On the air cleansing efficiency of an extended green wall: A CFDanalysis of mechanistic details of transport processes

Saumitra V. Joshi a, Sat. Ghosh a,b,n

a School of Mechanical and Building Sciences, VIT University, Vellore, Indiab School of Earth and Environment, University of Leeds, UK

H I G H L I G H T S

� Turbulent transport of pollutant from a line source to a green wall is modeled.� Numerical modeling of stomata simulating gas and ionic phase transport of SO2.� We establish that vegetated façades efficiently mitigate background pollution.� Removal rates of 1.05e-6 s�1 (dry) and 1.11e-6 s�1 (humid) are calculated.� Sensitivity studies are done for humidity, pore aperture, temperature and LAI.

a r t i c l e i n f o

Article history:Received 5 February 2014Received in revised form28 May 2014Accepted 16 July 2014Available online 30 July 2014

Keywords:Pollutant RemovalMass TransferDeposition Velocity

a b s t r a c t

The detrimental impact of rising air pollution levels in urban landscapes has become conspicuous overthe last decade, particularly in developing countries. This novel numerical study quantifies the cleansingefficiency of green façades draped with a copiously growing tropical creeper Vernonia elaeagnifolia.Turbulent transport of SO2 to the leaf boundary layer and subsequent diffusion across stomatal poresinto the mesophyllic cells is modeled at the micro level, including its ionic dissociation in the leaf'sinterior. A SEM analysis indicates stomatal dimensions and density. Whilst previous studies have usedeither spatially averaged equations or resistance models, a spatially discretized computational approachis adopted in this study. The resulting concentration distribution is used to calculate the depositionvelocity on stomatal pores, which is then extrapolated over the entire façade to yield bulk pollutantremoval rates. A deposition velocity of 1.53 mm s�1 and 0.72 mm s�1 is obtained for open and closedpores respectively, with removal rates equal to 1.11�10�6 s�1 and 1.05�10�6 s�1 for dry and humidweather respectively. Sensitivity studies on the removal rate are carried out based on humidity, stomatalaperture and leaf temperature. The removal rate dependence on the Leaf Area Index (LAI) is alsoinvestigated. It is inferred from simulations that vegetated façades are efficient at mitigation of residualpollution.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Automobiles have come as a sundry blessing for the humancivilization; while their use has allowed humans to conquerdistances and greatly reduce travel times, the side effectshave resulted in a flagrant destruction of environment (Sinha,1993). The transportation sector accounts for around a quarter ofgreenhouse emissions (Carbon Pollution Standards), the major

emissions from the automobiles being oxides of carbon, nitrogenand sulfur and particulate matter like PM2.5, PM10 etc. Outdoorair pollution is a key reason for premature deaths, and levels of airpollution still outstrip public health standards in many urbanregions, chiefly in constricted street canyons formed by tallbuildings on either side of the road (Pugh et al., 2012). Accordingto the Global Burden of Disease report 2013, air pollution is thefifth major cause of deaths across the world (Institute for HealthMetrics and Evaluation, 2010). Several studies in the past havefocused on quantification of air pollution levels in the urbanenvironments and efforts have been made towards finding solu-tions for the removal of these harmful gases and particulate matter(Gromke and Ruck, 2009; Gromke, 2011; Currie and Brass, 2008).

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Journal of Theoretical Biology

http://dx.doi.org/10.1016/j.jtbi.2014.07.0180022-5193/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: School of Mechanical and Building Sciences, VITUniversity, Vellore, India. Tel.: þ91 416 2202207.

E-mail address: satyajitg@vit.ac.in (Sat. Ghosh).

Journal of Theoretical Biology 361 (2014) 101–110

One method of reducing air pollution is to enhance the depositionof pollutants to surfaces by employing botanical solutions. Com-pared to hard solid surfaces like concrete façades, pollutant uptakeby plants is much higher.

It is widely known that stomata are the main routes for theexchange of gases between plants and the atmosphere. Themodeling of leaf stomata has been studied in great depths in theprevious studies. Parlange and Waggoner (1970) studied diffusionacross the stomata using a resistance modeling approach. Theirmodel considered for the first time the general slit model for astomatal pore, unlike the previous studies that assumed circularpores. Many studies in the past were focused on determination ofCO2 uptake rates by the stomata. Farquhar and Wong (1984), Ballet al. (1987), Leuning (1990), Collatz et al. (1991) and Buckley et al.(2003) worked on determining the physiological factors affectingthe stomatal conductance and gaseous diffusion transport inleaves. Jarvis and McNaughton (1986) gave comprehensive detailsabout the external processes contributing to diffusion taking placeacross the stomatal surface. However, all of these studies involveda resistance modeling approach. Research into multicomponentdiffusion of gases across the stomata has been done by Claibornet al. (1993), who modeled the uptake of SO2, H2O2 and ozone byconifers. They made use of spatially averaged equations in order toresolve the effect of stomatal geometry on diffusion patterns. Theirresearch gave a detailed sensitivity study and provided insightsinto multicomponent stomatal diffusion.

The use of computational tools in the study of diffusion hasdeveloped in recent decades. Use of computational mechanics toanalyze the gaseous uptake rates by the leaves still remains ahighly unexplored area (Defraeye et al., 2013). Vesala et al. (1996)gave a numerical model to solve steady state diffusion equation fora single stoma and the surrounding mesophyllic cells to determinethe CO2 uptake rates. Their study was one of the earliest notableworks on gaseous diffusion inside the leaves using a numericalanalysis approach. Aalto and Juurola (2002) developed a morerealistic three-dimensional CO2 transport model for a silverbirch leaf. Intricate details of the internal stomata structure and

airspaces were included for the first time. Parkhust (1994) gave anextensive review of gaseous diffusion inside the leaves (). Some ofthe more recent work on gaseous diffusion has been done by Rothand Nebelsick (2007), who proposed a cuboidal model of thestomata and depicted the concentration patterns of CO2 and watervapor around the pore, and Defraeye et al., (2013), who simulatedin two dimensions the process of transpiration, with slits forstomata.

This study focuses on the determination of the cleansingefficiency of a façade draped with a tropical creeper (Vernoniaelaeagnifolia) in an urban street canyon by calculating bulk gaseousremoval rates of the draped canyon walls. The problems ofdiscontinuous treatment (resistance nodes are very far apart,usually one node per domain – this makes the model too discrete),lack of physical similarity with respect to geometry and flowfield, and insufficiently resolved boundary conditions (Defraeyeet al., 2013) that are typical of resistance models are overcomeby adopting a computational approach. Individual stomata aremodeled in two dimensions. An in-house full multicomponentdiffusion code applied over it, including the dissociation ofparticipating gases into corresponding aqueous ions in the apo-plastic region. The deposition velocity is calculated and extrapo-lated to the entire façade to give bulk pollution removal rates as afunction of wall area and leaf area index. Sensitivity studies aredone to examine the effect of stomatal aperture, humidityand leaf temperature on the deposition velocity. Also, insightsare presented on the nature of pollution mitigation effected byvegetated walls.

2. On the Versatility of V. elaeagnifolia

The species of plant that has been draped over the façadeis V. elaeagnifolia, a tropical creeper. It is fairly abundant in India,significantly thick, with leaf area index calculated to be 3.835.A SEM analysis indicates stomatal density to be 41 mm�2. Theregion under study is a passageway that gives access to India's VIT

Nomenclature

ae; aje East node coefficient (s�1)an; ajn North node coefficient (s�1)anb; ajnb Sum of neighboring nodes (s�1)ap; ajp Central node coefficient (s�1)as; ajs South node coefficient (s�1)aw; ajw West node coefficient (s�1)A Total pore area (m2)B B-matrix in Fickian diffusion model (s m�2)Cc SO2 concentration in cavity (kg kg�1)Ci SO2 concentration at node (i,j) (kg kg�1)Cw SO2 concentration in apoplastic water (kg kg�1)Ci Concentration of specie i (kg kg�1)CSO2,amb Background SO2 concentration (kg kg�1)CSO2,I SO2 concentration extracted from Phase I (kg kg�1)dcavity Diameter of cavity (mm)dpore Diameter of open pore (mm)Di Fickian diffusivity of specie i (m2 s�1)Đ i Binary diffusivity of specie i in specie j (m2 s�1)hcavity Depth of stomatal cavity (mm)hLBL Depth of Leaf Boundary Layer (mm)hnet Total vertical distance between the LBL top and the

bottom of apoplastic water region (m)hpore Depth of stomatal pore (mm)

Hi Dimensionless Henry's constant for specie i (–)I Turbulence intensity (%)kc Removal rate for closed pores (s�1)knet Net removal rate (s�1)ko Removal rate for open pores (s�1)Ka;CO2 Dissociation constant of CO2 (M)Ka2;SO2 Second Dissociation constant of SO2 (M)Ka1;SO2 First dissociation constant of SO2 (M)N Number of participating species (-)Ni Flux of specie i (m s�1)P Pressure (N m�2)Uin Inlet velocity in façade control volume (m s�1)s Stomatal density (m�2)Si Source strength of specie i (kg s�1)te e-folding time (s)tp Time at node p on the axis of symmetry (s)U Velocity vector (m s�1)V Control volume (m3)Vi;net Net deposition velocity of specie i (m s�1)Vi;p Deposition velocity of specie i at node p (m s�1)yþ Y-plus value (–)Δx Grid spacing in x-direction (m)Δy Grid spacing in y-direction (m)ρ Density of air (kg m�3)m Dynamic viscosity of air (kg m�1 s�1)

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110102

University's hostel blocks (Fig. 1 – left). It constitutes an 8 meterwide L-shaped concrete road of arm-lengths 48 m and 35 m. Thepassageway is bound on both sides by concrete walls, which arecovered with the vegetation drape. An earlier study (Joshi et al.,2013) looked at only the thermal efficiency of this facade and didnot consider the creeper's air cleansing efficiency – this forms thebasis of the current paper.

3. Model details

The complete process of pollutant uptake by plants can bediscretized into two phases: Phase I involves carriage of speciemolecules from vehicular source to the greened wall and yieldsaverage concentration of SO2 molecules at the façade surface (CSO2,I).Typical length scales for this phase are of the order of 1 meter.Modeling and simulation of Phase I is done via the commercialcomputational fluid dynamics (CFD) code ANSYS-CFX (ANSYSAcademic Research, 2010). Phase II simulates diffusion of thesegas molecules across the stomata to the mesophyllic sink, within aspatial scale of few micrometers. CSO2,I is given as an input to thesecond phase. An in-house finite difference code has been devel-oped on MatLab for Phase II. The need for developing a separatecode was felt in order to establish a computationally robustcoupling between the two physical scales, enabling implementationof Henry's law in phase II as elucidated in Section 3.2.

3.1. Phase I

This is modeled in a rectangular control volume (Fig. 1 – right)as a three dimensional turbulent diffusive flow to the surface ofthe vegetation. Based on vehicular emissions data, the source ofpollution is approximated as a ground line source 2 meters awayfrom the wall with an emission rate of 231.1 μg/s. It is assumedthat at any instant there is only one vehicle in the passageway.This is a reasonable assumption given the low frequency ofvehicles in the passageway. Background level of SO2 concentrationis taken as 10 ppb (Chennai Ambient Air Quality Monitoring Data,2012) as referenced in a report of the Tamil Nadu Pollution ControlBoard (2012). Average wind velocity of 1 m/s is prescribed at theinlet, and zero gauge pressure at the outlet. Shear Stress Transport(SST) k-ω turbulence model is used, with assumed atmosphericturbulence intensity (I) of 0.1%. The equations solved are:

∇:U ¼ 0 ð1Þ

∂ðρUÞ∂t

þ U:∇ðρUÞ ¼ �∇pþ μ∇2U ð2Þ

∂ðρCiÞ∂t

þ ∇:ðρUCiÞ ¼ �∇:ðρDi∇CiÞþSi ð3Þ

Eqs. (1), (2) and (3) represent the continuity, momentum andspecie transport equations respectively. The near-wall region isresolved using inflation in the meshing and wall functions of theturbulence model are invoked. A yþ value of 15 is chosen, whichgives the first-layer thickness of the mesh to be approximately13 cm (See Appendix). A sensitivity study is done to ensure gridindependence of the solution. An initial distance of 100 meters isprovided for the onset of concentration and flow uniformity alongthe passageway length (Defraeye et al., 2013). Beyond that, a 10 mlong region of the wall provides the value of SO2 concentration atthe façade, which is supplied to the second phase of the study.

3.2. Phase II

The second phase is specie transport across the stomata. Thethin layer of air in laminar flow over the leaf surface is known asthe leaf boundary layer (LBL) and is usually laminar (Parkhust,1994), below which the stomata are present as pores on the leafsurface. The mesophyllic cells are embedded below the stomatalpore and cavity. It needs to be clarified at the outset, that thepurpose of this study is the calculation of a bulk pollutant removalrate for the sake of an engineering solution. Thus, even thoughstomatal models at much greater levels of detail have beendeveloped in the past, the model used here incorporates onlythe basic structure of stomata i.e. the pore, the substomatal cavity,and the mesophyllic cells (Fig. 2). Since the pores for the specie inquestion are circular in size, a two-dimensional axisymmetricmodel of a stomatal cross-section is created (Claiborn et al.,1993; Defraeye et al., 2013; Vesala et al., 1996).

Transport of species in this entire region is predominantlydiffusive (Leuning, 1990), and occurs through the Maxwell–Stefanmulticomponent diffusion (Claiborn et al., 1993), represented bygoverning Eq. (4).

Ni ¼ �∇ DiiCiþ ∑ja i

DijCj

!ð4Þ

The Maxwell–Stefan model simplifies to the Fickian model whennon-ideal thermodynamic behavior is absent (Taylor and Krishna,1993), which is the case with our system. The same approachis used in the mesophyllic cells with the appropriate diffusivitiesof the corresponding ions. However, in the mesophyllic cells, thecross-species diffusion (i.e. the inter-diffusion of ions) is negligibleand hence not considered. In Eq. (4), Dij represents the Fickianmulticomponent diffusivities obtained by inversion of the matric [B]given by (Taylor and Krishna, 1993)

Bii ¼Ci

Đ inþ ∑

n

1;ka i

Ck

Đ ikð5Þ

Fig. 1. (A) The green façade draped with V. elaeagnifolia at VIT University's passageway and (B) the first phase schematic diagram depicting control volume dimensions andpollution source along the passageway.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110 103

Every Dij represents the binary diffusivity between species i and jand is calculated using the very accurate 6–12–12 Lenard Jones model.It includes the effect of dipole moment, and has been outlinedsuccinctly in literature by Ghosh (1993) and Ghosh and Jonas (1998).

On reaching the bottom of the sub-stomatal cavity, sulfurdioxide is absorbed by the apoplastic water of the leaf, andthereafter dissociates to sulfite in two stages (Grill et al., 2002);these three processes are governed by three parameters: the non-dimensional Henry's constant HSO2, the first dissociation constantKa1,SO2 and the second dissociation constant Ka2,SO2 respectively(See Table 1). The extent of dissociation also depends on the pHof the leaf's apoplastic water region, which is calculated to be 4.65.At this pH, the dominant ion is bisulphite, and therefore itsdecomposition to sulfite is not modeled.

SO2þH2O⇋SO2.H2O

SO2.H2O⇋HSO3�þHþ

HSO�3 ⇋SO2�

3 þHþ ð6a;b; cÞ

Carbon dioxide absorption is also modeled using the non-dimensional Henry's constant HCO2 and the dissociation constantKa,CO2. Although not the case in reality, the carbon dioxide sinkis also assumed to be located in the mesophyll cells as itdoesn’t significantly alter the result, and improves computationalrobustness.

CO2þH2O⇋CO2.H2O

CO2:H2O⇋CO2�3 þ2Hþ ð7a;bÞ

We shall now describe the model dimensions and discretiza-tion. Thickness of the leaf boundary layer is calculated to be0.5 mm (Nobel, 1991). A SEM analysis of the species yielded thediameter of the stomata as 10 μm. This complies with the typicalstomatal ranges for mesophytic plants (Parkhust, 1994). Thedepth of the pore is taken as 10 μm (Metcalfe and Chalk, 1979).The depth of the substomatal cavity is approximated as ten timesthe characteristic stomatal pore dimension (Parlange andWaggoner, 1970), i.e. 100 μm. As the substomatal cavity is often

Fig. 2. (A) Discretized domain of study showing leaf boundary layer dimensions, (B) enlarged section of stomatal geometry showing grid dimensions around stomata and(C) SEM image showing a stomatal pore.

Table 1(Col 1) Boundary values of constituent species (Col 2) Chemical constants for constituent chemical reactions (T¼300 K) (Col 3) Various dimensions of the geometry.

Boundary Values Constants Dimensions

CSO2,amb (ppb) 10 Ka1,SO2 (M) Tanaka (2010) 1.61�10�2 hLBL (mm) 0.5CCO2,amb (ppm) 360 Ka2,SO2 (M) Tanaka (2010) 6.30�10�8 dpore (μm) (open/closed) 10/5CH2O,amb (kg/kg) Variable Ka,CO2 (M) Lide and Frederikse (1995) 4.6�10�7 hpore (μm) 10CSO2,sink (ppb) 0.0 HSO2 (–) Lide and Frederikse (1995) 84.10 dcavity (μm) 100CCO2,sink (ppm) 250 HCO2 (�) Lide and Frederikse, (1995) 1.47 hcavity (μm) 100

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110104

quasi-rectangular or sometimes hemispherical in shape, for thisstudy we approximate it to a rectangle (Defraeye et al., 2013;Parkhust, 1994). This greatly eases the computation and does notinduce any errors because the effective areas of the two shapes areidentical. The width of the cavity is taken to be 100 μm. Theapoplastic water below the cavity is modeled as liquid water(Vesala et al., 1996) of 45 μm width in which mesophyll cells arelocated, modeled as nodal points placed successively at a distanceof 10 μm. These nodes act as chemical sink for the ionic species.Bicarbonate concentration is assumed to be 70% of the ambientCO2 concentration (Roth and Nebelsick, 2007). During nighttime,stomatal pores remain ‘closed’ as photosynthesis does not occurand the plant needs to mitigate rising internal CO2 levels. Foranalyzing closed pores, a stomatal diameter of 5 μm is used. Wewish to emphasize here, that even for C3 plants, the stomata arenever impenetrable – the aperture size is reduced. For example, intheir study on conifers, Claiborn et al (1993) use stomatalapertures of 5 μm and 2.4 μm for day and night time respectively(Claiborn et al., 1993). Likewise, Roth and Nebelsick (2007) usestomatal apertures of 10 μm and 4 μm to replicate daytime andnight-time conditions respectively.

A 2D steady-state finite difference in-house code is developed onMatLab for the simulation of this phase. The region of study isrepresented as a spatially varying, rectangular grid. Second-order finitedifference, centered-difference discretization, selected for its higherorder of accuracy and appropriateness for many diffusion problems,yields the following equation for concentration at any point p:

Cnip ¼ a�1

p : ∑anbCninbþ ∑

ja iðajpCn

jp þ∑ajnbCnjnbÞ

( )ð7Þ

The constants used in the above equation have been defined inTable 2. At LBL, pore and cavity walls, zero gradient condition is

applied along the normal surface. Forward and backward differ-ence discretization is employed at the appropriate boundaries.

Cip:vlower ¼ Ci;top; Cip:vupper ¼ Ci;bot ; Cip:hlef t ¼ Ci;r; Cip:hright ¼ Ci;l

ð8a;b; c;dÞHere, Eq. (8a, b, c and d) depict zero gradient conditions at the

vertical (lower and upper) and horizontal (left and right) bound-aries respectively. At the interface of the cavity and mesophyllicregion, Henry's Law of partial pressure is obeyed.

Ci;w ¼ ð1=HiÞCi;c ð9ÞFor high accuracy of calculations, a fine resolution of the

domain is crucial. The computation grid is resolved to appropriatelevels, and a finer mesh is developed near the pore. The LBL partcloser to the pore (‘lbl2’ henceforth) is finer than the one furtheraway (Fig. 2A). After sensitivity analyses of the resolved grid forgrid independence of the solution, inter-nodal distances in themesh are of the order of 5 μm in the LBL, 2.5 μm in the stomatalpore, 5 μm in the stomatal cavity and 2.5 μm mesophyllic region.

4. Simulation results

4.1. Pollutant distribution in the Canyon

In the first phase, the simulation was run until convergencewas achieved. Convergence criteria are enforced up to a toleranceof 10�5 for all variables. Two categories of simulations are run:(i) Steady state simulation to determine average concentration ofSO2 at the façade, (ii) Transient simulations to study the timedependence of pollutant transfer. The latter is further split intosimulation with (a) The pollutant source turned off with vegetatedfaçade (background pollutant removal), (b) the pollutant sourceturned on with vegetated façade, and (c) the pollutant sourceturned on with an undraped façade. A typical Gaussian concentra-tion distribution of SO2 is observed in the passageway's cross-section (Fig. 3B and C). As expected, the concentration at thefaçade gradually decreases with height. The average concentrationvalue at the façade CSO2,I is extracted from a 10 meter-long section100 m from the inlet as specified before, which comes out to be1.007�10�8, or 10.07 ppb.

Two important qualitative observations are made in the firstphase. Firstly, one of the most significant findings of this study isthat the green façade draped with the chosen species is anefficient cleanser of residual background pollution. When a

Table 2Values of the constants present in the discretized equation for multicomponentspecies transport (Eq. (7)).

Values for Constants of the Discretized Eq. (7)

anb aeþawþanþas ajnb ajeþajwþajnþajsae Dii=ðΔxÞ2 aje Dij=ðΔxÞ2aw Dii=ðΔxÞ2 ajw Dij=ðΔxÞ2an Dii=ðΔyÞ2 ajn Dij=ðΔyÞ2as Dii=ðΔyÞ2 ajs Dij=ðΔyÞ2ap 2Dii=ðΔxÞ2þ2Dii=ðΔyÞ2 ajp �2Dij=ðΔxÞ2�2Dij=ðΔyÞ2

Fig. 3. (A) Variation of average SO2 concentration in passageway region with and without the biological sink (B and C) Contours of SO2 concentration on a passageway cross-section at t¼13 h (B) without and (C) with the façade.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110 105

polluting line source is released in the passageway, mechanicaldilution caused by winds and atmospheric turbulence far over-whelms any reduction in the pollutant concentration by the first-order sink mediated by open stomata – transient simulations showa rise in SO2 levels (Fig. 3A). This has been shown to be true forlarge forests (Picardo and Ghosh, 2011). However, even with theline source turned off, there hovers a pall of residual pollution – itis this residual pollution that is removed by the living façade overa time period of several hours (Fig. 4A and B). Also, even thoughthe façade removes background pollution, it still plays an impor-tant role in mitigation of pollutant efflux into affected regions. Therate of increase of SO2 concentration is much slower in case of avegetated façade than that of a naked canyon wall (Fig. 3A). Also,concentration contours clearly indicate the extent to which highSO2 concentration has pervaded the control volume in the case ofthe naked canyon. This important conclusion could be establishedonly after a detailed CFD analysis.

Secondly, the significance of the reading's source location has abearing on the correctness of the solution. As in most CFDsimulations, even with the finest of meshes, edge effects showup at the boundaries. A state of equilibrium can be approximatedonly when one chooses representative data points sufficiently faraway from the boundary. A distance of 100 m ensures that this isindeed achieved and the results are not biased by the boundaryconditions (Fig. 4C).

4.2. Pollutant diffusion in stomata

The second phase is simulated to a specie concentrationresidual of the order of 10�5. A sharp concentration gradient isobserved across the stomatal pore (Fig. 5A–C). Typical cup-shapedconcentration contours (Roth and Nebelsick, 2007) are observed inthe vicinity of the stomata pore (Fig. 6). In case of closed stomata,the gradient is observed to be much steeper as expected becauseof a reduction in the pore area (Fig. 6D–F). Spatial variation of thebisulphite and bicarbonate ions is shown in Fig. 7.

Just as streamlines of flow are always perpendicular to equi-potential lines, the pathways of SO2 molecules lie perpendicular tothe contour lines of concentration. Clearly, the simplest of thesepaths is the line that passes through the center of the model i.e.the axis of symmetry. Thus, all calculations for deposition velocityand total time are performed on the axis of symmetry. In thefollowing calculations, the x-coordinate is fixed on the axis ofsymmetry of the model and is therefore not explicitly stated. FromFick's first law of diffusion, the expression for deposition velocityVi,p of any specie i between any two consecutive nodes p and pþ1

is derived:

Vi;p ¼ � ∑n�1

k ¼ 1Dik;p

Ci;pþ1�Ci;p

Ci;p Δypð10Þ

Dik;p stands for the diffusivity of specie k in specie i at nodep. Δyp is the distance between nodes p and pþ1. Thus a quasi-continuous velocity distribution is determined over the depth ofthe control volume along the axis of symmetry. The time taken fora molecule to travel between the nodes p and pþ1 is:

tp ¼ΔypVp

ð11Þ

This time required for a molecule to travel from node p to nodepþ1 is calculated for all nodes on the axis of symmetry and thetotal deposition time required for a molecule from the LBL to themesophyllic cell sink is determined. In the apoplastic water region,the ionic specie corresponding to gas i is used in calculations.The time required to reach the sink by the ion is found by takinga weighted average over the four possible mesophyll cells (i.e. thesink nearest to the pore is given the highest weightage, and so on).With total time tp, the net deposition velocity of specie i iscalculated according to Eq. (12).

Vi;net ¼hnet∑tp

ð12Þ

Here, hnet is the total vertical distance between the LBLthickness and the bottom of mesophyllic cells calculated fromthe model, and equals 0.65 mm. The value of the net depositionvelocity is calculated to be about 1.5 mm s�1 for open pores and0.8 mm s�1 for closed pores, ranges that match existing results(Kumar and Kumari, 2012). From these values, it is clear that areduction in stomatal aperture reduces the deposition velocity bymore than 50%.

4.2.1. Sensitivity to ambient water vapor concentrationThe model is run for two different cases of ambient concentra-

tion of water vapor (relative humidity of 75% and 40%), with otherparameters kept constant. The dipole moment of water vaporplays a major role in enhancing the diffusivity of the polar SO2 andH2O molecules – the stronger the gradient of water vapor, thebetter is the transfer of SO2. The drop in the deposition velocitiesbetween dry and humid conditions is 3.96% with open pores and11.99% with closed pores (See Section 3.2 for details on closedpores). This shows that uptake of SO2 (or any polar gas) is sensitiveto humidity at night time. One possible reason for higher sensi-tivity of closed stomata towards humidity could be the smallaperture.

Fig. 4. (A) Background SO2 concentration (kg/kg) distribution at t¼13 hours and (B) at different time intervals (C) SO2 concentration variation with height at differentdistances from inlet – this shows stabilization of the SO2 concentration profile at sufficient distance from the inlet.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110106

4.2.2. Sensitivity to stomatal apertureStomata of plants are usually closed at night to mitigate effects

of excess concentrations of CO2 inside the leaf. This obviouslyreduces the flux of gaseous species into the plant. As explained inSection 3.2, many researchers in the past have assumed thediameters of closed pores to be half of open pore diameters.Therefore, we modified our geometry for closed pores by reducingthe diameter of the stomatal pore to 5 μm. Simulations were runfor both humid and dry conditions, and the correspondingdeposition velocities were calculated and compared with thoseof open pores.

Deposition velocity of SO2 is reduced by 53.1% and 48.82% inhumid and arid weather respectively. This proves that the sinkstrength of vegetated façades for gases drops to half its daytimevalue at night.

4.2.3. Sensitivity to leaf temperatureResearch by Pallas et al. (1967) has shown that temperature

fluctuations of the leaf (including effects of transpiration) do notexceed 3.41C above and 1 1C below the ambient temperature. Wetherefore apply this observation here, and run the Phase II code for

Fig. 5. Graphs showing concentration gradient of (A) SO2, (B) CO2 and (C) H2O along the axis of symmetry (PT shows the top opening of the pore). Note the sharper gradientof species for closed pores.

Fig. 6. Concentration distribution of (A and D) SO2 in ppb, (B and E) CO2 in kg kg�1 and (C, F) H2O in kg kg�1 in the vicinity of the pore for the cases of open and closed poresrespectively. The depth covered in these contours is from the top of lbl2 (see page 6) to bottom of the stomatal cavity. Typical cup-shaped contours are observed in thevicinity of the pore.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110 107

every 11 interval between 26 1C and 30 1C with alterations in gas-state and ionic diffusivities, Henry's constants, and ionic dissocia-tion constants for change in temperature. The simulation resultsshow a maximum change of 3.2% in the deposition velocity due tochange in leaf temperature over the entire range of possible leaftemperatures (Fig. 8A and B).

To account for ambient temperature changes caused due tochanges in season, we also determine the change in depositionvelocity when the temperature is increased to 40 1C. Even for sucha sharp increase in temperature, the deposition is increased byonly 7.6%. Therefore, it is safe to conclude that the bulk removalrate of a plant is independent of the leaf temperature and does notalter the results significantly (Claiborn et al., 1993).

4.3. Cleansing by the plant cover: the first order removal rates

The deposition velocity is a micro-scale characteristic of asingle stomata. Our concern, however, is with the large-scale

implications of employing a vegetated wall to cleanse pollution –

to analyze this, it is necessary to extrapolate the depositionvelocity over the entire wall in the form of a parameter calledthe first order removal rate. It quantifies the fractional reduction inpollution concentration effected by the vegetated wall per unittime, and has units of s-1. The removal rate is a function of thestomatal density of the drape species (s), the volume beingcleansed (V), the area of the drape (A), and the deposition velocity(Vi,net) calculated for gaseous species i. Once the value of the netdeposition velocity is known, the removal rate is calculated as:

k¼ Vi;netAsV

ð13Þ

Here, V is the integrated volume of the region being cleansedby the vegetated façade. In our case it is the control volume, i.e.600 m3. It is important to state here that, for modeling purposes,the entire façade is assumed to a leaf surface with uniformstomatal density (LAI¼1). The total pore area is the area of onestomatal pore opening times the total number of stomata on thefaçade. With stomatal density on V. elaeagnifolia equal to 36 mm�2

and wall area of 300 m2, this is calculated to be 0.848 m2 for openpores and 0.212 m2 for closed pores. Removal rates for open (ko)and closed (kc) stomatal pores of V. elaeagnifolia towards atmo-spheric SO2 for the humid weather found in Vellore are calculatedto be 2.17�10�6 s�1 and 2.54�10�7 s�1 respectively. Thus thecleansing efficiency of open pores is 2.17�10�4%, and that ofclosed pores is 2.54�10�5%. In order to calculate the cumulativeremoval rate over the period of a day, a net removal rate knet iscalculated by assuming the stomata to be open for 10 hours of theday (Talbott and Zeigler, 1998). Hence,

knet ¼ ð10koþ14kcÞ=24 ð14ÞA more practically useful interpretation is given by the e-

folding time (the time taken for the specie concentration tobecome 1/e times the initial concentration) (Table 3). Thus,

te ¼ k�1net ð15Þ

The e-folding times for dry and humid weather are calculatedto be 10.43 days and 11.02 days respectively. This observationagain stresses on the nature of cleansing done by green façades –

such slow but steady removal of pollution suggests that they areeffective at mitigating background pollution levels.

4.3.1. Density of green façades: effect on pollutant removalAll calculations thus far have been performed considering an

LAI of 1. More often than not, the vegetation commonly encoun-tered in practical situations has LAI greater than 1; it is important

Fig. 7. Concentration distribution of (A) HSO3� and (B) HCO3

� in the apoplasticwater region. The intermittent ‘wells’ on the contour surface represent themesophyll sink.

Fig. 8. (A) Deposition velocity and (B) Percentage change versus deviation of leaf temperature from ambient temperature. (C) Change in removal rate with LAI for dry andhumid conditions.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110108

to represent the removal rate as a function of the LAI. Pastmodeling studies have assumed the removal efficiency of canopies(particle removal) to vary linearly with the LAI (Huang et al., 2013).The dependence has been modeled with a factor of 1. However, theoverlap of leaves in a dense façade means that the actual increasein the removal rate would be lesser than the apparent removal rateobtained from a linear relationship. Also, this effect would becompounded with greater increase in LAI.

On these lines, studies have used a quadratic relationshipbetween LAI and different scaled parameters. Of particular sig-nificance to us is the relationship between photosynthesis and LAI– De Pury and Farquhar (1997) have scaled daily canopy photo-synthesis using an inverse exponential relationship with the LAI.Thus, based on the same reasoning, we propose the followingrelationship between the uptake rate and façade LAI:

kLAI ¼ k1alnð1þLAIÞ ð16ÞThe value of a can be calculated by substituting kLAI¼k1 at

LAI¼1. i.e., a¼1/ln2. The variation of removal rates with LAI hasbeen plotted for different cases in Fig. 8C. Based on the formula-tion shown in Eq. (16), the removal rate for the drape under study(LAI¼3.8) is calculated to be 2.5�10�6 s�1, which corresponds toan e-folding time of 4 days and 14 h.

5. Conclusion

This study identifies V. elaeagnifolia as a draping material for longextended façades. V. elaeagnifolia (the Parda Bel) has unique proper-ties: its long, drooping trellises interlace profusely to form a naturalgreen mesh to hold oval shaped leaves, lending a lush coveragewithin a matter of months as shown by the high value of its leaf areaindex. This natural interlacing also lends it a structural stability whenplanted atop a wall. Moreover, they are evergreen – the greencoverage varies only a little during the harsher summer monthsand drops to approximately 90% of that during other months.

In this analysis, we quantify the cleansing efficiency of anextended wall draped with V. elaeagnifolia, measuring 100 m inlength and 3 m in height. It is found that the façade has a significantremoval rate for SO2 gas – if this quantity of pollutant was notflushed out from the passageway, it would have had a cumulativeeffect on the campus dwellers. A detailed multicomponent CFDanalysis revealed interesting caveats of the accompanying masstransfer processes. It is determined that the pollutant source strengthdoes not directly cause any significant alteration its concentration atthe façade; rather, the latter is a strong function of the backgroundpollutant levels, which are indirectly linked to strength of pollutantsource. A quasi-continuous approach to calculation of depositionvelocities presents a significant advantage over the resistance mod-eling approach, converting discrete modeling into a continuous one.Open pores are shown to have deposition velocities of 1.53 mm s�1

and 1.60 mm s�1 respectively for humid and dry weather. Similarly,closed pores have deposition velocities of 0.72 mm s�1 and0.82 mm s�1 respectively. These are a strong function of the stomatalaperture, and are almost halved during nighttime when the stomata

are closed. The effect of humidity on the deposition velocity can beseen at night with a 12% increase from humid to dry weather. This isexpected, as the transfer of SO2 is enhanced by a stronger water-vapor gradient in dry weather. The temperature of the leaf on theother hand has a negligible effect on the deposition velocity.

The net removal rate of the drape of V. elaeagnifolia is computedto be 1.01�10�6 s�1 and 1.11�10�6 s�1 in humid and dryweather respectively, assuming a LAI of 1. This corresponds toe-folding times of approximately 10 to 11 days – an observationthat proves that vegetated walls are effective at removal of back-ground pollution. A non-linear, logarithmic relationship is pro-posed between the removal rate and the vegetated façade's LAI.This accounts for the increased leaf density as well as thehindrance to gaseous uptake due to overlapping of leaves. Sincevegetated walls normally have an LAI higher than 1, this formula-tion is important to accurately predict their removal rate. Forexample, changing the LAI from 1 to 3.8 causes reduces thee-folding time from 11 days to 5 days for V. elaeagnifolia.

The study does have its limitations – detailed chemical inter-linkage is absent in the apoplastic region. Presence of trace speciesalso alters the path of incoming ions. The effects of these chemicaldynamics would make for interesting observations and possiblypresent opportunities to artificially enhance gaseous uptake byplants.

Finally, it must be stated without any ambiguity, that greenfaçades are efficient at removal of residual background pollutiononly. Nevertheless, residual background pollution is a big issue – aline source of pollution may leave its trail even when it is turnedoff – the resulting pall hovers and moves to a new wind directioneven when the source is switched off. Vegetated façades providea medium of controlling the rate at which pollution pervadesan environment, an urgent requirement in many developing anddeveloped countries.

Acknowledgments

The authors would like to acknowledge Prof. Jacob Varghese(School of Mechanical and Building Sciences, VIT University,Vellore, India) for the SEM analysis of the species of study. Theauthors also acknowledge Mr. Atin Jain (School of Mechanical andBuilding Sciences, VIT University, Vellore, India) for his contribu-tion to the work.

Appendix

Calculation of the first layer thickness:

The first layer thickness for an inflation layer is calculated fromthe following empirical relation:

Δy¼ffiffiffiffiffiffi74

pLyþ ðReÞ� 13

14 ðA:1Þ

Table 3A summary of the calculated values of deposition velocity, removal rate and e-folding time for SO2 absorption by the vegetated green façade.

Parameter Humid weather (RH¼75%) Dry weather (RH¼40%)

Open Closed Open Closed

Deposition velocity (mm s�1) 1.533 0.719 1.596 0.817Removal rate (s�1) 2.17�10�6 2.54�10�7 2.26�10�6 2.89�10�7

Net removal rate (s�1) 1.05�10�6 1.11�10�6

e-folding time (days) 11.02 10.43

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110 109

Where, L is the length of the surface of inflation, Re is the Reynoldsnumber, yþ is assumed based on the turbulence model used (411and o30 for SST k-ω turbulence model used here with wallfunctions invoked).

References

ANSYSs Academic Research, Release 11. Canonsburg, PA, USA 2010.Aalto, T., Juurola, E., 2002. A three-dimensional model of CO2 transport in airspaces

and mesophyll cells of a silver birch leaf. Plant, Cell Environ. 25, 1399–1409.Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatal conductance

and its contribution to the control of photosynthesis under different environ-mental conditions. In: Biggins, I. (Ed.), Progress in photosynthesis research.MartinusNijhoff Publishers, Dordrecht, pp. 221–224.

Buckley, T.N., Mott, K.A., Farquhar, G.D., 2003. A hydromechanical and biochemicalmodel of stomatal conductance. Plant, Cell Environ. 26, 1767–1785.

Carbon Pollution Standards: US Environment Protection Agency ⟨http://www2.epa.gov/carbon-pollution-standards⟩.

Chennai Ambient Air Quality Monitoring Data 2012. Tamil Nadu Pollution ControlBoard (⟨www.tnpcb.gov.in/pdf/ambient_airquality_rpt-2012.pdf⟩.

Claiborn, C.S., Carbonell, R.G., Aneja, V.P., 1993. Transport and fate of reactive tracegases in red spruce needles. 2. Interpretations of flux experiments using gastransport theory. Environ. Sci. Technol. 27, 2593–2605.

Collatz, G.J., Ball, J.T., Grivet, C., Berry, J.A., 1991. Physiological and environmentalregulation of stomatal conductance, photosynthesis, and transpiration: a modelthat includes a laminar boundary layer. Agric. For. Meteorol. 54, 107–136.

Currie, B.A., Brass, B., 2008. Estimates of air pollution mitigation withgreen plantsand green roofs using the UFORE model. Urban Ecosyst. 11, 409–422. http://dx.doi.org/10.1007/s11252-008-0054-y.

De Pury, D.G.G., Farquhar, G.D., 1997. Simple scaling of photosynthesis from leavesto canopies without the errors of big-leaf models. Plant, Cell Environ. 20,537–557.

Defraeye, T., Verboven, P., Derome, D., Carmeliet, J., Nicolai, B., 2013. Stomataltranspiration and droplet evaporation on leaf surfaces by a microscale model-ling approach. Int. J. Heat Mass Transf. 65, 180–191.

Defraeye, T., Verboven, P., Ho, Q.T., Nicolai, B., 2013. Convective heat and massexchange predictions at leaf surfaces: applications, methods and prespectives.Comput. Electron. Agric. 96, 180–201.

Farquhar, G.D., Wong, S.C., 1984. An empirical model of stomatal conductance. Aust.J. Plant Physiol. 11, 191–210.

Ghosh, S., 1993. On the diffusivity of trace gases under stratospheric conditions. J.Atmos. Chem. 17, 391–397.

Ghosh, S., Jonas, P.R., 1998. On the application of the classic Kessler and Berryschemes in Large Eddy simulation models with a particular emphasis on cloudautoconversion, the onset time of precipitation and droplet evaporation. Ann.Geophys. 16, 628–637.

Grill, D., Tausz, Michael, M., Kok, L.J., 2002. Significance of Glutathione to PlantAdaptation to the Environment. Springer, Dordrecht, The Netherlands p. 188(Chapter 8).

Gromke, C.B., 2011. A vegetation modeling concept for building and environmentalaerodynamics wind tunnel tests and its application in pollutant dispersionstudies. Environ. Pollut. 159 (8–9), 2094–2099.

Gromke, C.B., Ruck, B., 2009. On the impact of trees on dispersion processes oftraffic emissions in street Canyons. Boundary-Layer Meteorol. 131, 19–34.

Huang, C.-W., Lin, M.-Y., Khlystov, A., Katul, G., 2013. The effects of leaf area densityvariation on the particle collection efficiency in the size range of ultrafineparticles (UFP). Environ. Sci. Technol. 47, 11607–11615.

Institute for Health Metrics and Evaluation 2010. Human Development Network,The World Bank. The Global Burden of Disease: Generating Evidence, GuidingPolicy – East Asia and Pacific Regional Edition. Seattle, WA: IHME.

Jarvis, P.G., McNaughton, K.G., 1986. Stomatal control of transpiration: scaling upfrom leaf to region. Adv. Ecol. Res. 15, 1–49.

Joshi, S.V., Jain, A., Bhatt, P.M., Ghosh, S., Autade, A. 2013. Heat and mass transfercalculations around a green façade in a residential university campus in India.World Green Infrastructure Congress 2013, 9–13 September 2013, Nantes,France.

Kumar, R., Kumari, K.M., 2012. Experimental and parameterization method forevaluation of dry deposition of S compounds to natural surfaces. Atmos. Clim.Sci. 2, 492–500.

Leuning, R., 1990. Modeling stomatal behaviour and photosynthesis of Eucalyptusgrandis. Aust. J. Plant Physiol. 17, 159–175.

Lide, D.R., Frederikse, H.P.R., 1995. CRC Handbook of Chemistry and Physics, 76thEdition CRC Press Inc., Boca Raton, FL.

Metcalfe, C.R., Chalk, L., 1979. (Systematic Anatomy of the Leaf and Stem). 2nd ed.Anatomy of the Dicotyledons, vol. I. Clarendon Press, Oxford.

Nobel, P.S., 1991. Physiochemical and Environmental Plant Physiology. 325. Aca-demic Press, San Diego.

Pallas Jr., J.E., Michel, B.E., Harris, D.G., 1967. Photosynthesis, transpiration, leaftemperature, and stomatal activity of cotton plants under varying waterpotentials. Plant Physiol. 42, 76–88.

Parkhust, D.F., 1994. Diffusion of CO2 and other gases inside leaves Tansley ReviewNo. 65. New Phytol. 126, 449–479.

Parlange, J.Y., Waggoner, P.E., 1970. Stomatal Dimensions and Resistance toDiffusion. Plant Physiol. 46, 337–342.

Picardo, J.R., Ghosh, S., 2011. Removal mechanisms in a tropical boundary layer:quantification of air pollutant removal rates around a heavily afforested powerplant. In: Moldoveanu, Anca (Ed.), Air Pollution – New Developments. InTech,Croatia, ISBN: 978-953-307-527-3.

Pugh, T.A.M., MacKenzie, A.M., J Whyatt, J.D., Hewitt, C.N., 2012. Effectiveness ofgreen infrastructure in improvement of air quality in urban street canyons.Environ. Sci. Technol. 46, 7692–7699. http://dx.doi.org/10.1021/es300826w.

Roth, A., Nebelsick, 2007. Computer-based studies of diffusion through stomata ofdifferent architecture. Ann. Bot. 100, 23–32.

Sinha, R.K., 1993. Automobile pollution in India and its human impact. TheEnvir-onmentalist 13 (2), 111–115.

Talbott, L.D., Zeigler, E., 1998. Central roles for potassium and sucrose in guard-cellosmoregulation. Plant Physiol. 111, 1051–1057.

Tanaka, Y., 2010. Water dissociation reaction generated in an ion exchangemembrane. J. Membr. Sci 350, 347–360.

Taylor, R., Krishna, R., 1993. Multicomponent Mass Transfer. John Wiley & Sons, Inc.,Canada (Part I, Chapter 3).

Vesala, T., Ahonen, T., Hari, P., Krissinel, E., Shokirev, N., 1996. Analysis of stomatalCO2 uptake by a three-dimensional cylindrically symmetric model. New Phytol.132, 235–245.

S.V. Joshi, Sat. Ghosh / Journal of Theoretical Biology 361 (2014) 101–110110