Measurements and Modeling of Deposited Particle Transport by Foot

Feb 28, 2014 - foot traffic are needed. Laboratory experiments measured uptake and downlay mass transfer efficiencies of particles between shoes and f...
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Measurements and Modeling of Deposited Particle Transport by Foot Traffic Indoors Mark R. Sippola,*,† Richard G. Sextro, and Tracy L. Thatcher‡ Indoor Environment Department, Environmental Energy Technologies Division, Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States S Supporting Information *

ABSTRACT: Deposited particles are transported into and within buildings by adhering to and releasing from people’s shoes. To better understand transport of deposited particulate contaminants and exposures to these materials, experimental data on tracking by foot traffic are needed. Laboratory experiments measured uptake and downlay mass transfer efficiencies of particles between shoes and floors in a step-simulation chamber. Equilibrium uptake transfer fractions, the net mass fraction transferred from floors to shoes after several steps, were also measured. Single-step uptake and downlay transfer efficiencies ranged from 0.02 to 0.22 and equilibrium uptake transfer fractions were 0.10−0.40. Particle size, particle loading, shoe type, floor type, step pressure, and step sequence were all investigated. Experiments demonstrated that single-step downlay transfer efficiencies decrease with each successive step onto clean floors. A simple empirical model is proposed to estimate these transfers as a function of step number. Simulations using the transfer efficiency values measured here illustrate the spread of deposited particles by people walking in a hypothetical hallway. These simulations show that in locations where a few people walk over the same area each minute, tracking can spread deposited material over length scales comparable to building dimensions in just a few hours.

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INTRODUCTION After settling onto floors, particulate matter moves throughout interior spaces by tracking, the two-way transfer of particles between the floor and footwear of walking people. Particles on floors can adhere to shoes and then be transferred back to the floor during subsequent steps. Understanding this transport process is especially important if the settled material is toxic. Occupants may unknowingly spread deposited particles from a contaminated area by tracking and resuspension, influencing exposures and leading to decontamination needs outside the initial contamination area.1,2 Tracking is an important route by which particle-associated contaminants, like lead and pesticides, enter indoors.3,4 Tracking combined with resuspension can be a significant source of inhalation exposure to settled particles.5 Tracking is a dynamic process with continual loading and unloading of particles between the floor and footwear; this process has not previously been well-characterized. Experimental data on tracking are necessary to better understand the transport and fate of particulate-phase contaminants within buildings and to improve predictions of particle dispersion by human activity. Understanding tracking could inform decisions about sampling and decontamination after a toxic material release by addressing the following questions: What fraction of settled material is transported to nearby areas by people walking over a contaminated floor? How far do particles spread by tracking? What controls these processes? © 2014 American Chemical Society

A literature review revealed few published reports on tracking by footsteps. Downlay transfer of material from shoes to carpet and tile were measured during successive steps by a volunteer in a laboratory.5,6 Downlay transfer efficiencies decreased with each successive step in both studies. Thornburg and Rosati also measured single-step uptake transfer efficiencies from carpet to shoes in a laboratory and conducted field tests to determine tracking rates in carpeted residences.5 Investigations of particle contact transfer between surfaces or to hands from a variety of surfaces provide potential insights into tracking by footwear.7−11 There is wide variability and some lack of consistency among these measured hand transfer rates, suggesting that these processes are poorly understood and apparently influenced by multiple parameters. More details on this literature are in the Supporting Information (SI). This study had three main objectives: (1) to determine twoway particle transfer efficiencies between shoes and floors; (2) to identify parameters that influence these transfer efficiencies; and (3) to evaluate characteristic times and distances for particle dispersion by tracking. Measurements and modeling presented here address these issues. Transfer of fluorescein Received: Revised: Accepted: Published: 3800

November 4, 2013 February 23, 2014 February 28, 2014 February 28, 2014 dx.doi.org/10.1021/es404886x | Environ. Sci. Technol. 2014, 48, 3800−3807

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particles between shoes and floors was investigated in a stepsimulation chamber. Parameters studied were particle size, particle loading, shoe type, floor type, step pressure, and step sequence. Model calculations based on the experimental data illustrate particle dispersion by people walking in a hypothetical hallway.

APS measures particle number counts in 51 size bins in the range 0.5−19.8 μm. The size distribution of deposited particles was assumed equal to the measured airborne size distribution: the differences should be small for these supermicrometer particles that settled for several hours, especially for the broad 1−4 μm and 5−10 μm size bins that were used here. Step Simulation. After floor samples were loaded, they were removed one at a time from the deposition chamber and placed in the step-simulation chamber shown in Figure S1 in the SI. This was a 38 × 61 × 53 cm clear acrylic box with an internal aluminum structure which supported two pneumatic pistons (6.3 cm diameter, 10.2 cm stroke length; Bimba, Model NRM-504-DXP) connected to compressed air. Shoes were new, and shoe soles were precleaned by soaking in water and air-drying for 48 h. Shoes were attached at the heel and toe of the inner sole to mounts at the bases of the piston rods, which extended and contracted to mimic the heel- and toe-strikes of footsteps. Pressure regulators on the compressed air managed piston forces, and computer-controlled valves controlled the piston stroke timing to give a heel-first strike and a rollingforward, toe-last liftoff. Exterior switches on the pistons controlled their starting position and stroke length. Tian et al. gives additional description of the stepping device.12 The athletic shoe sole was soft rubber and heavily treaded with an approximate 3 mm tread depth. The outer heel and sole of the dress shoe were very lightly textured hard rubber with a texture depth well below 1 mm. Both were men’s US size 9 shoes with a 160 cm2 apparent floor contact area; because of the treading, the actual area of contact was less than this. Both shoe types had two distinct apparent floor contact areas, 80 cm2 at the heel and 80 cm2 at the ball of the foot and a region between with no shoe−floor contact owing to its arched shape. Each piston applied the full step force; extensions and contractions were timed to approximate the heel-to-toe weight transfer of a real footstep. Three contact pressures were evaluated, 0.45, 0.90, and 1.36 kg/cm2, which correspond to steps by a person weighing 80, 160, and 240 pounds, respectively. During a real stride, the heel strikes first and the heel momentarily bears the entire weight of the person, and prior to foot liftoff at the end of a step, the entire weight is on the toe area. It is these pressures at heel strike and toe liftoff that were used to translate step pressures to person weights. The contact time for each heel and toe strike was approximately 0.5 s. Relative humidity was not controlled during step simulation, but was measured to be 35−44% for all experiments. Static charge was neither measured nor controlled. Two different step-simulation sequences were performed for each of the 24 experiments. Step sequence A was a single step by a clean shoe onto a particle-laden floor sample followed by a single step of the newly particle-laden shoe onto a clean floor sample of the same material. This sequence allowed determination of single-step uptake and single-step downlay transfer efficiencies. Step sequence B was 20 steps by a clean shoe onto the same location of a single particle-laden floor sample followed by a single step of the particle-laden shoe on a clean floor sample of the same material. Sequence B enabled measurement of the equilibrium uptake transfer fraction and the single-step downlay transfer efficiency once equilibrium had been achieved. Scoping experiments showed that the net mass on a shoe did not change significantly after about six steps in the same location; the 20 steps in sequence B were sufficient to achieve equilibrium. After loading particles onto eight floor

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EXPERIMENTAL METHODS Overview of Experimental Approach. Experiments measured fluorescein particle mass on shoes and floor samples by rinsing surfaces with a known liquid volume and measuring the rinse liquid fluorescence in a calibrated fluorometer. These masses were used to calculate mass transfer efficiencies and equilibrium mass transfer fractions of particles between floors and shoes in a step-simulation chamber. Each experiment had three phases: (1) particle deposition on floor samples in a deposition chamber; (2) contact of shoes with floor samples in a step-simulation chamber; and (3) particle mass quantification on the shoes and floor samples. The step-simulation included step sequences to evaluate floor-to-shoe uptake, shoe-to-floor downlay, and equilibrium uptake transfer fractions. A matrix of 24 experiments was completed with two particle size ranges (1−4 μm and 5−10 μm), two shoe types (lightly textured dress shoe, and heavily treaded athletic shoe), two floor types (tile and carpet), and three step pressures (0.45, 0.90, and 1.36 kg/cm2). For each set of conditions, four tests measured single-step uptake and downlay transfer efficiencies, and four tests determined equilibrium uptake transfer fractions and the subsequent single-step downlay transfer efficiency. Additional investigations evaluated how single-step transfer efficiencies changed during a series of steps. Particle Loading of Floor Samples. Particle loading of tile and carpet floor samples took place in a 76 × 76 × 91 cm (L × W × H) aluminum deposition chamber. Tile samples were new commercial-grade vinyl tile with a slightly polished surface. Carpet samples were new, with woven loop-pile construction of synthetic olefin yarn, 3 mm yarn diameter, 8 mm average loop height, and medium packing density. For a given experiment, eight 15 × 30 cm tile or carpet samples were precleaned by soaking in water and air drying for 48 h and then placed on the deposition chamber floor. Test particles were solid fluorescein powder (Aldrich Chemical, St. Louis, MO). Air was forced through a jar containing dry fluorescein to generate an aerosol with most of its mass in the size range 1− 10 μm (GM = 3.1, GSD = 1.8). The aerosol was injected into the sealed chamber through a dispersion bottle near the chamber ceiling for 5−20 min and then fluorescein particles settled onto floor samples for about 24 h as two small fans with horizontal flows mixed the air. When loading floor samples with 1−4 μm particles, the aerosol passed through two cyclones (built in-house) immediately before injection into the chamber. For 5−10 μm particles, a virtual impactor (built in-house) processed the aerosol and only the large particle fraction was directed into the chamber. Initial particle loadings on floors ranged between 0.8 and 2.0 μg cm−2 for 1−4 μm particles and 1.5−5.5 μg cm−2 for 5−10 μm particles. The average coefficient of variation for eight simultaneously loaded floor samples was 9.1% and the range was 2.9−23%. On the basis of these particle sizes and loadings, the particles always formed less than a monolayer on the floor samples. An Aerodynamic Particle Sizer (APS; TSI Inc., Model 3321) continuously sampled the aerosolized fluorescein through a port in the chamber floor during deposition. The 3801

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We found minimal net particle transfer between shoes and floors after six steps in the same location, similar to the 4−5 contacts reported to achieve equilibrium in previous hand press trials.10 Thus, the 20 shoe-loading steps during sequence B were sufficient to achieve the equilibrium uptake transfer fraction, Fu,eq, defined by the following:

samples in the deposition chamber, four were subjected to step sequence A and four to sequence B. In addition to the matrix of 24 main experiments, tests were conducted where shoes were loaded with particles by a single step on a particle-laden floor sample and then the particle-laden shoe made consecutive steps upon 12 identical clean floor samples. Each clean floor sample was stepped upon once, and the mass laid down by each step was quantified to determine how the single-step downlay transfer efficiency changed during 12 successive steps. This was similar to sequence A, but included multiple steps onto clean floor samples after the shoe was loaded instead of just one. Other experiments used a variation on step sequence B where a clean shoe made multiple steps in the same location on a single particle-laden floor sample (3−15 steps instead of the 20 in sequence B) followed by a single step on a clean floor sample. These experiments evaluated the influence that the number of prior steps on a particle-laden surface had on subsequent downlay transfer efficiencies. After step simulations were completed, particle masses on shoes and floor samples were quantified by fluorescent analysis using equipment and well-established wet chemistry methods that have been previously described.13 Blank experiments with identical procedures as the real experiments, except that no fluorescein particles were introduced during the deposition phase, confirmed the method integrity, and established minimum particle mass detection limits for shoes and floor samples of 25 ng, much lower than the typical measured mass. Definitions of Measured Parameters. Single-step uptake transfer efficiencies, Tu,1, measured during sequence A were calculated by the following: Tu,1 =

Fu,eq =

(1)

where Mshoe,1 is the particle mass on the shoe after one step on a particle-laden floor, Ashoe is the apparent shoe area that contacted the floor (160 cm2), Mfloor,0 is the initial mass on the floor, and Afloor is the floor surface area (450 cm2). Values of Mfloor,0 were determined by adding the measured mass transferred to the shoe, Mshoe,1, to the measured mass remaining on the floor after the step. Downlay transfer efficiencies to an initially clean floor after one shoe-loading step, Td,1+1, measured during sequence A were determined by the following:

Td,1 + 1 =

M floor,1 + 1 Mshoe,1

(2)

where Mfloor,1+1 is the mass on the initially clean floor after a single step by the particle-laden shoe and Mshoe,1 is the mass on the shoe after stepping on the loaded floor, but prior to stepping on the clean floor. Values of Mshoe,1 were determined by adding the final mass on the shoe to the mass transferred to the initially clean floor. Similarly, during sequence B, downlay transfer efficiencies following 20 shoe-loading steps, Td,20+1, were determined by the following: Td,20 + 1 =

M floor,20 + 1 Mshoe,20

M floor,0 /A floor

(4)

Note that Fu,eq describes an overall transfer fraction resulting from multiple steps, while eqs 1−3 describe the fraction transferred in a single step. Measurement of the uptake transfer efficiency from a particle-laden surface for any step in a series other than the first is difficult because material is transferred both to and from the shoe. Net transfer is easily quantified, but the uptake and downlay transfer efficiencies cannot be easily determined. In separate experiments under the same conditions as these transfer experiments, the fraction of particles resuspended from floors with each step during step-simulation was measured to be in the range from 1 × 10−5 to 8 × 10−5, small enough to have no influence on the mass balance or the measured transfer efficiencies described here. Experimental Results and Discussion. Figures 1−4 summarize measured single-step particle uptake and downlay transfer efficiencies and equilibrium transfer fractions for 1−4 μm and 5−10 μm particles. All figures have the same format with different y-axis scales. The same data in Figures 1−4 are presented numerically in Tables S1 and S2 in the SI for reference. Figure 1 shows measured single-step uptake transfer efficiencies, Tu,1, for the three step pressures and four combinations of shoe and floor types for both 1−4 μm and 5−10 μm particles. Each bar is the average of four separate measurements with 95% confidence intervals. The shoe−floor combination typically accounted for factor of 2 differences in Tu,1, but the difference was nearly 4-fold for 5−10 μm particles and 1.36 kg/cm2 steps. Of the four shoe−floor combinations, dress shoes on tile had the largest transfer efficiencies for a given step pressure and particle size, possibly because these two smooth surfaces allow for more intimate contact than other material combinations. The apparent areas are the same for both shoe types, but the athletic shoe treading reduces its actual contact area relative to the dress shoe. Average single-step uptake transfer efficiencies from tile were equal to or greater than those from carpet. This is in qualitative agreement with previous findings where measured transfer efficiencies from steel to bare hands were much greater than those from carpet.10 There are two potential explanations for lower uptake efficiencies from carpet. First, some particles on carpet are buried in the fibers and less available for transfer, and second carpet may hold a higher electrostatic charge than tile so particles may adhere more strongly to carpet. Values of Tu,1 were also modestly larger for higher step pressures, possibly because greater flattening of the surfaces increases the contact area at higher step pressures. Increasing step pressure from 0.45 to 1.36 kg/cm2 generally led to less than doubling the uptake transfer efficiency, and the differences are sometimes not significant. Average values of Tu,1 were slightly larger for 5−10 μm particles than 1−4 μm particles for most cases except for dress shoes on carpet.

Mshoe,1/A shoe M floor,0 /A floor

Mshoe,20 /A shoe

(3)

where Mfloor,20+1 is the mass on the initially clean floor after a single step by the loaded shoe, and Mshoe,20 is the mass on the shoe after 20 steps on the loaded floor, but prior to stepping on the clean floor. 3802

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Figure 2. Equilibrium uptake transfer fractions, Fu,eq, after 20 steps for 0.45, 0.90, and 1.36 kg/cm2 steps and four combinations of shoe and floor surface type for (a) 1−4 μm and (b) 5−10 μm particles measured during step sequence B.

Figure 1. Single-step uptake transfer efficiencies, Tu,1, for 0.45, 0.90, and 1.36 kg/cm2 steps and four combinations of shoe and floor surface type for (a) 1−4 μm and (b) 5−10 μm particles measured during step sequence A.

Figure 3 shows single-step downlay transfer efficiencies after a single shoe-loading step, Td,1+1, measured during sequence A and Figure 4 shows single-step downlay transfer efficiencies after 20 shoe-loading steps, Td,20+1, measured during sequence B. Dress shoes showed generally higher higher values of Td,1+1 and Td,20+1 compared to athletic shoes for both floor types. Of the four shoe−floor combinations, dress shoes on tiles showed the highest single-step downlay fractions for most cases. Downlay efficiencies were generally greater for higher step pressures and for the larger particle size, but both parameters were only weakly influential. Values of Td,1+1 were 2−4 times larger than Td,20+1, even though the multistep uptake values, Fu,eq, are higher than the corresponding single-step uptake values. After stepping on a particle-laden surface, there is likely a distribution of adhesion strengths for particles on the shoe. Upon floor contact in the next step, the most easily dislodged particles are transferred back to the floor, leaving behind those that are more tightly adhered. During the 2nd through 20th shoe-loading steps, while material is continually transferred from floor to shoe, the most easily removed particles are also transferred from the shoe back to the floor. After 20 shoe-loading steps, the average level of adherence for particles remaining on the shoe is likely greater than the average level after a single shoe-loading step leading to lower values of Td,20+1 than Td,1+1.

Table S3 in the SI presents values of Tu,1 for three different levels of floor particle loading. No differences in Tu,1 were observed for a given floor type as particle loadings varied over the range 0.13−7.2 μg/cm2. Figure 2 presents equilibrium uptake transfer efficiencies, Fu,eq, measured during step sequence B. Similar trends as in Figure 1 are seen here; the shoe−floor combination was the most important variable controlling the process, especially for the larger particles. One difference from the single-step uptake case, where dress shoes on tile had the highest transfers, is that values of Fu,eq were highest for athletic shoes on tile, possibly because additional steps by the athletic shoe are more likely to contact portions of the tile floor that were not contacted by previous steps because of the treaded sole. The shoe steps in the same apparent area, but the actual contact area between treads and tile may shift slightly with each step allowing tread ridges to contact previously untouched portions of the tile. Stepping on carpet produced lower values of Fu,eq, possibly because the carpet pile moved against the shoe sole during liftoff. There was no clear trend in Fu,eq when the step pressure varied. Values of Fu,eq for 5−10 μm particles were generally equal to or greater than those for 1−4 μm particles for similar experimental conditions. 3803

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Figure 3. Single-step downlay transfer efficiencies, Td,1+1, after one uptake step for 0.45, 0.90, and 1.36 kg/cm2 steps and four combinations of shoe and floor surface type for (a) 1−4 μm and (b) 5−10 μm particles measured during step sequence A.

Figure 4. Single-step downlay transfer efficiencies, Td,20+1, after twenty uptake steps for 0.45, 0.90, and 1.36 kg/cm2 steps and four combinations of shoe and floor surface type for (a) 1−4 μm and (b) 5−10 μm particles measured during step sequence B.

Figure 5 displays single-step downlay transfer efficiencies of 1−4 μm particles for 12 sequential steps by particle-laden shoes on 12 clean tile floor samples with 0.90 kg/cm2 steps. Shoes were loaded by a single step on a particle-laden tile prior to the 12 steps on clean tiles. Circles (referring to the left axis) show the fraction of remaining particle mass on the shoe that was transferred to the clean tile for that step. For dress shoes on tile, the downlay efficiency decreased from 0.168 on the first downlay step (Td,1+1) to 0.028 for the 12th downlay step (Td,1+12). A similar decrease in the downlay efficiency was observed for athletic shoes on clean tiles, falling from 0.102 for Td,1+1 to 0.018 for Td,1+12. This decay in transfer efficiency with successive contacts is similar to the decrease in uptake efficiencies observed in previous hand press trials.8,10 A simple inverse first-order model is proposed to estimate from the data downlay transfer efficiencies from particle-laden shoes to clean floors for a given step in a sequence:

predicted by eq 5. This simple model yields reasonable agreement with the experimental data, although eq 5 will tend to overpredict transfer efficiencies for step numbers of 12 and greater. The absolute error of this overprediction will be small because only a very small fraction (∼1%) of the remaining material is transferred with each additional step for step numbers larger than 12. The squares and dashed lines in Figure 5 refer to the right axis and respectively represent the measured cumulative fraction of initial particle mass on the shoe transferred back to the clean floor and the values predicted by eq 5 when summed on step number. Figure 5a shows that the dress shoe had redeposited 50% of the mass to the clean tile floor after seven steps; 50% redeposition was not achieved in the data for the athletic shoe on tile in Figure 5b, but extrapolating eq 5 suggests that approximately 25 steps would be required. Figures S2 and S3 in the SI display measured transfer efficiencies during multistep sequences. SI Figure S2 shows that the downlay transfer efficiency decreases as the number of prior shoe-loading steps increases from one to five, but then levels off as the number of shoe-loading steps increases beyond five. SI Figure S3 illustrates that the net floor-to-shoe transfer gradually decreased with each successive step during multiple uptake

Td,1 + j ,calc = Td,1 + 12 +

Td,1 + 1 − Td,1 + 12 j

(5)

where j is the step number on a clean surface after one initial particle-loading step. The solid lines (referring to the left axis) in Figure 5 show single-step downlay transfer efficiencies 3804

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Figure 5. For 12 successive steps by a particle-laden shoe, the fraction of remaining mass on shoe transferred to a clean floor (circles, solid line and left axis) and the cumulative fraction of initial mass on shoe transferred to the floor (squares, dashed line, and right axis) for (a) dress shoes and (b) athletic shoes on tile floors. These data are for 1−4 μm particles and 0.90 kg cm−2 steps.

steps. More detailed discussion of these results is available in the SI. Modeling and Implications of Transport by Tracking. One goal of these experiments was to measure transfer efficiency data that could be used to model the spread of particle surface contamination in buildings. To investigate the implications of particle transport by tracking, we consider a hypothetical example of people walking one-way through a hallway with a known initial distribution of deposited particle mass. For each simulation, we use constant single-step uptake and downlay fractions described by eq 5 in a simple model to estimate how footsteps redistribute mass on the hallway floor. This example is greatly simplified compared to a real-world scenario and is intended only to explore characteristic steps and distances associated with dispersion by tracking. The modeled hallway is 66 m long and 2 m wide, with the first 18 m initially contaminated uniformly at a level of 10 mg/ m2 (total particle mass of 360 mg) and the final 48 m initially clean. A one-way flow of people walks through the hallway, first crossing the contaminated portion, proceeding through the initially clean portion and then exiting the opposite end. A plan view of the hallway in its initial state with the flow direction of

people is shown at the top of Figure 6. Each person in the simulation is identical, with the same type of initially clean shoes, the same shoe-to-floor contact area per step (0.02 m2), and the same stride length (0.75 m). With a 0.75 m stride, each person takes 24 steps in the initially contaminated zone (12 steps per shoe) and then 64 steps (32 steps per shoe) in the initially clean zone. To account for changes in particle loading, the hallway length is divided into 1.5 m sections (44 sections, each 1.5 m long by 2 m wide). The particle loading within each section is assumed uniform. With a shoe-to-floor contact area of 0.02 m2 per step and a 0.75 m stride, 75 people are needed to completely cover a 3 m2 section with footsteps. People are considered in 75-person groups, and it is assumed that within each group, each person steps on a different location in each floor section. Thus, the mass loadings on the floor sections experienced by each person in a group of 75 are the same, and the mass loadings on each floor section can be reaveraged after each 75-person group passes through. This method yields results similar to reaveraging the mass loading within each section after every person passes. 3805

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airport or transit terminal, tracking could significantly broaden the contamination area in a few hours. Figure 6 shows the calculated loading on the hallway floor for the case of dress shoes and tile after 450, 1350, and 2250 people (∼P1/2, 3P1/2, and 5P1/2) have passed through. The figure illustrates the expected mass decrease in the initially contaminated zone as people enter with clean shoes and leave with particle-laden shoes. The hallway mass loading becomes increasingly uniform as the number of people increases. Figure 7 shows the change in loading at four floor locations (10, 20, 40, and 60 m from the entrance) versus the number of

Figure 6. Modeled redistribution of particle mass density for 5−10 μm particles on the floor from tracking by a one-way flow of people in the hypothetical hallway for the case of dress shoes, tile floors, and a step pressure of 0.9 kg/m2.

A person with a 0.75 m stride takes two steps in each 1.5 m long hallway section, one with each shoe. Because both the left and right shoes step in each floor section in the same order, both shoes of a single person are conceptually identical. All mass is assumed to be equally available for transfer, so mass deposited by the footstep of a previous person is taken up by a shoe with the same efficiency as the initially deposited mass. For shoe-to-floor downlay transfer, eq 5 was applied independently for particles taken up at each floor section. For example, the fraction of particles laid down by stepping in floor section 7, was calculated to be the sum of Td,1+1 multiplied by the mass the shoe picked up in section 6, Td,1+2 multiplied by the remaining mass on the shoe picked up in section 5, Td,1+3 multiplied by the remaining mass on the shoe picked up in section 4, and so on. This calculation method gives reasonable agreement with the experimental data presented in Figure S3b in the SI, which is for the equivalent case. Details of the mathematical model are presented in the SI. Four simulations were performed with different input values for Tu,1, Td,1+1 and Td,1+12 to represent the four shoe−floor combinations explored in the experiments. For a given simulation, every person had the same type of shoes, and the floor material is uniform throughout the hallway. Inputs for the four simulations are summarized in Table S4 in the SI; they are drawn from the experimental data for 5−10 μm particles and 0.90 kg/cm2 footsteps. Two metrics are used to compare the modeling results in Table S4 in the SI: the number of people required to transport half of the particle mass out of the initially contaminated zone, P1/2, and the fraction of initial mass transported beyond the hallway exit, Fexit, when the number of people exiting is equal to P1/2, 3P1/2, and 5P1/2. Among the simulations, the combination of dress shoes and tile floors leads to the most rapid transport (i.e., the lowest value of P1/2, 470 people) because of the relatively high values of both Tu,1 and Td,1+1. The case of dress shoes and carpet leads to the slowest transport (P1/2 = 2010 people), primarily because of the low single-step uptake transfer efficiency. For all simulations, Fexit > 0.5 after 3P1/2 people have walked through, and Fexit is between 0.8 and 0.9 after the passage of 5P1/2 people. These results suggest that in locations where several hundred people pass through in an hour, as in an

Figure 7. Modeled change in the particle mass density at four floor locations (distance from the entrance) versus the number of people walking one-way through the hypothetical hallway. Model input parameters are the same as those in Figure 6

people for dress shoes and tile flooring. The decrease in loading in the initially contaminated zone (10 m location) is clear. For locations in the initially clean zone, the loading increases to a maximum and then decreases as more people pass through; this maximum is greater and occurs sooner for locations closer to the initial contamination. For example, at 20 m a maximum particle loading of 2.6 mg/m2 is experienced after 600 people passed, while the maximum of 1.0 mg/m2 at the 60 m location is achieved after passage of 1275 people. The same trends are seen in simulations with other shoe−floor combinations when the number of people on the x-axis is normalized by P1/2 for that shoe−floor pairing. These simulations suggest that for crowded locations where a few people walk over the same area each minute, tracking can spread deposited material over building length scales in a few hours.

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ASSOCIATED CONTENT

S Supporting Information *

Literature review; step-simulation chamber photograph; experimental data tables; discussion of multistep transfer figures; transport model details; and model inputs and results table. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (916) 323-1095; e-mail: [email protected]. Present Addresses †

Stationary Source Division, California Air Resources Board, Sacramento, CA 95814. ‡ Department of Civil & Environmental Engineering, California Polytechnic State University, San Luis Obispo, CA 93407. 3806

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the Office of Chemical Biological Countermeasures, of the Science and Technology Directorate of the Department of Homeland Security, and performed under U.S. Department of Energy Contract No. DEAC02-05CH11231.

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REFERENCES

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