vegetation, I. Air Pollut. Control Assoc. 27: 1110- 1116. 14. Shepherd, J.G. 1974. Measurements of the direct deposition of sulphur dioxide onto grass and water by the profile method, Atmos. Environ. 8:69-74. 15. Harriot, P., and R.M. Hamilton. 1965. Solid-liquid mass transfer in turbulent pipe flow, Chem. Eng. Sci. 20:1073. 16. Hubbard, D.W. and E.N. Lightfoot. 1966. Correlation of heat and mass transfer data for high Schmidt and Reynolds numbers, I!EC Fundamentals 5:370. 17. M~zushina, T., F. Ogino, Y. Oka, and H. Fukuda. 1971. Turbulent heat and mass transfer between wall and fluid streams of large Prandtl and Schmidt numbers, Inter. 1. Heat and Mass Transfer 14:1705-1716. 18. Clough, W.S. 1973. Transport of particles to surfaces, Aerosol Sci. 4:227-234. 19. Liu, B.Y.H., and J.K. Agarwal. 1974. Experimental Observation of aerosol depo- sition in turbulent flow, Aerosol Sci. 5: 145-155. 20. Sehmel, G.A., and S.L. Sutter. 1974. Particle deposition rates on a water surface as a function of particle diameter and air velocity, I. Recherches Atmosphenques 3:911- 920. 21. Monteith, J.L. 1963. Dew, facts and fallacies, in The Water Relations of Plants {A.J. Rutter and F.H. W~itehead, eds.~. John Wiley: New York. 22. Goldsmith, P., and F.G. May. 1966. Diffusiophoresis and thermophoresis in water vapor systems, in Aerosol Science {C.N. Davies, ado. Academic Press: London. 23. MAP3S. 1981. The MAP3S/RAINE precipitation chemistry network: Statistical over- view for the period 1976-1980, authored by The MAP3S/RAINE Research Community, submitted to Atmos. Environ. 24. Feely, H.W. and R.J. Larsen. 1979. The chemical composition of precipitation and dry atmospheric deposition. U.S. Department of Energy Environmental Quarterly Report EML-356, I-251 to I-350.