ARTICLE pubs.acs.org/JPCC
Novel Methodology for the Estimation of Chemical Warfare Agent Mass Transport Dynamics. Part II: Absorption Matthew P. Willis,* Brent A. Mantooth, and Teri A. Lalain Decontamination Sciences Branch, U.S. Army, Edgewood Chemical and Biological Center, 5183 Blackhawk Road, Aberdeen Proving Ground, Maryland 21010-5424, United States ABSTRACT: A novel experimental and computational methodology has been developed for estimating Fickian mass transport parameters of organic molecules through stagnant mediums such as air, paints, or polymeric substrates. Dynamic contact angle experiments were performed to measure the droplet volume evolution with the chemical warfare agent bis(2-chloroethyl) sulfide (distilled mustard, known as the chemical warfare agent HD) on military-relevant substrates. A finite element model for simultaneous evaporation and absorption was used to analyze the experimental data and determine the mass transport parameter values of the agent in the absorptive material. The computational model was validated by comparison with the results of a complementary experimental technique involving testing for HD vapor emission from the contaminated material. The model predicted HD vapor emission rates from a silicone elastomer substrate for contamination conditions not directly tested. The simulation results show that the model parameters can be used to provide an accurate prediction of the absorbed mass and concentration distribution in the substrate at a range of environmental temperatures (20 to 50 °C) and contamination times (0 to infinite min). Predicting the absorbed mass in various substrate types and environmental conditions enables an accurate prediction of the resulting hazards from contaminated materials.
’ INTRODUCTION
mass transport of the chemical agent through the material and into the environment. The objective of the developed methodology is to characterize the mass transport mechanism and transport coefficients of the chemical warfare agent bis(2-chloroethyl) sulfide (distilled mustard, known as the agent HD) into the air and into various types of substrates, such as polymers including paints, plastics, and elastomers at various temperatures. The techniques provide a simple methodology for accurately estimating the values of physics-based parameters (i.e., saturation and diffusivity) that enable accurate modeling for a wide range of agent-substrate combinations and variable temperatures. HD mass transport has been studied extensively in porous systems such as cement,1 sand,2,3 or fabrics4 as well as nonporous elastomeric systems.57 Contact angle measurements have been used to evaluate the mass transport of chemical warfare agents into porous substrates such as sand.2 These studies determined that the experimental observation of liquid penetration depth into the substrate could be used in conjunction with computational models8 to estimate the magnitude of single-phase mass transport permeability coefficients. Additional testing was performed to develop models for liquid spreading on porous substrates.911 During the porous substrate testing, there were competing forces between lateral mass transport, due to liquid spreading, and vertical mass transport, due to liquid sorption into the substrate. Typically, the substrate of interest is assumed to have infinite thickness,12 which minimizes its applicability to thin
Background. The contamination of a substrate by a chemical warfare agent is a complex system of interacting processes involving various mechanisms of mass transport, chemistry, and physics. Understanding the contamination process is vital to the development of decontaminants and decontamination predictive models and toward developing an understanding the driving forces that generate exposure hazards to unprotected personnel. It is vital to the recovery and restoration of assets that have been contaminated with chemical agent to develop robust decontaminants that are safe for operator use. Simulating such systems requires a firm understanding of the processes that occur during agent-substrate interactions. The present model represents the mass transport, chemistry, and physics of the agent substrate contamination process. These physics-based models are used to predict the absorbed agent and subsequent vapor emission from the substrate, which, in turn, enables the prediction of potential vapor hazards. Models of the contamination process are the framework used to develop models for decontamination and postdecontamination hazard prediction. Vapor emission models can be composed of empirical correlations or physics-based evaluations. Although a comprehensive physics-based model is more computationally expensive, it enables an accurate scale-up of phenomena from lab-scale experiments to operationally relevant scenarios. Furthermore, physics-based models enable the prediction of mass transport rates beyond the explicit conditions evaluated. Unprotected personnel can be exposed to contaminant from contaminated or postdecontaminated items as a result of the This article not subject to U.S. Copyright. Published 2011 by the American Chemical Society
Received: September 12, 2011 Revised: December 5, 2011 Published: December 06, 2011 546
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The Journal of Physical Chemistry C paint films or long contaminant residence times that could yield agent “breakthrough” through the substrate. In addition, most porous transport testing was performed with nonvolatile liquids, so mass loss due to evaporation was neglected. Whereas the experimental techniques presented in this document are applicable to both porous and nonporous transport mechanisms, the substrates of interest and contaminants in this study exhibited a nonporous transport system. Systems that are mediated by molecular diffusion depend on the magnitude of the diffusion coefficient. Traditionally, three main approaches are used to determine the diffusion coefficient of a molecule in a substrate: the sorption, integral, and differential methods.13 In the sorption method, the substrate is immersed in the liquid or vapor of interest (at a constant pressure), and the absorbed mass is measured gravimetrically as a function of time. An analytical solution to Fick’s second law of diffusion can be empirically fit to the experimental data to calculate the diffusion coefficient. However, the accuracy of the method is limited by the ability to measure small changes in mass absorbed by the substrate over very long time periods. Such methods have been used to estimate the mass transport rate of various chemical warfare agents into polymeric substrates.7 The differential method applies a constant partial pressure gradient across a substrate and measures the mass flow rate across the sample. Typically, the differential method requires advanced mass transport-measuring techniques and an independent sample of the substrate, which can be difficult for paint systems (because paints are typically applied to an impermeable base substrate). The integral method, which is more commonly used, relies on a variable pressure gradient across the film to measure diffusivity.14 However, the integral method is also limited to thicker and more physically robust samples. Recent contact angle measurements have been used in conjunction with a finite element model to evaluate the evaporation rate of HD on impermeable substrates.15 Additional models, used to represent uptake of a liquid into a permeable surface, have utilized a thin film of liquid applied to a surface, resulting in a uniform, one-dimensional system.16 However, the interaction between sessile droplets and a permeable substrate presents a multidimensional system with simultaneous transport events of evaporation, adsorption, absorption, and surface spreading. Therefore, there has been a disparity of comprehensive mass transport studies. There are models for the transport of nonvolatile chemicals into porous or permeable substrates and models for the transport of volatile chemicals into the air from impermeable substrates but few that model simultaneous evaporation, adsorption, and absorption into permeable substrates. For this reason, a novel experimental and computational methodology has been developed for estimating Fickian mass transport parameters of organic molecules through stagnant mediums such as air, paints, or polymeric substrates. Dynamic contact angle experiments were performed with HD on military-relevant substrates of interest to measure experimentally the liquid droplet volume evolution over time. A finite element model for simultaneous evaporation and absorption was used to analyze the experimental data and determine the mass transport parameter values. The computational model was validated by comparison with the results of HD vapor emission testing from additional substrates of interest. In addition, the model was able to predict HD emission rates from a silicone substrate for contamination conditions that were not directly tested. The simulation results show that the model parameters can be used to provide an
ARTICLE
accurate prediction of the remaining agent mass and concentration distribution in the substrate at a range of environmental temperatures (20 to 50 °C) and contamination times (0 to infinite min). Predicting the absorbed mass in various substrate types and environmental conditions enables an accurate prediction of the resulting hazards from contaminated materials.
’ EXPERIMENTAL SECTION The experimental setup used to measured the dynamics of droplet volume over time was described in Part I of this manuscript series.15 The chemical used in this study was Chemical Agent Standard Reference Material (CASARM, 98.0% purity) grade bis(2-chloroethyl) sulfide (distilled mustard, or HD). Purity information was obtained from either NMR or GS-MS analyses and maintained on file. Chemical agents and other select contaminants are used only in properly certified surety facilities, capable of handling such chemicals safely. The personnel handling the chemical agents for this study were fully trained and certified for such operations. A suite of independent experimental methods are used to validate the model results. The panel test is intended to evaluate indirectly the contamination profile of an absorbed chemical within a substrate. During the panel test, panels are preconditioned, contaminated with a chemical, and aged for a specified residence time. The residual agent test measures the total quantity of agent present in and on the test material that could pose a future health hazard. The vapor test measures the vapor flux of a contaminant from a sample material (panel) after the contamination process that could pose a hazard to unprotected personnel. The test methods are detailed in the 2007 source document17 developed at the U.S. Army Edgewood Chemical Biological Center in Maryland. The residual agent test was performed in accordance with the 2007 source document test procedure 6-E, step 8.17 The substrate was placed face-up in an 8 oz clear, straight-sided glass vial with Teflon-lined polypropylene lid (Thomas Scientific, product number 1755F12). Extraction solvent (20 mL chloroform, Sigma-Aldrich) was added to the vial using a bottle-top organic solvent dispenser (BrandTech, part number 4701351). The substrate remained in the extraction solvent for 60 min. A Pasteur transfer pipet (Fisher Scientific, part number 13-678-8C) was used to place a sample into a gas chromatography (GC) vial as an undiluted sample. Samples were diluted such that the concentration was within the analytical calibration range. All dilutions were prepared using Gilson Microman positive displacement pipettes (Gilson product numbers M10, M25, M100, M250, and M1000). Separation of analytes was performed by GC, and detection was performed by a mass spectrometer (MS) for confident quantification and identification of the analytes of interest (Agilent 6890/7890 GC equipped with a 5975 mass selective detector (MSD)).18 The vapor emission test was performed in accordance with 2007 Source Document Test Procedure 7-A, step 8, immediately after the chemical residence period.17 The panel was placed in a sealed stainless-steel dynamic vapor chamber, and airflow was initiated at the appropriate experimental settings, including chamber and sampling airflow, temperature, and relative humidity. The vapor samples, collected on Markes sorbent tubes, were analyzed on an Agilent 6890 GC, equipped with a 5975 MSD. Introduction of a vapor sample was performed using a Markes thermal desorption system (TDS), which includes the Markes 547
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The Journal of Physical Chemistry C
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Ultra 100-tube Autosampler, the unity thermal desorber, and a sample mass flow controller.18 The vapor flux was calculated according to the source document test methodology. Data Review. A data quality assessment was performed for each data set. The processed data file was acceptable for mass transport parameter estimation modeling, if the following four criteria were met: (1) The droplet remained sessile. (2) The radius did not increase by >50% during the experimental time period (model assumes constant base radius during evaporation). (3) If spreading occurred, then it was axisymmetric from the initial touch-off location. (4) The droplet volume decreased during imaging period.
function of time ∇ 2 Pa ¼
1 Da, air
∂Pa ∂t
ð1Þ
where P a is the partial pressure of agent in the air and D a,air is the diffusivity of agent in the air. The agent distribution within the substrate is also described by Fick’s Law ∇ 2 Ca ¼
1 Da, sub
∂Ca ∂t
ð2Þ
where Ca is the concentration of agent in the substrate and D a,sub is the diffusivity of agent in the substrate. The adsorption and desorption of agent at the interface between the air and the substrate are described by a linear isotherm
’ MATHEMATICAL MODEL AND METHOD OF ANALYSIS
Ca ¼ kPa
Mathematical Model for Absorption. The mathematical
ð3Þ
where the isotherm constant k is defined as the ratio of saturation concentrations in the substrate and air, respectively
system of interest is a sessile drop of liquid with the form of a spherical cap, situated on a horizontal substrate. The spherical cap geometry is assumed to be valid when gravitational forces can be neglected in the system. The spherical cap approximation can typically be used for small values of the dimensionless Bond number (Bo), which gives the ratio between hydrostatic forces and surface tension forces. For a 1 μL droplet at 20 °C, Bo = 0.176 for HD, indicating that the spherical cap assumption is valid for the present system. Extrand et al.19 developed an expression for the critical volume at which droplets will change from a sphericalcap shape to a shape distorted by gravity. According to this expression, the critical volume at 20 °C is 16 μL for the distortion of HD on glass, further demonstrating the validity of the spherical cap geometry. On permeable substrates, droplets evolve from their equilibrium shape due to simultaneous evaporation into the air and absorption into the substrate. Fick’s second law describes the change in agent distribution within the air as a
k¼
Csat, sub Psat, air
ð4Þ
The simulation code is composed of a multiphysics model that couples agent distribution within the air, agent distribution within the substrate, and a moving boundary code, which describes the droplet shape’s evolution with time. Because of symmetry in the system, an axi-symmetric 2-D radial geometry was employed in the model. The system geometry is given in Figure 1, and the boundary conditions are given in Table 1. The top domain in Figure 1 represents the air within the environmental chamber, and the bottom domain represents the substrate. The saturation concentration of agent in the air (Psat,air) is given by the agent’s vapor pressure at the specified temperature. The diffusivity of agent in the air (Da,air) is specified by the values predicted in Part I of this Article series. The height of the droplet at a given radial location r is given by hdrop(r). For the purposes of the simulation, it was assumed that the radius of the droplet was static throughout the contamination process after the initial droplet shape equilibration (validated with experimental results for the current agent-substrate combinations). The initial interaction area (obtained within seconds) between the liquid contaminant and the polymeric substrate is mediated by the difference between the critical liquid surface tension and the critical surface energy of the substrate. The elastomeric substrate chosen for the current study had a surface energy value lower
Figure 1. Simulation domain for COMSOL model-predicting droplet shape change on permeable substrates.
Table 1. Boundary Conditions for COMSOL Permeable Substrate Model boundary
description
diffusion: Pagent,air
diffusion: Cagent,sub
moving mesh
1
radial symmetry
axial symmetry
n/a
z: free displacement
2
chamber boundary
insulation
n/a
no displacement
3
chamber boundary
insulation
n/a
no displacement
4
substrate surface
Pagent,air = kCagent,sub
Cagent,sub = Pagent,air/k
no displacement
5
liquidair interface
Pagent,air = Psat,air
n/a
z: hdrop(r)
6
liquidsubstrate interface
n/a
Cagent,sub = Csat,agent
r: no displacement n/a
7
radial symmetry
n/a
axial symmetry
n/a
8
substrate bottom
n/a
insulation
n/a
9
substrate edge
n/a
insulation
n/a
r: no displacement
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than the critical surface tension of HD to minimize liquid spreading after the initial droplet shape equilibration period. The agentmaterial combination provided a system where the model assumption of a constant contaminated area was maintained. At time zero, the mass of agent on the surface of the substrate is given by moagent ¼ Vdrop Fagent
ð5Þ
where Vdrop is the drop volume as specified by the experimental conditions and Fagent is the liquid density of the agent. The droplet contact angle (θ), radius (Rdrop), and height (H) characterize the droplet geometry, which mediates the interaction area between the liquid droplet and the vapor phase. The droplet radius (which is assumed constant throughout the contamination period) mediates the interaction area between the liquid droplet and the substrate. At any given time (t) during the simulation, the mass of agent in the air is given by a volume integral over the domain mðtÞair agent ¼ 2πMW
ZH ZR chamber chamber air 0
Cagent ðt, r, zÞr dr dz
0
Figure 2. Profile images of HD on silicone and glass substrates at 20 and 50 °C. The images illustrate different disappearance rates of the drops based on evaporation and absorption.
substrate to predict the drop volume evolution. The simulation results are compared with experimental data to estimate the values of the unknown mass transport parameters for the substrate. The error term that is used as a metric for the optimization routines goodness-of-fit is the mean-square error of the drop volume over time compared with the experimental data. The finite element simulations were developed in COMSOL v. 3.4, a commercially available multiphysics simulation tool. A Windows 7, 64-bit Pentium, quad-core dual processor, 2.2 GHz system with 12 GB of memory was used to perform the simulations, which typically took
