Predicting indoor emissions of cyclic volatile methylsiloxanes (cVMS

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Environmental Modeling

Predicting indoor emissions of cyclic volatile methylsiloxanes (cVMS) from the use of personal care products by university students Tao Yang, Jianyin Xiong, Xiaochen Tang, and Pawel K. Misztal Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b00443 • Publication Date (Web): 08 Jun 2018 Downloaded from http://pubs.acs.org on June 9, 2018

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Environmental Science & Technology

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Predicting indoor emissions of cyclic volatile methylsiloxanes

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(cVMS) from the use of personal care products by university

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students

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Tao Yang1, Jianyin Xiong1,2,*, Xiaochen Tang3, Pawel K. Misztal2,4

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China

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California, Berkeley, California 94720, United States

School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081,

Department of Environmental Science, Policy and Management, University of

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Laboratory, Berkeley, CA 94720, United States

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Indoor Environment Group, Energy Technologies Area, Lawrence Berkeley National

Centre for Ecology & Hydrology, Edinburgh, Midlothian, EH26 0QB, UK

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*

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address: [email protected]

Corresponding author. Tel.: +86 10 68914304; Fax: +86 10 68412865; E-mail

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ACS Paragon Plus Environment


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Abstract

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Characterization of indoor emissions of cyclic volatile methylsiloxanes (cVMS) due

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to the use of personal care products is important for elucidating indoor air

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composition and associated health risks. This manuscript describes a mass transfer

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model to characterize the emission behaviors of decamethylcyclopentasiloxane (D5,

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the most abundant indoor cVMS) from skin lipids. A C-history method is introduced

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to determine the key parameters in the model, i.e., the initial concentration and

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diffusion coefficient of D5 inside the skin lipids. Experiments were conducted in a

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university classroom to examine the D5 emission behaviors by using a

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proton-transfer-reaction time-of-flight mass spectrometer (PTR-TOF-MS). Data from

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the first class session of two typical days was applied to obtain the key parameters,

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which were subsequently used for predicting D5 concentrations in other class sessions.

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Good agreement between model predictions and experiments demonstrates the

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effectiveness of the model and parameter determination method. With the model, we

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found that the re-use of personal care products has a significant impact on the D5

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emissions. In addition, the time-dependent emission rate and remaining amount of D5

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inside the skin can also be calculated. These results indicate a fast decay pattern

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during the initial emission period, which is consistent with prior experimental studies.

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Introduction

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The emission of cyclic volatile methylsiloxanes (cVMS) from the use of personal

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care products is regarded as an important contributor influencing indoor air quality.1,2

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cVMS are defined as volatile, low-viscosity, silicone fluids containing different

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numbers of “Si-O” bonds making up the chain. cVMS are organic ingredients or

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solvents used in a wide spectrum of personal care products due to their low surface

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tension, high thermal stability and smooth texture. These products include

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antiperspirants, skin and hair formulations, sunscreen creams, and cosmetics.3-5 Three

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widely

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decamethylcyclopentasiloxane (D5), and dodecamethylcyclohexasiloxane (D6).2

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These cVMS are currently of particular concern, and being considered for regulation,

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because they are potentially persistent, bioaccumulative and toxic6,7, and have been

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shown to be associated with connective tissue disorders, adverse immunologic

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responses, and fatal liver and lung damage.3, 8-11 cVMS are ubiquitous in the indoor

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environment, since they emit from the original sources and then partition into the

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indoor air due to their high Henry’s law constants. In addition to their presence in

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indoor atmosphere, cVMS are also detected in indoor dust, water and wastewater.12,13

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Therefore, characterization of cVMS due to the frequent use of personal care products

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in the indoor environment is needed, to understand its transport and fate. A rapid

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progress can be achieved thanks to the development of time-resolved analytical tools

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that strengthen our ability on the characterization of cVMS emissions.

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used

cVMS

are

octamethylcyclotetrasiloxane

(D4),

Previous studies have generally focused on investigating the occurrence and

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concentration level of cVMS in typical personal care products, or in the indoor

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environment. The concentrations or contents of cVMS in personal care products may

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differ due to variations in countries and types of personal care products and

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compounds. For collected 76 personal care products in U. S. and Japan, the

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concentrations of D4, D5 and D6 were measured to be 0.35-9380 µg/g, 0.39-81800

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µg/g and 0.33-43100 µg/g.3 By testing 252 cosmetic products in Canada, the results

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for the above three cVMS were reported to be 10-11000 µg/g, 20-683000 µg/g and

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10-97700 µg/g.14 Lu et al.4 examined 158 personal care products in China, and the

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concentration ranges of D4, D5 and D6 were determined to be 0-72.9 µg/g, 0-1110

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µg/g and 0-367 µg/g. These results indicate that the total cVMS (sum of D4, D5 and

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D6) can account for as much as 80% of the total content of some personal care

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products (e.g., cosmetics, hair care products), meaning that they are an important

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source of cVMS in the indoor environment. Up to now, there are limited reports of

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measured indoor gas phase cVMS concentrations and most of them lack the

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time-resolved data to assess cVMS dynamics. Tests from 91 samples in different sites

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in UK and Italy indicated that the D4, D5 and D6 concentrations in indoor air were in

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the range of 19-270 µg/m3, 2.4-440 µg/m3 and 0.47-79 µg/m3.15 By collecting 3857

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samples in Canadian residential indoor air, Zhu et al.16 reported that the representative

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levels of indoor D4 and D5 concentrations were within 5.45-7.94 µg/m3 and

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35.47-47.18 µg/m3. In Chicago, the indoor concentrations of the three cVMS were

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measured to be 0.03-0.5 µg/m3, 0.97-56 µg/m3 and 0-2.8 µg/m3.17 Tang et al.2

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measured the cVMS levels from engineering students in a classroom in California,

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and the average D4, D5 and D6 concentrations were 3.9 µg/m3, 99 µg/m3 and 2.0

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µg/m3 in a typical day. For most of these previous experimental studies, D5 is

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recognized as being the dominant cVMS, both in personal care products and in the

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indoor air, even comprising over 90% of total cVMS in some studies2,17. For this

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reason, the research presented here mainly looks at the characterization of D5

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emissions.

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At present, some modelling work is being done to predict D5 emissions. The

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transport modeling of D5 concentrations in the outdoor atmosphere is well-developed,

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and good agreement has been found between the model predictions and experiments,

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implying that the sources, transport paths and sinks of D5 in the outdoor atmosphere

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are well-understood.18-20 However, very little research has been done to systematically

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model D5 emissions in the indoor environment, especially from human skin after the

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use of personal care products. Some limited investigations aimed at understanding

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dermal absorption of D5 in the skin have been carried out by introducing a

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compartmental model.21 However, the model did not consider the internal diffusion

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process. In addition, subsequent experimental dermal absorption studies5,22

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demonstrated that only less than 0.2% of the applied D5 was absorbed through the

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skin, and it was reported that the majority of the applied D5 would volatilize from the

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skin surface. These results imply that the dominant pathway of D5 to the indoor

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environment is from skin emissions after the use of personal care products, and the

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main exposure pathway of D5 is probably via inhalation. The lack of a model for

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characterizing D5 emissions from the skin surface prevents a deep understanding of

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D5 occurrence in indoor air, as well as limiting the ability to assess exposure. In

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addition to model development, the characteristic parameters (initial concentration,

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diffusion coefficient) in the model need to be determined as a prerequisite for

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prediction. To our knowledge, no attempt has been made to measure the diffusion

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coefficient of D5 in the skin.

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The objectives of this research are therefore to: (a) describe a model of D5

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emission from an occupant’s skin due to the use of personal care products and

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determine the key parameters in the model; (b) test the model efficacy by comparing

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predictions with observations of D5 concentrations in a university classroom; (c)

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perform a dimensionless analysis to show how the model could be generalized to

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other cVMS emissions.

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Methods

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Model development

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When personal care products (e.g., antiperspirants, sunscreen creams) are applied,

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the ingredients are initially assumed to be present in a separate layer on top of the skin

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lipids. Here we make a further assumption that this separate layer will partition into

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the skin lipids. Emissions of the dominant cVMS, D5, from the skin lipids of the

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human body are modeled as a physical process. Since the skin lipids form a thin layer,

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it is assumed that the diffusion of D5 inside the skin lipids can be represented as

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one-dimensional. The skin is assumed to form an impermeable barrier with regard to

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D5 penetration. Such an assumption is consistent with earlier dermal absorption

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studies as mentioned in the previous section.5, 22 We also make an estimation to verify

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this. According to the multi-pathway exposure model,23 the depletion of chemicals in

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the skin lipids is controlled by two rate constants, i.e., the product to air rate constant

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(kp,a) and the product to skin (dermal intake) rate constant (kp,s). For D5 emission from

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skin lipids, based on the formula for kp,a and kp,s,23 and the physical-chemical property

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data from EPI Suite, it is calculated that the ratio of kp,a to kp,s for D5 is about 27 (see

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detail in Section S1 of the Supporting Information), meaning that most of D5 are

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volatilized from the skin lipids surface and dermal intake can be neglected. In addition,

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adsorption or absorption of D5 to interior surfaces is assumed to be negligible. A

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further assumption is that the D5 level indoors is well mixed. With these assumptions,

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the emission process can be represented as shown in the schematic in Figure 1. In this

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figure, hm represents the external mass transfer coefficient.

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Figure 1. Schematic of D5 emission from skin lipids. 139 140

The governing equation describing the transient diffusion through the skin lipids,

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together with the boundary conditions and the initial condition, are described by

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equations (1) - (4):

∂Cm ∂ 2Cm = Dm ∂t ∂x 2

(1)

∂Cm = 0, x = 0 ∂x

(2)

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− Dm

C ∂Cm = hm ( m − Ca ), x = L K ∂x

Cm ( x, t ) = C0 , t = 0, 0 ≤ x ≤ L

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(3) (4)

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where, Cm is the concentration of D5 in the skin lipids, µg/m3 or ppb; Ca is the

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concentration of D5 indoors, µg/m3 or ppb; Dm is the diffusion coefficient of D5 in the

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skin lipids, m2/s; L is the thickness of the skin lipid layer, m; K is the skin/air partition

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coefficient, dimensionless; C0 is the initial concentration of D5 in the skin lipids (i.e.,

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at the time the emitters enter the indoor space), µg/m3 or ppb.

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Equation (1) stands for the one-dimensional diffusion process of D5 inside the

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skin lipids, while equations (2) and (3) stands for two kinds of boundary conditions

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(no mass flux and convective mass flux). The mass balance of D5 indoors is given as:

V

dCa ∂C = QCin − ADm m |x = L −QCa dt ∂x

(5)

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where, V is the volume of the indoor space, m3; A is the total area of the skin lipid

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layer emitting D5, m2, which can be calculated by Ne × Ap (Ne is the number of

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emitters; Ap is the area of the skin lipid layer of one emitter including face and hand;

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the value of Ap is taken as 0.095 m2 from reference5, which is in accordance with

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standard clinical applications for personal care products); Cin is the inlet D5

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concentration via ventilation system from outdoors, µg/m3 or ppb; Q is the ventilation

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rate, m3/s.

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It should be noted that equations (1)-(5) are widely used for building material

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emissions.24,25 Here we apply these equations to characterize D5 emissions from skin

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lipids.

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We assume here that D5 is absent from the indoor air prior to the arrival of occupants:

Ca (t ) = 0, t = 0 163 164

(6)

By virtue of Laplace transforms, equations (1) - (6) can be solved to determine the indoor D5 concentration in this form26: ∞

Ca (t ) = A1 + 2 A2 ⋅ ∑ n =1

A3 ⋅ qn sin qn − A4 ⋅ cos qn − Dm L−2 qn2t e Gn

(7)

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where, Gn = [ K β + (α − qn2 ) KBim−1 + 2]qn2 cos qn + [ K β + (α − 3qn2 ) KBim−1 + α − qn2 ]qn sin qn ;

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A1=Cin; A2=C0; A3=β; A4=0; α = QL2 / DmV ; β = AL / V ; Bim = hm L / Dm ; qn are the

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positive roots of qn tan qn =

α − qn2 K β + (α − qn2 ) KBim−1

(n = 1, 2,...)

(8)

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For real occupant emission tests, the volume of the environment is often very

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large (room or full-scale chamber), and the convective mass transfer coefficient is

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very small (natural convection in many scenarios). Under this condition, the term Kβ

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will be much smaller than αK/Bim (generally by 2-4 orders of magnitude smaller) in

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equation (8), and thus can be ignored. Equation (8) can then be simplified: qn tan qn =

Bim K

( n = 1, 2,...)

(9)

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Such simplifications can significantly reduce the calculation complexity and

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increase the accuracy of finding the root of a trigonometric equation. Finding the root

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is the key point of applying the analytical solution to predict the D5 concentration or

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emission rate. With equation (9) and the condition Kβ 0.125 ), the SL and INT can be obtained, following which C0 and

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Dm can be determined by solving two equations with these two key parameters. When

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applying the C-history method to obtain the two key parameters, an initial value of K

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is pre-assumed and taken as known. The rationality of such treatment is demonstrated

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by the sensitivity analysis in the following section, which shows that the mid-term or

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long-term emission behaviors are insensitive to the pre-assumed K (K only influences

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the short-term emission behaviors), meaning that the measured C0 and Dm based on

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mid-term emission data should be also insensitive to the pre-assumed K. For some

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emission scenarios, once the C0 and Dm have been obtained, these values together

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with the short-term emission data can be further used to obtain an updated K.

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Experimental section

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Generally, there are two approaches to experimentally examine the emission

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characteristics of D5 from skin lipids. One is to perform the experiment in a

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controlled environmental chamber with occupants, and the other is to conduct the

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experiment in the field. We used the latter approach in this study. The field campaign

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was conducted in a university classroom in California. The volume of the classroom

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was about 670 m3. The air-exchange rate during the daytime 8:00-20:45 was

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evaluated through CO2 tracer decay method (utilizing deliberate releases) in a prior

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study for the same classroom.32 It was determined to be 5 ± 0.5 h-1 (replacing

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ventilation), and was adopted in the present study. The real-time occupant (student)

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number in the classroom was recorded for several days. The D5 concentrations in the

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classroom were continuously monitored by an on-line sampling instrument

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proton-transfer-reaction time-of-flight mass spectrometer (PTR-TOF-MS) (IONICON

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Analytik GmbH). This instrument uses H3O+ as the primary reagent to softly ionize

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volatile organic compounds across the mass spectrum for mass-to-charge ratio (m/z)

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of 20.00-500.00 Th. PTR-TOF-MS enables fast response time measurements (a full

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mass spectrum in seconds or minutes), has high sensitivity (tens of parts per trillion or

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ppt in a second), and high mass resolution.2,33 Since the supply air (outdoor air) could

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contain certain amount of D5, a three-way valve was used to switch the sampling of

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PTR-TOF-MS between the supply air and the classroom air every 5 min. To reduce

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possible effects from valve switching and sampling tube interactions, the data for the

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first 2 min after every switching were discarded. The gas phase D5 concentration was

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then averaged based on the data in the remaining 3 min, to get relatively smooth

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results.

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Results and discussion

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Determination of the key parameters

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To check that the model provides reasonable results, the key parameters in the

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model are first determined. The experimental data from the classroom tests are used to

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achieve this goal. The key parameters can be extracted based on data from the first

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class session observed on Nov 6 and Nov 13, 2014 (class session 1: 8:10 - 9:40 AM).

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For D5 emission from skin lipids, the initial K can be approximately predicted by the following correlation:34

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log K = log Kow + log( HRT )

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(16)

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where, Kow is the octanol-water partition coefficient; H is the Henry constant; R is the

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gas constant; T is the temperature. The use of equation (16) is based on that octanol

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represents a good surrogate for the liquid-like material described in the present study.

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Based on the physical-chemical property data from EPI Suite, the K for D5 at

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305 K (32 oC) is calculated to be 3.27 × 104. The thickness of the skin lipid is an

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important parameter for D5 emission. Some previous studies investigated the

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thickness of the skin lipids, and found variations in different persons and different

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regions of the body.35,36 The determined thickness of skin lipids is generally in the

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range of 0.5-1.3 µm.37 To simplify the analysis, the thickness of skin lipids in the

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present study is taken as uniformly 1 µm. The calculation of hm is based on the

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Chilton-Colburn analogy for heat and mass transfer.38,39 The environmental conditions,

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and dimensions of the classroom and skin lipids are summarized in Table 1. Other

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information such as the recorded data of inlet D5 concentrations via ventilation

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system from outdoors for different class sessions are given in SI Figure S1.

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Table 1. Environmental conditions, and dimensions of the classroom and skin lipids 274 275

Figure 2 gives the linear curve fitting results using equation (13). Based on the

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SL and INT, the C0 and Dm determined for class session 1 on Nov 6 (student number:

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24) are: C0 = (8.80 ± 0.62) × 1010 µg/m3, Dm = (1.46 ± 0.08) × 10-16 m2/s, while the

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values for class session 1 on Nov 13 (student number: 26) are : C0 = (1.93 ± 0.16) ×

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1011 µg/m3, Dm = (1.35 ± 0.07) × 10-16 m2/s. The standard deviations for C0 and Dm

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are calculated based on the method in the reference.28 These results indicate that the

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relative standard deviation for C0 and Dm is less than 10%, which is relatively small.

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In performing curve fitting with equation (13), the time t should belong to the

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mid-term emission period (Fom > 0.125 or t > 0.125L2/Dm). Since Dm is unknown

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before the experiment, we can check whether or not the selected time t meets the

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condition after determining Dm. By validation, the selected time of the field campaign

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for curve fitting meets the requirement (t > 0.125L2/Dm). By comparing the

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determined key parameters in different test days, we find that Dm is very close, while

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C0 differs by about 1 fold. The environmental conditions in Table 1 indicate that the

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temperature on Nov 6 and Nov 13 is almost the same, while the relative humidity

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changes a lot (It’s a rainy day on Nov 13). The above results imply that the relative

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humidity can significantly influence C0 while has negligible effect on Dm. This

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conclusion is consistent with prior studies which examined the emissions of other

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types of VOCs.40,41 Moreover, detailed analysis based on tests in another two days

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(Nov 5 and Nov 12) demonstrates that the average emission rate in the morning

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differs less than 20% if the environmental conditions are similar (temperature

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difference < 0.5 oC, humidity difference < 3%). Further study is needed to deeply

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explore the impact mechanism of relative humidity on D5 as well as other cVMS. In

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addition to relative humidity, the rainy weather on Nov 13 was responsible for a

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decrease of 4 oC in outdoor temperature compared with that on Nov 6. Under this

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condition, students probably use more personal care products, which may partly

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contribute a high C0 on Nov 13. The removal of coats and sweaters worn by students

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due to the cooler outdoor weather (Nov 13) after they enter into the classroom may

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also cause a burst of D5 emissions as pointed out by Tang et al.2 The impacts of these

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two factors also merit further examination.

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The emissions of D5 from skin lipids are analogous to the emissions of VOCs

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from building materials. For building material emission scenarios, two approaches are

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generally applied to determine the key parameters, i.e., the direct measurement

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approach42,43 and the indirect regression approach28,29,44-46. Both approaches are

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effective and gain big success in characterizing pollutant emissions. For the present

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study, it is difficult to directly obtain the initial D5 concentration for university

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students since it is a field campaign. Therefore, we apply the indirect regression

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approach to get the key parameters. As far as we know, this is the first attempt by

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applying the principle of methods for measuring key parameters of VOCs from

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building materials to the human emissions.

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Figure 2. Linear curving fitting results by virtue of equation (13) for class session 1 on Nov 6 and Nov 13. 316 317

Validation of the emission model

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With the above key parameters, the D5 concentration for other class sessions can

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be predicted based on the semi-analytical solution. Figure 3(a) shows the comparison

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between model prediction and experimental data for class session 1 and class session

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2 (student number: 57) on Nov 6, while Figure 3(b) shows the comparison for class

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session 1 and class session 2 (student number: 54) on Nov 13. In the calculation,

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different C0 and similar Dm determined in the above section are used for different

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tested days. The agreement for the mid- and long-term emissions in Figure 3 is fair,

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demonstrating the effectiveness of the emission model as well as the parameter

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determination method. The difference in the short-term emissions (during the first 20

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min especially in class session 2) is probably due to two reasons: (1) the partition

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coefficient predicted by equation (16) may introduce some deviations, which will

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accordingly cause some discrepancies in the gas phase concentration in the initial

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period (K influences the short-term emission patterns); (2) the indoor air is not well

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mixed especially for the initial unsteady period when students enter into the classroom.

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In the field test, the class session 1 and class session 2 have different student numbers

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(both on Nov 6 and Nov 13), thus can be regarded as independent experiments. The

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good accordance between model predictions and experimental data for class session 2

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can be taken as an independent validation, which solidly proves the effectiveness of

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the present model.

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In addition, we compare simulated results between the present model and two

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other simple models, i.e., the multi-pathway exposure model23 (model 1) and the

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adsorption/desorption model47 (model 2). The multi-pathway exposure model23 is

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applied to predict chemical emission from personal care products which considers

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mass transfer from the product on skin surface to air and into the stratum corneum.

342

The adsorption/desorption model47 is applied to predict chemical emission from

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indoor materials and products, which neglects the internal diffusion process. The

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detailed introduction of these two models in included in SI Section S1. Figure S2

345

shows the calculated gas phase D5 concentrations for class session 1 on Nov 6 based

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on different models. This figure indicates that the present model agrees better with

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experimental data, which further demonstrates the effectiveness of the present model.

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Compared with the adsorption/desorption model, the parameters in the present model

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have more distinct physical meanings, and can be measured through independent

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experiments (e.g., by performing independent environmental chamber tests).

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Moreover, the key parameters determined here are the physical parameters of the skin

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lipids, thus can be generalized to other indoor environment with different settings

353

(e.g., varied room volume, air-exchange rate, occupants with similar usage habit).

354

More discussion is included in Section S1.

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Figure 3. Comparison between model predictions and experimental data for D5 concentrations for different class sessions on (a) Nov 6 and (b) Nov 13. 356 357

Analysis of the re-use of personal care products

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When one class is ended, some students may remain in the classroom for the

359

next class, and some new students may enter. Here we analyze the impact of these

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factors on D5 emissions in the classroom. According to the schedule, the time interval

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between the beginning of class session 1 and class session 2 is about 1.5 h. Figure S3

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shows the impact of the remaining students in the classroom on the D5 emissions. In

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the figure, Nr stands for the number of the remaining students. This figure indicates

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that Nr doesn’t significantly affect the D5 concentration (as well as the emission rate)

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in the classroom after emitting for 1.5 h. The reason is that the emission of D5 from

366

skin lipids is very fast, and only a small proportion of D5 is left in the skin lipids after

367

1.5 h (see the following section).

368

It has been reported that the frequency of use of personal care products (PCPs) of

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a typical U.S. consumer is on average 1.1-1.4 times/day.5,48 This factor is also

370

analyzed and the results are shown in Figure S4. This figure reveals that the re-use of

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personal care products has a significant impact on the D5 emissions. Once students

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repeatedly apply personal care products, the D5 concentration will increase sharply to

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a peak and then decrease gradually, which is much higher than the D5 concentration

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without the re-use of personal care products. If 21 students (including the remaining

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students and new incoming students; C0=8.80 × 1010 µg/m3) in class session 3 on Nov

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6 (total student number: 58) repeatedly apply personal care products (this is

377

equivalent to use frequency of 1.36 times/day), the calculated D5 concentration is

378

consistent with the experimental data. This can be regarded as an effective validation

379

of re-use of personal care products.

380 381 382 383

Prediction of emission rate using the model Using the emission model, the D5 emission rate (or loss rate) can be calculated using equation (12) or the following equation:

E (t ) = − ADm

∂Cm dCa |x = L = V + Q (Ca − Cin ) dt ∂x 19


(17)


384

The calculated D5 emission rate over time for class session 1 on Nov 6 is shown

385

in Figure S5 (results are similar for other class sessions). The results indicate that the

386

emission rate decreases over time (sharply in the short-term period and gradually in

387

the mid- and long-term period). Since the activity of new coming students may lead to

388

an unstable emission period for the first 3 min of every class session, the emission rate

389

for the first 3 min is removed from the data analysis, thus is not included in Figure S5.

390

Based on the time-dependent emission rate, the average emission rate for every class

391

session can be determined. Table S2 lists the calculated average emission rate for the

392

first two class sessions on Nov 6 and Nov 13, and compares these with results found

393

in the literature2 that were evaluated based on a mass balance approach. We can see

394

that the maximum deviation between the calculated results and experimental data is

395

less than 10%, demonstrating the effectiveness of model prediction. Analysis on the

396

remaining amount of D5 on the skin is included in Section S2 and Figure S6.

397 398

Sensitivity analysis

399

Since the key parameters Dm, K and the convective mass transfer coefficient hm

400

will influence the D5 emission behaviors, we perform a sensitivity analysis to check

401

how much they will affect these behaviors. The benchmark values for sensitivity

402

analysis are: C0 = 8.80 × 1010 µg/m3, Dm = 1.46 × 10-16 m2/s, K = 3.27 × 104, hm = 9 ×

403

10-4 m/s. Figure S7 gives the results for the class session 1 on Nov 6 after changing

404

the above parameters. This figure implies that: Dm can influence the short-term, the

405

mid-term as well as the long-term emission behaviors; K and hm only influence the

20


Page 20 of 36

Page 21 of 36


406

short-term emission behaviors while having little impact on the mid-term and

407

long-term emission behaviors. Further calculation indicates that when hm and K are

408

changed 10 times, the mean emission rate in 1.5 h varies within just 2%, while the

409

value due to the changed Dm is about 100%. For this study, the key parameters were

410

determined from the mid-term emission data by pre-assuming a K value. According to

411

the sensitivity analysis, such treatment will not affect the determined parameters. In

412

some scenarios, if we want to have a good agreement between the model prediction

413

and experimental data for the short-term emission period, we can use the determined

414

C0 and Dm to fit the short-term emission data and obtain an improved K value. By

415

taking the D5 emission in class session 2 on Nov 6 as an example, such treatment is

416

shown in Figure S8.

417 418

Analysis of the generalization of the model

419

The above sections demonstrate the effectiveness of the model for describing D5

420

emission behaviors in the classroom. To examine the generalization of the model for

421

other cVMS emissions, we perform a dimensionless analysis. To make this analysis

422

process more concise, we use just the analytical solution (similar to the

423

semi-analytical solution). The following dimensionless parameters are introduced for

424

the analysis:

C* =

425 426

D t Ca − Cin , Fom = m2 C0 L

(18)

where, C* is the dimensionless concentration. Based on these dimensionless parameters, equation (10) can be transformed into: 21



2 2β e − qn Fom 2 2 2 n =1 (α − q )(1 + K / Bim + qn K / Bim )

Page 22 of 36

∞

C* = ∑

2 n

(19)

427

All the parameters (β, α, K/Bim, qn, Fom) on the right-hand side of equation (19)

428

are dimensionless, and these parameters are related to the key parameters Dm and K. If

429

equation (19) is generally applicable for cVMS emissions, the dimensionless

430

concentration C* shouldn’t differ greatly for cVMS with similar Dm and K (i.e.,

431

compounds with similar chemical structure). Here, D4 and D5 are used to

432

preliminarily illustrate this point. According to reported data, the mean maximum D4

433

and D5 concentrations in personal care products in the U.S. and Canada3,14 are 10.2

434

mg/g and 382.4 mg/g (these values are taken as C0), respectively. The corresponding

435

mean maximum D4 and D5 concentrations in indoor air in the U.S. and Canada2,16,17

436

are 4.1 µg/m3 and 67.4 µg/m3 (these values are taken as Ca), respectively. Based on

437

these data, the C* for D4 and D5 are calculated to be 0.4 mg/m3 and 0.2 mg/m3

438

respectively (they can be easily transferred into dimensionless concentrations by

439

dividing the density of the personal care products). Since this is just a rough estimate

440

(there are some uncertainties in the measured concentrations of D4 and D5 in the

441

personal care products and indoor air), we can regard the consistency of C* for D4 and

442

D5 as being acceptable. These results are consistent with the analysis based on

443

equation (19) that C* for D4 and D5 shouldn’t differ greatly since they have a similar

444

chemical structure. This dimensionless analysis preliminarily verifies the feasibility of

445

the model for characterizing the D4 emission behaviors.

446 447

Limitations 22


Page 23 of 36


448

It should be noted that the detailed and full description of D5 (or cVMS)

449

emissions from human skin is indeed challenging, since so many factors (temperature,

450

relative humidity, clothes, occupant movement, usage habit, etc.) are involved. The

451

time-varying thermal environment on the skin49 may affect the D5 emission behaviors

452

for the classroom test. Students walk some distance to class, and their skin

453

temperature might be higher at the start of class, and then cool over the class period. It

454

is known that the emission characteristics are temperature sensitive, which means that

455

the depletion of D5 from the source (occupant) is partly due to the changing

456

temperature conditions at the source location. In addition, for some positions on the

457

human body (e.g., antiperspirant applied in the underarm area), the applied personal

458

care products may be firstly adsorbed by the covering clothes, then penetrate the

459

clothes and emit to the indoor atmosphere. This observation implies that the role of

460

clothes on D5 transportation may need to be considered.

461

For the emission of D5 from skin lipids, the initial concentration C0 is very large

462

(8.80 × 1010 µg/m3), and the diffusion coefficient (Dm) may be dependent on the

463

concentration. At present, satisfactory theoretical or experimental relationship

464

between the Dm and VOC concentration is lacking.50 In another commonly

465

encountered emission scenario, i.e., VOC emission from wet coatings, the initial VOC

466

concentration is also very high, generally in the range of 109-1011 µg/m3 for typical

467

VOCs.51,52 These values are comparable to the C0 of D5 in skin lipids. The

468

assumption of constant Dm in these studies gives good results, meaning that it is

469

acceptable to use constant Dm for analysis if exact relationship between Dm and the

23



470

concentration of target VOC is unavailable. The development of theoretical

471

correlation between the Dm and D5 (or other cVMS) concentration is a very valuable

472

topic. Further study is needed to take the above-mentioned complex factors into

473

account to improve the model predictions.

474 475

Acknowledgments

476

This work was supported by the Alfred P. Sloan Foundation (Grant No.

477

2016-7050), and the National Natural Science Foundation of China (Grant No.

478

51778053, No. 51476013). The authors are grateful to Allen H. Goldstein and William

479

W. Nazaroff (University of California, Berkeley) for interesting discussions and

480

supplying helpful comments on the manuscript.

481 482

Supporting Information

483

Additional detail on model comparison (Section S1), analysis of remaining D5

484

amount (Section S2); Tables S1-S2; Figures S1-S8. This material is available free of

485

charge via the Internet at http://pubs.acs.org.

486 487

References

488

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637 638

31



639

TOC Art

640

641 642

32


Page 32 of 36

Page 33 of 36


643

Figure captions

644

Figure 1. Schematic of D5 emission from skin lipids.

645

Figure 2. Linear curving fitting results by virtue of equation (13) for class session 1 on

646 647 648

Nov 6 and Nov 13. Figure 3. Comparison between model predictions and experimental data for D5 concentrations from different class sessions on (a) Nov 6 and (b) Nov 13.

649

33



650 651

Page 34 of 36

Figure 1.

Air Ca hm K

x=L x=0

652

C0 Skin lipids

653 654

Figure 2.

655 656 657 658 659 660 34


Dm

Page 35 of 36


661

Figure 3.

662 663

(a)

664 665

(b)

666 667 35



Table

668 669

Page 36 of 36

Table 1. Environmental conditions, and dimensions of the classroom and skin lipids Parameters

Nov 6

Nov 13

Temperature (8:10-11:50 AM, oC)

23.3 ± 0.6

22.8 ± 0.2

Relative humidity (8:10-11:50 AM)

(46.2 ± 1.8)%

(62.6 ± 3.5)%

V (m3)

670 a

N (1/h)

5 ± 0.5

Q (m3/h)

3350 ± 335

L (µm)

1

Ap (m2)

0.095

hm (m/s)

9 × 10-4

670

a

671

for the two tested days.

The values of this parameter and the following parameters in this table are the same

672

36


Predicting indoor emissions of cyclic volatile methylsiloxanes (cVMS

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