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Shift in Mass Transfer of Wastewater Contaminants from Microplastics in Presence of Dissolved Substances Sven Seidensticker, Christiane Zarfl, Olaf Arie Cirpka, Greta Fellenberg, and Peter Grathwohl Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02664 • Publication Date (Web): 01 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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Environmental Science & Technology

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Shift in Mass Transfer of Wastewater Contaminants

2

from Microplastics in Presence of Dissolved

3

Substances

4

Sven Seidensticker*, Christiane Zarfl, Olaf A. Cirpka, Greta Fellenberg, Peter Grathwohl*

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Center for Applied Geosciences, Eberhard Karls Universität Tübingen, Hölderlinstraße 12,

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Tübingen, Germany

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Corresponding Authors (*):

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Sven Seidensticker: Tel: +49 7071 29 77452; email: [email protected]

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Peter Grathwohl: Tel: +49 7071 29 75429; email: [email protected]

10

ACS Paragon Plus Environment

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Abstract

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In aqueous environments, hydrophobic organic contaminants are often associated with particles.

13

Besides natural particles, microplastics have raised public concern. The release of pollutants

14

from such particles depends on mass transfer, either in an aqueous boundary layer or by

15

intraparticle diffusion. Which of these mechanism controls mass-transfer kinetics, depends on

16

partition coefficients, particle size, boundary conditions, and time. We have developed a semi-

17

analytical model accounting for both processes, and performed batch experiments on desorption

18

kinetics of typical wastewater pollutants (phenanthrene, tonalide, benzophenone) at different

19

dissolved-organic-matter

20

microplastics and water. Initially, mass transfer is externally dominated while finally

21

intraparticle diffusion controls release kinetics. Under boundary conditions typical for batch

22

experiments (finite bath), desorption accelerates with increasing partition coefficients for

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intraparticle diffusion, while it becomes independent of partition coefficients if film diffusion

24

prevails. Contrary, under field conditions (infinite bath), pollutant release controlled by

25

intraparticle diffusion is not affected by partitioning of the compound while external mass

26

transfer slows down with increasing sorption. Our results clearly demonstrate that

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sorption/desorption time scales observed in batch experiments may not be transferred to field

28

conditions without an appropriate model accounting for both mass transfer mechanisms and the

29

specific boundary conditions at hand.

concentrations,

which

change

overall

partitioning

between


2

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TOC Art

31


3


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Introduction

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The pollution of freshwater ecosystems by an increasing number of chemicals causes adverse

34

effects on aquatic organisms and even human health.1 Within these systems, however,

35

hydrophobic contaminants are often associated with various kinds of particles rather than being

36

freely dissolved. Thus, the investigation of particle facilitated transport is important.2,3 The

37

relevant particle types include colloids, such as natural organic substances, suspended sediments,

38

different kinds of black carbon, and plastic-debris.4-7 The contamination and ubiquitous detection

39

of plastic particles in freshwater ecosystems has attracted both public and scientific attention.8,9

40

Microplastics are defined as particles made of any synthetic polymer with a size smaller than 5

41

mm.10 These particles can be ingested and accumulated by organisms.11,12 Whether they

42

significantly contribute to pollutant transfer is currently discussed in literature.13 They can also

43

influence the ecosystem by releasing plastic additives, such as plasticizers and flame retardants,

44

and by acting as a vector for transport of hydrophobic contaminants.14,15 It is of relevance to

45

which extent microplastics facilitate the transport of organic contaminants in freshwater

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ecosystems, particularly in light that they are often introduced in urban, polluted areas.16,17 The

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potential for microplastics to act as a sorbent for hydrophobic contaminants has been shown in

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several studies.15,18-22 Most of these studies focused on equilibrium partitioning of contaminants

49

between microplastics and water.

50

The aim of this study is to investigate the sorption kinetics of wastewater pollutants from

51

microplastics. Specifically, we analyze shifts of mass transfer from external film diffusion to

52

intraparticle diffusion in batch systems as a function of partition coefficients.23 We used

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frequently occurring wastewater contaminants to study their sorption properties from low-

54

density-polyethylene (LDPE) particles, which are frequently detected in the environment.24,25 In


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addition, we used standard humic acids (HA) which solubilizes organic contaminants in water

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and thus allows to cover a wide range of partition coefficients.26,27 Previous studies revealed that

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humic acids significantly impact desorption of hydrophobic compounds from organic phases into

58

aqueous solutions.28,29 This, however, depends on whether mass transfer is controlled by

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intraparticle or external film diffusion. The latter may be expressed by two mass-transfer

60

processes in series, an external and an internal one, respectively.30,31 In the present study, we

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derived a semi-analytical solution of mass transfer between particles and the bulk fluid

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considering both processes and experimentally validated it with compounds of different

63

hydrophobicity at different concentrations of dissolved organic matter.

64 65 66

Materials & Methods The suppliers of all chemicals and instruments are reported in the Supporting Information.

67 68

Batch experiments

69

Desorption kinetics was studied in batch experiments involving polyethylene spheres pre-

70

loaded with hydrophobic pollutants (phenanthrene, tonalide and benzophenone) with different

71

concentrations of humic acid in aqueous solution. Humic acid solutions were prepared by adding

72

2 g of a raw humic-acid standard to 1 L ultrapure water containing 2 mM phosphate-buffered

73

saline (PBS) buffer solution leading to a slightly alkaline pH of 7.7 and shaken overnight.

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Particles were removed by subsequently passing the solution through 1.5 µm, 0.7 µm, and 0.45

75

µm pore sized filters. To obtain a final concentration of 1 g L-1, the solution was diluted in 2 mM

76

PBS solution. The organic carbon fraction of the dissolved humic acids was 0.41. In the course

77

of the experiments, frequent DOC and pH measurements were performed to control the stability.


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Blank measurements of DOM solutions revealed that they contained no substances which might

79

distort the measurement of the dissolved pollutants. The polyethylene (PE) spheres were clear

80

particles without dye (density = 0.92 kg L-1) that are usually used as an ingredient of cosmetic

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products. The particles were approximately spherical shaped and had a diameter of 260 µm. The

82

microplastics were loaded with pollutants by shaking 2 g of them in a 200 mL methanol/water

83

solution (20/80 v/v) for 96 h and adding 80 µg of phenanthrene and 250 µg of tonalide or

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benzophenone. Chemicals were added one at a time in separate experiments to avoid mixture

85

effects. Methanol was added to decrease the partition coefficients which accelerates loading with

86

hydrophobic compounds. After shaking and sieving with 75 µm mesh, the microplastics were

87

rinsed three times with ultrapure water to prevent pollutants precipitating on the surface during

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subsequent drying under a gentle nitrogen stream. A subsample of microplastics were extracted

89

afterwards to determine the amount of pollutant uptake in the spheres. The extraction of

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microplastics was performed with cyclohexane. Analyzed concentrations (± relative standard

91

deviation) in the plastic were 42.8 (± 2.9%), 124 (± 1.4%), and 15.8 (± 0.5%) µg g-1 of

92

phenanthrene, tonalide, and benzophenone, respectively. Relevant properties of the selected

93

compounds are shown in Table 1. The concentration of microplastics in batch experiments was

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kept constant (1 g L-1) while six different concentrations of humic acids (0, 0.15, 0.25, 0.50,

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0.75, 1.00 g L-1) were used. We added 0.25 g microplastics, loaded with the contaminants, to 250

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mL of contaminant-free aqueous solutions in 0.25 L amber glass bottles. To avoid

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biodegradation as well as photooxidation, we added 0.05 g L-1 of NaN3 and kept the bottles in

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the dark. The lids were equipped with PTFE seals. The bottles were constantly shaken on a

99

horizontal shaker with rotational speed of 150 rpm and kept in a room constantly tempered to

100

20° C. We took samples of 1 mL solution in duplicates at 10, 20, 40 min, 1, 2, 4, 8, 24, 48, 96 h,


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and last sampling after 120, 170, or 240 h and processed them as described below. Due to the

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sampling procedure, the liquid-to-solid ratio changed less than 10%, which was neglected in the

103

subsequent analysis of the data since the change is in the range of the analytical error. As shown

104

later (Figure 3), equilibration occurred latest after 8 h. Sorption to glass walls, seals etc. of the

105

batch system was determined in triplicate using a 200 µg L-1 solution of the pollutants and was

106

found to be smaller than the uncertainty of the GC measurements.

107 108

Chemical Analysis

109

We determined the concentrations of the selected pollutants in the bulk aqueous solution

110

(water including dissolved organic matter) by GC-MS. Samples of 1 mL solution were taken at

111

the described time points using a glass pipette and 10 µL of deuterated internal standard were

112

added. Subsequently the samples were extracted with 400 µL of cyclohexane and analyzed by

113

GC-MS. For separation, a 30 m long dimethylsiloxane-coated capillary column with 0.025 mm

114

inner diameter and 0.25 µm film thickness and helium as carrier gas were used (flow rate 0.7 mL

115

min-1). The mass-to-charge ratios used for quantification were 105, 178, and 243 for

116

benzophenone, phenanthrene, and tonalide, respectively.

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Table 1: Compound-specific properties of the chosen compounds. Daq and DPE are the diffusion

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coefficients in water and polyethylene, respectively. Data were obtained as specified in the

120

subtext. Parameter molecular weight [g mol-1]a molecular volume [cm3]a Daq [m2 s-1] after WORCHb DPE [m2 s-1] after LOHMANNc DPE [m2 s-1] after RUSINAd water solubility [mg L-1]a,e melting point [°C]a,f subcooled liquid solubility [mg L-1]g

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log KOWa,e

Phenanthrene

Tonalide

Benzophenone

178.2

258.2

188.2

157.7

280.9

167.5

7.6×10-10

6.2×10-10

7.4×10-10

4.1×10-13

6.7×10-15

3.0×10-13

3.5×10-13

2.8×10-14

2.6×10-13

1.15

1.25

137

99.2

57.0

47.8

4.2

2.9

260

4.5

5.7

3.2

a data obtained from the ChemSpider database (www.chemspider.com)

122

b calculated according to Worch32

123

c calculated according to Lohmann33 based on the molecular volume

124

d calculated according to Rusina et al.34 based on the molecular weight

125

e values for Tonalide were taken from Balk and Ford35

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f value for Tonalide was taken from Paasivirta et al.36

127

g calculated according to Kan and Tomson37 and Liu et al.38

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Theory

130

Equilibrium Partitioning

131 132

Linear partitioning of a compound between two phases, here polyethylene (PE) and water, is given as the concentration ratio in equilibrium (i.e. the partition coefficient in L kg-1):

= in equilibrium

(1)

133

By introducing a second dissolved phase, here humic acids, the chemical has to equilibrate

134

∗ between the overall between the three phases in the system and the partition coefficient

135

aqueous solution and the solids decreases with increasing concentration [kg L-1] of dissolved

136

organic matter (DOM) is:39 ∗ =

137

= ∗ 1 + ,

(2)

is the partition coefficient [L kg-1] between the dissolved organic matter and pure water.

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Only if the product ∙ becomes larger than unity, a significant change in partitioning

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of a compound between aqueous solution and solids may be expected. Since DOM contents

140

typically are below 0.001 kg L-1, only compounds with larger than 1000 are significantly

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∗ affected. represents the concentration in the bulk solution, i.e. the freely dissolved

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concentration plus the concentration in the DOM phase. Based on the mass balance in the three-

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∗ [µg L-1] in the DOM-inclusive aqueous phase phase system, the equilibrium concentration ",

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∗ for given initial concentration (0) [µg kg-1] in the PE and (0) [µg L-1] in the aqueous

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phase (in our experiments always zero) can be computed as a function of the liquid-to-solid ratio

146

&" ⁄'( [L kg-1] and via the partition coefficients on the DOM-concentration by: ∗ , =

∗ (0) & (0) + '

& ∗ ' +

(3)


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Mass Transfer Model

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The mass transfer of organic pollutants between the particles and a bulk surrounding solution

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of finite volume comprises diffusion within the plastic particles and subsequent transfer from the

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particle surface through an aqueous boundary layer into the bulk solution.40,41 The slower process

151

controls the overall kinetics. The underlying assumptions for the analysis of our finite-volume

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batch experiments are: (i) the bulk solution is homogeneously mixed, (ii) the external mass

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transfer between the particles and the bulk solution is proportional to the difference of the

154

aqueous (DOM-inclusive) concentrations between the bulk solution and the particle surface, (iii)

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at the particle surface, local equilibrium between the two phases exists, and (iv) the mass flux

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within the plastic particles is by diffusion in the polymer. Additionally, we assumed equilibrium

157

partitioning between water and DOM. This conceptual framework is illustrated in Figure 1,

158

where we implicitly assume that the contaminant is restricted to the plastic particle with uniform

159

concentration in the initial state.

160 161

To consider both internal and external mass transfer in series, we formulate a coupled transport model. Within the plastic particles, we consider the diffusion equation in spherical coordinates:

162

163 164

* * . 2 * − + 1 = 0 *+ */ . / */

(4)

* 2 = 0 ∀+ */ 345

(5)

(/, + = 0) = (0)∀/

(6)

with a uniform initial concentration:

where DPE [m2 s-1], r [m], and t [s] denote the diffusion coefficient in PE, the radial coordinate, and time, respectively. CPE [µg kg-1] is the concentration in the plastic sphere. The mass flux


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through the external boundary layer must be identical to the internal mass flux at the particle

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surface: ∗ : = − ; −

167 168 169 170 171

(/( ) * < = = − > 2 ∗ */ 3

(7)

in which J [µg m L-1 s-1] and kW [m s-1] are the mass flux density and the aqueous mass transfer

∗ [µg L-1] denotes the concentration in the bulk solution, rP is the coefficient, respectively.

radius of the spherical particle, and ρPE [kg L-1] denotes its mass density.

In a finite bath, the concentration in the bulk phase changes according to the total mass flux across the area of all particles, leading to the following balance equation: ∗ (/( ) B 3 '

∗ =; ∗ − < = B+ / > &

(8)

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∗ which is subject to a known initial concentration (0), where mP [kg] and VW [L] denote the

173

mass of particles and the volume of water, respectively. No mass is stored in the aqueous

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boundary layer.

175

We derived the analytical solution of equations 4-8 after Laplace transformation in time (see

176

SI), and consider three cases of mass-transfer controls: (1) by external mass-transfer only, i.e. in

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the limit of → ∞, (2) by intraparticle diffusion only, i.e. in the limit = → ∞, and (3) by

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both processes. The analytical Laplace-transform solution of the bulk-phase concentration is

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back-transformed into the time domain by the numerical method of de Hoog42, implemented in

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Matlab.

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We fitted the model to the contaminant concentration data in water of the experiments

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described above. The initial concentrations (0) in the microplastics and "∗ (0) = 0 in the

183 184

water are known from the experimental set-up as well as liquid-to-solid ratio & ⁄' , the radius

/ and mass density > of the spheres. The partition coefficients of the three pollutants


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between PE and the pure water were determined from the late-time concentrations. We assumed

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that the external mass-transfer coefficient = of different pollutants scales with the known

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aqueous diffusion coefficient by H

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on the hydrodynamic conditions in the batch,43,44 which did not differ among the tests. Then,

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= /H , three values of , and three values of (one for each compound) were the

./J

(see Sherwood-relationship in SI). and depends otherwise

./J

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∗ fitting parameters. We fitted all experiments jointly, computing the partition coefficients

191

for each DOM-concentration by equation 2. Note, that the intensity of shaking affects the

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external mass transfer, but the shaking was kept constant in all experiments of the present study.

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Thus, the fitted coefficient = /H

./J

is identical for all compounds and needs to be identified by

194

jointly fitting all experiments. Fitting = for each compound individually, would have added

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more degrees of freedom, and we may not have retrieved the H -scaling valid for turbulent

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boundary layers.43,44

./J

197

Log-parameters were estimated using DREAM(ZS), a Markov-Chain Monte-Carlo method

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that estimates distributions of the log-parameters conditioned on the measurements.45,46 A

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uniform prior distribution within a wide range for each log-parameter was considered. As

200

objective function, we took the sum of the absolute differences between all measurements and

201

simulated values. The computed mean absolute errors (MAE) and root mean square errors

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(RMSE) as reported in the results are based on a conditional sample size of 3000. Furthermore,

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we report the 5-95% quantiles of the estimated parameters to assess their uncertainty.

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Analysis of Characteristic Times

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As explained above, overall mass transfer is controlled by an external and an internal process

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in series. To evaluate the relative importance of the two mass transfer processes, we derived the

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characteristic time τch [s] from our Laplace-transform analytical solution. It is defined as: NOP

T

Q5 R"∗ (+) − SB+ = "∗ (0) −

(9)

209

and summarizes how long equilibration between the bulk solution and the spheres takes. The

210

characteristic time can be split into a characteristic time for the case of external mass transfer: UV3WHX NOP =

211

∗ > /

' ∗ Y1 + & Z 3 =

(10)

and a characteristic time for the case of internal mass transfer: [WV3WHX NOP =

/ . ' ∗ Y1 + & Z 15

(11)

212

The two characteristic times are additive, i.e. the overall mass transfer is slower than either of

213

∗ the single processes. Note, that for increasing , the characteristic time in the case of

214

∗ externally controlled mass transfer (equation 10) becomes independent of whereas the

215

characteristic time of the internally controlled mass transfer (equation 11) decreases with

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∗ increasing . In rivers or lakes, & tends to infinity (“infinite bath”) and the term in the

217

parentheses of equations 10 & 11 becomes 1. While in equation 10 the characteristic time refers

218

to 63.2% of the equilibrium concentration achieved, this does not hold for equation 11 where the

219

∗ degree of equilibration depends on the liquid-to-solid ratio and (see SI). Hence, for

220

∙ ' /& ranging from 0.01 (infinite bath) to 30 (maximum in our experiments),

221

[WV3WHX NOP corresponds to the timepoint when 67.5 - 88.9% of the equilibrium concentration has

222

been reached.


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The relative importance of the respective mass-transfer process for the overall mass transfer can be expressed as the ratio of their characteristic times: UV3WHX NOP [WV3WHX NOP

∗ 5 > = = /

(12)

225

For values > 1, the mass transfer in the water is limiting, whereas mass transfer in the particles

226

controls kinetics for values < 1. Equation 12 exemplifies that the relative importance of the two

227

mass-transfer processes does not depend on the liquid-to-solid ratio. Mass transfer of

228

hydrophobic substances with high partition coefficients are externally limited. Furthermore,

229

equation 11 shows that for internally limited kinetics a decreasing partition coefficient slows

230

down kinetics in a batch system despite increasing the equilibrium concentration in the water

231

(equation 3).

232 233

Results & Discussion

234

Equilibrium Partitioning

235

Figure 2 (top) shows the measured equilibrium concentrations in the aqueous phase as function

236

of the DOM concentration in the respective batches. The concentration in water increases with

237

increasing DOM as expected from equation 3. Figure 2 (bottom) shows the calculated partition

238

∗ coefficients between PE and the aqueous solution as function of the DOM concentration.

239

∗ ∗ We fixed the measured for zero DOM and calculated as a function of DOM

240

according to equation 2 within the joint fit of all experiments. Figure (2) bottom shows that

241

∗ ∗ predicted with equation 2 matches measured values very well. The measured -

242

values increase with increasing octanol-water partition coefficient of the compounds as

243

expected. Measured and calculated partition coefficients into humic acid ( ) for


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phenanthrene and tonalide show good agreement whereas the partition coefficients for

245

benzophenone show relatively large deviations, which we attribute to the insignificant influence

246

of DOM. Under equilibrium conditions, increasing the DOM concentration caused the fraction of

247

pollutants remaining in the microplastics to decrease.

248

Table 2 lists the fitted -values, together with their uncertainty range, for every substance

249

and the associated -values in which the humic acid concentrations are normalized with

250

respect to the fraction of organic carbon (0.41). Table 2 also includes two metrics of the quality

251

of the model fits for each compound: the mean absolute error (MAE), and the root mean square

252

error (RMSE). All obtained - values are in good agreement with literature values.47-50

253

Possible sorption of DOM on/in microplastics could furthermore alter both the sorption

254

behavior of certain compounds and the sorption properties of the particles themselves.51,52

255

However, we performed fluorescence measurements with DOM and different amounts of

256

microplastics indicating that no sorption occurred. These results are confirmed by previous

257

findings reporting that interactions between DOM and soil particles mainly took place between

258

DOM and the mineral phase and that interactions between humic acids and PE were found to be

259

negligible, respectively.52,53

260 261

Desorption Kinetics

262

We analyzed desorption kinetics by fitting the complete coupled model described above.

263

Figure 3 shows the measured concentration time series and model results of the fitted complete

264

model (blue solid lines), model predictions considering only external mass transfer using the

265

parameters of the complete model (red dashed line), and predictions considering only

266

intraparticle diffusion (green dashed lines). Equilibrium in the batches was usually reached at


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latest after 8 h. Table 2 contains the estimated values of the mass transfer coefficients and the

268

intraparticle diffusion coefficient as well as the ranges of their 5-95% quantiles.


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Table 2: Partitioning and mass transfer parameters. Mean absolute errors (MAE) and root mean

270

square errors (RMSE) were calculated based on the variability of the experimental data. KDOM,

271

kW, and DPE were fitted within the model (geometric means of the posterior distribution). KDOC

272

was subsequently calculated from the 41.2% of OC in the DOM. The estimated values are

273

reported together with their respective 5-95% quantiles (range).

Parameter MAE [µg L-1] RMSE [µg L-1] KPE-W [L kg-1] KDOM [L kg-1] range [L kg-1] KDOC [L kg-1] range [L kg-1] kW [m s-1] range [m s-1] DPE [m2 s-1] range [m2 s-1]

Phenanthrene

Tonalide

Benzophenone

0.47 0.61 9,630 5,500 5,200-5,800 13,400 12,500-14,100 7.2×10-5 5.6×10-5-9.4×10-5 1.6×10-13 1.3×10-13-1.9×10-13

0.81 1.15 31,800 4,000 3,700-4,300 10,000 9,100-10,400 6.3×10-5 5.0×10-5-8.3×10-5 5.6×10-13 1.4×10-13-5.4×10-12

0.34 0.38 75 700 100-3,000 1,700 200-7,100 7.0×10-5 5.5×10-5-9.3×10-5 1.7×10-12 1.5×10-12-1.9×10-12

274


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Phenanthrene

276

Figure 3A shows an excellent agreement between experimental and simulation results for

277

phenanthrene. At very early times, experimental data are lacking. At these times, the model

278

shows that external mass transfer always controls the overall mass transfer. At later times,

279

intraparticle diffusion becomes limiting. At zero or small DOM concentrations, the relative

280

importance of external mass transfer is larger than at high DOM concentrations. With increasing

281

∗ decreases and this shifts mass transfer control to intraparticle DOM concentrations

282

diffusion and slows down release kinetics in the batch system, which is predicted by equation 11.

283

The good agreement between the model jointly fitted over all DOM concentrations and the

284

measurements indicates that dominant mechanisms are captured well by the model.

285

Tonalide

286

Figure 3B shows the experimental and simulation results for the comparably hydrophobic

287

compound tonalide. Here, the kinetics are strongly controlled by the external mass transfer for all

288

DOM concentrations. Only at the highest DOM concentrations, the full model and the model

289

disregarding intraparticle diffusion start to deviate slightly. Compared to phenanthrene and

290

benzophenone, the equilibrium concentration in the aqueous phase is the lowest, which is in

291

accordance with the higher hydrophobicity. KDOM is lower than expected from hydrophobicity

292

which may be due to less specific interactions compared to the highly aromatic phenanthrene. As

293

explained above, the data are not sensitive to intraparticle diffusion, which results in a high

294

uncertainty in the fitted intraparticle diffusion coefficient (Table 2).

295

Benzophenone

296

Figure 3C shows the experimental and simulation results for the least hydrophobic compound

297

investigated in this study, benzophenone. In comparison to the other compounds, it has the


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298

highest equilibrium concentration in the aqueous phase. The fraction of benzophenone remaining

299

in the microplastics after equilibration ranged from only 6% (without any DOM) to less than 3%

300

(for the three highest DOM concentrations). The effects of DOM on desorption of benzophenone

301

are negligible so that the fitted -values are extremely uncertain. Desorption kinetics are

302

always controlled by intraparticle diffusion, and the associated diffusion coefficient is fairly

303

certain. However, the estimated value is about one order of magnitude larger than values

304

calculated from empirical relationships (see Table 1).

305 306

While comparable studies indicated that increasing the DOM concentration generally

307

accelerates mass-transfer kinetics, we found the opposite in the batch system. This apparent

308

contradiction is explained by different boundary conditions (different liquid-to-solid ratios, finite

309

bath vs. infinite bath) and the use of different polymers.28,29 Note, that increasing DOM

310

accelerates the external mass transfer in the infinite bath and slows it down slightly in the finite

311

bath (Figure 4). Since the diffusion coefficients of DOM are a factor of two to three lower than

312

for our compounds mass transfer changes would be less pronounced if a large fraction partitions

313

into DOM.54 In our study this would, if at all, affect tonalide at high DOM concentrations.

314

However, the data and model do not show any significant influence of DOM and hence we did

315

not specifically account for this effect.

316

Regarding mass transfer under field conditions, studies on passive sampling indicated that it is

317

usually clearly limited by external mass transfer, for compounds with values similar to or

318

higher than for phenanthrene.55,56 Such passive samplers are frequently made of PE but are far

319

thinner than the spheres used in our study33 so that intraparticle diffusion is less restrictive

320

because of shorter diffusion distances. Only a limited number of studies indicated that


19


Page 20 of 37

321

intraparticle diffusion might be important for assessing the vector function of microplastics.19

322

Koelmans et al.57 investigated the role of surfactants and organic matter on desorption kinetics,

323

concluding that the internal mass transfer might typically be the rate limiting process. While the

324

latter authors modeled the kinetics by two first-order mass-exchange processes in series, we

325

considered true intraparticle diffusion. Both our model and the experimental findings suggest

326

that intraparticle diffusion is not permanently controlling the kinetics. However, Koelmans et

327

al.57 applied their model to larger particles with diameters of 0.4 and 1.3 mm which might

328

explain this contrast since internal mass transfer times becomes more relevant with increasing

329

particle size.

330

Other polymers such as polystyrene (PS), polyvinyl chloride (PVC), and polyamide (PA) have

331

glass transition temperatures > 50° C which are much higher than in polyethylene (-78° C) and

332

thus smaller diffusion coefficients.58,59 Therefore, we expect that diffusion coefficients of organic

333

compounds are lower within PS, PVC, and PA than in PE, so that the intraparticle diffusion may

334

be more restrictive in the overall mass-transfer process. Furthermore, for porous (as PS) or

335

weathered particles the effective diffusion coefficient needs to be derived for each individual

336

case. On the other hand, diffusion in polydimethylsiloxane (PDMS), which is frequently used as

337

a passive sampler, is much faster and hence mass transfer is often controlled by external mass

338

transfer.34 Often thin PDMS fibers are used (i.e. diameters of 6.5 µm)29 which also favors

339

external mass transfer control.

340

Finally, DOM concentrations used in the batch experiments are higher than concentrations

341

usually found in rivers or lakes. High DOM-concentrations are more likely for (urban)

342

wastewater which are also hotspots for organic contaminants and microplastics.17,60 Since

343

sorption and desorption kinetics are equal, the mass transfer under high DOM conditions can be


20

Page 21 of 37


344

used to estimate the loading of microplastics with contaminants in wastewater whereas the

345

results from experiments without or with low DOM concentrations can be applied to assess the

346

microplastics-facilitated transport of pollutants in large aquatic ecosystems (rivers and lakes).

347

The equilibration times would increase under field conditions where the volume-to-solids ratio

348

∗ for intraparticle diffusion, but increase approaches infinity (and become independent on

349

∗ with increasing for external mass transfer control).

350 351

Mass Transfer Analysis and Implications

352

While the experimental data reflect the specific conditions of the analyzed batch system, the

353

model can be applied to different conditions from a finite bath with high solid-to-liquid ratio to

354

the infinite bath in which particles are strongly diluted. In the experiments, we could show how

355

differences in effective partition coefficient alter not only sorption equilibrium but also the mass-

356

transfer kinetics. In this section, we use the calibrated model to explore conditions which are

357

more comparable to the field. We do this by means of the characteristic times, computed by

358

∗ and solid-toequations 10-12, spanning wide ranges of effective partition coefficients

359

liquid ratios ' /& .

360

Figure 4 shows the corresponding characteristic times, keeping the diffusion coefficients

361

constant. While Figures 4C and 4D show the individual contributions of internal and external

362

mass transfer to the characteristic time according to equations 11 and 10, respectively, Figure 4A

363

shows the total characteristic time of mass transfer (equation 9), and Figure 4B the ratio of the

364

two times (equation 12). At high ' /& ratios, overall mass-transfer kinetics are accelerated

365

∗ with increasing , whereas they are slowed down at very low ' /& ratios, and approach

366

infinite bath conditions. Under finite bath conditions, a decreasing effective partition coefficient


21


367 368

Page 22 of 37

[WV3WHX increases the characteristic time NOP of internal mass transfer while that of external mass

UV3WHX transfer NOP is hardly affected when considering strongly sorbing compounds (Figure 4 C

369

∗ and D). We manipulated the effective partition coefficient in our experiments by adding

370

DOM, thus covering a wide range of kinetics limited by both internal and external mass transfer.

371

Nevertheless, the microplastic concentration used in our study was considerably higher than

372

values found in the environment. Mintenig et al.61 sampled effluents of wastewater treatment

373

plants and identified and quantified microplastics down to a size of 20 µm. Using a microplastics

374

concentration of 9 × 10J `a/+bcdef ' J as it was detected in the effluent of a wastewater

375

treatment plant in Germany61 and assuming that a quarter of these particles might be PE with a

376

radius comparable to that of the particles used in our study, we estimate environmentally relevant

377

PE concentrations in urban areas on the order of 1.7 × 10 i kg L l and correspond to infinite

378

bath conditions. We further assume partition coefficients as assembled for various organic

379

pollutants in the literature,33 resulting in the parameter range indicated by the red dashed line in

380

Figure 4. Applying such ' /& ratio, characteristic times of mass transfer may range between

381

hours (for compounds with low partition coefficients: intraparticle diffusion limits) and weeks

382

(for those with high partition coefficients external mass transfer limits). As discussed above, the

383

relative importance of internal and external mass transfer does not depend on the solid-to-liquid

384

ratio, improving the transferability from experimental lab conditions to the field. However, it

385

may depend on particle size (which can easily be measured) and on the mass-transfer constant

386

=" , which depends on the strength of turbulence in rivers. The exact expression of mass transfer

387

depend on the shape of the particles and can be derived for other geometric forms. The

388

qualitative findings on the relative importance of external and internal mass transfer are not

389

affected by the shape. Furthermore, microplastics may be covered with biofilms affecting the


22

Page 23 of 37


390

external mass transfer.62 Since the effective diffusion in biofilms is slower than in water, the

391

external mass transfer would be slowed down. To consider this, diffusive mass transfer through

392

the biolayer could explicitly be modelled. The water film thickness in our experiments was in the

393

range of 10 µm and hence the external mass transfer may be substantially slowed down if the

394

biofilm cover exceeds a certain thickness or density. A reliable model on this, however, requires

395

more experimental data, in particular on diffusion coefficients in biofilms and biofilm-plastic

396

partitioning.

397

The theoretical considerations of our study also apply to other suspended particles such as

398

suspended sediments in rivers where the solid-to-liquid ratio is typically in the range of

399

10 m kg L l to 10 J kg L l (which corresponds to our laboratory conditions).63 Well-defined

400

microplastic particles, as used here, are ideally suited for mass transfer studies under controlled

401

conditions but ultimately are only surrogates for particles occurring in the environment,

402

including microplastics in urban runoff and contaminated sediment particles. The latter are very

403

likely much more frequent than microplastics but undergo the same mass transfer characteristics

404

as discussed in this study.

405 406

Supporting Information

407

Details on the used chemicals and instruments as well as on the derivation of the model, mass

408

transfer analysis, and the fitting procedure. Furthermore, three Matlab codes are provided for

409

detailed comprehensibility.

410 411

Acknowledgements


23


Page 24 of 37

412

We would like to thank Thomas Wendel and Renate Seelig for their support regarding the

413

work in the laboratory. Furthermore, we thank Jana Meierdierks and Beate Escher for valuable

414

discussions and their support during the preparation of this manuscript. This work was funded by

415

the Deutsche Forschungsgemeinschaft (DFG) under the grant agreement GR 971/13-1. We also

416

thank three anonymous reviewers for valuable remarks and useful comments.


24

Page 25 of 37

417 418


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Figure 1: Conceptual framework of the mass transfer model. A hypothetical concentration profile of a substance is shown. The concentration in the particle decreases from the center to the edge whereas the concentration in water decreases with increasing distance from the ∗ particle. and denote the concentration in water and particle, respectively. At the

interface, local equilibrium is assumed hence the concentration at the interface is: =

596

∗ ∗

597


34

Page 35 of 37


Figure 2: Measured equilibrium concentrations in the aqueous phase against the concentration ∗ of DOM in the batch (top) and relationships between partition coefficients and the

concentration of DOM in the solution (bottom), dashed lines are calculated by equation 3 (top) and equation 2 (bottom) based on values reported in Table 2.

598 ACS Paragon Plus Environment

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Page 36 of 37

Figure 3: Desorption kinetics of, phenanthrene (A), tonalide (B), and benzophenone (C) from microplastics at different DOM contents. Models for film diffusion, intraparticle diffusion, and the coupled diffusion are shown with the red dashed, 599

the green dashed, and the solid blue line, respectively. The horizontal black dotted line shows the equilibrium ACS Paragon Plus Environment

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Page 37 of 37


Figure 4: Characteristic times of mass transfer as function of the solid-to-liquid ratio ' /& and ∗ the partition coefficient . A: total characteristic time; B: ratio of external to internal

characteristic time; C: internal characteristic time; D: external characteristic time of mass transfer. The solid red line shows the range of experimental conditions while the dashed red line refers to microplastics concentrations found in the environment.61 Solid-to-liquid ratios of suspended sediments in rivers typically range from 10 m − 10 J kg L l .63 600


37

Shift in Mass Transfer of Wastewater Contaminants ... - ACS Publications

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