ARTICLE pubs.acs.org/JPCC
Novel Methodology for the Estimation of Chemical Warfare Agent Mass Transport Dynamics, Part I: Evaporation 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 contact angle experimental and computational methodology has been developed to estimate mass transport parameters for the evaporation of water and bis(2chloroethyl) sulfide (distilled mustard, known as the chemical warfare agent HD) on homogeneous, impermeable, substrates of interest. The model uses a finite element technique to simulate the evaporation of a liquid droplet into air. A regression technique is applied to experimental contact angle data to determine the temperature-dependent mass transport parameters (i.e., the diffusivity of the agent in air). The technique predicted the diffusion coefficient for water in air within 1% at 40 °C. The methodology was used to evaluate the evaporation of HD into air at several temperatures, which may be used to develop accurate predictions for vapor emission hazards due to vapor-phase HD. Evaporation of liquid HD generates potential hazards to unprotected personnel. Modeling this process on nonsorptive substrates is the first step toward enable modeling contamination on absorptive substrates. The novel methodology can be applied to other chemicals and therefore may be implemented as a preliminary assessment of the chemicals’ ability to evaporate, which can generate the potential for a chemical vapor hazard. The physics-based models, combined with the generated physical parameter values, enable the prediction of vapor emission hazards from the substrate. The application of this model is intended to simulate chemical warfare agents; however, it is applicable to any liquid on a surface.
’ INTRODUCTION
The evaporation rate of a liquid into an environment is mediated by its diffusion rate through the surrounding air environment. Previously, Hu and Larson used contact angle measurements in conjunction with a quasi-steady-state, finite element model to evaluate the evaporation rate of water on impermeable substrates.1 An empirical correlation between droplet evaporation rate and the droplet geometry was established, which demonstrated good agreement with experimental observations. However, the derived correlation was valid only for the specific system studied (free convection into an open-air environment). For the results to be applicable beyond the scope of the experimental regime studied, mass transport parameters, such as the diffusivity, must be determined. Erbil et al. have reviewed some of the empirical relationships to approximate the temperaturedependent diffusivity of gases.2 However, more accurate estimates or experimental confirmation of the transport parameters are needed for accurate modeling of the contamination system and an accurate assessment of vapor hazards. Computational fluid dynamics (CFD) models have been used to predict the emission of volatile organic compounds (VOCs) into the air from various building materials.35 One challenge with CFD models is solution convergence due to the stiffness of the transport model. As a result, the dynamics within the material contrast with dynamics in the air by several orders of magnitude.
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 of 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 agentsubstrate interactions. The model represents the mass transport, chemistry, and physics of the agentsubstrate contamination process to predict vapor emission resulting from liquid evaporation from nonpermeable substrates. This technique provides the foundation to determine mass transport coefficients for absorbing materials. 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. 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 538
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One-dimensional discrete analytical models have been developed to characterize VOC emissions into the environment,6,7 and additional 1-D stochastic models have been developed to predict vapor-phase transport.8 Such models enable bulk-phase characterization of mass transport rates. However, for characterization of the discrete concentration distribution around an evaporating droplet, a multidimensional model is required. Several comprehensive models have been developed to characterize the physics mediating the evaporation rate of sessile liquid droplets.915 However, the implementation of such models as hazard prediction tools relies on accurate estimates of mass transfer coefficients over a wide range of experimental conditions. The mass transport of the chemical warfare agent bis(2chloroethyl) sulfide (HD, distilled sulfur mustard) has been studied extensively in porous systems such as cement,16 sand,17,18 or fabrics19 as well as nonporous elastomeric systems.2022 However, the characterization of mass transport rates through the air for vapor hazard evaluation has not been thoroughly employed. For this study, droplets of chemical warfare agent were placed on an impermeable substrate and allowed to evaporate into a temperature-controlled environment. A finite element model was developed to predict the transport of the chemical agent into the air for the prediction of mass transport parameters. The parameter estimation results demonstrate that the values obtained from the present methodology can be used to provide an accurate prediction of the evaporation rate at a range of environmental temperatures (20 to 50 °C), which enable the prediction of vapor hazards from contaminated substrates. Such predictions were previously difficult because of the complicated and restrictive conditions used to estimate the mass transport parameters. However, this novel technique provides the foundation required to characterize mass transport parameters for permeable substrates.
safely. The personnel handling the chemical agents for this study were fully trained and certified for such operations. Laboratory tools, such as pipettes, were used in accordance with the vendor’s instructions and any applicable ISO standards. All liquid-dispensing tools were regularly calibrated, and the calibration history was maintained by the quality manager. The cameras were calibrated for pixel distance using a machined stainless steel calibration sphere (outer diameter 3.969 ( 0.0025 mm). The substrate types used for the present study were aluminum 7075 and borosilicate glass. Each substrate was rinsed with deionized (DI) water, allowed to air-dry for 10 min, and placed into the environmental chamber at the specified temperature setting ranging from 2060 °C for water and 2050 °C for HD. The environmental chamber was allowed to equilibrate for at least 10 min prior to contamination. The contaminant was removed from cold storage and allowed to equilibrate to room temperature in the test location’s chemical surety hood prior to testing. The agent delivery tool (Hamilton 10 μL syringe) was then filled with 1 μL of liquid agent and placed into the dosing syringe holder. The syringe needle was inserted into the chamber and allowed to equilibrate to the chamber temperature for at least 5 min. After the preconditioning period, a 1 μL droplet of the liquid agent was slowly dispensed from the syringe and then lightly touched off onto the substrate. Image acquisition was triggered automatically by the software as the droplet was touched off on the substrate. Images were acquired at a rate of 60 per second to enable the capturing of shortscale droplet dynamics immediately following droplet touch-off on the substrate. The capture frame rate was decreased throughout the experiment to accommodate long time scale imaging. The sessile droplet was imaged for times ranging from 10 to 300 min. 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 more than 50% during the experimental time period (model assumes constant base radius during evaporation). (3) If spreading occurred, it was axisymmetric from the initial touch-off location. (4) The droplet volume decreased during imaging period. The images acquired during the experiment were analyzed to measure the droplet height, droplet radius, and contact angle. The image analysis results apply the spherical cap assumptions to calculate the liquid volume as a function of time. The parameter estimation routines used by the model are optimized to the experimentally calculated droplet volume as a function of time.
’ EXPERIMENTAL PROCEDURES, MATERIALS, AND EQUIPMENT Experimental Setup. The experimental setup was composed of a contact angle analyzer (First Ten Angstroms, 1000C) modified to accommodate simultaneous profile and top-down imaging. The imaging system was composed of a profile camera (Prosilica GC750) with microscope lens (Edmund), illuminated by a blue LED backlight. The top-down image was taken by a camera (Prosilica GC750) illuminated by a ring light (Edmund, NT54173). The experiment was performed inside an aluminum and glass environmental chamber with an internal volume of 105 cm3. The environmental chamber provided a shield for airflow and currents within the fume hood to minimize the forced convection rate of the droplet. The environmental chamber temperature was controlled by a Peltier element with PID controller (monitored by steady-state probe, EE Elecktronik EE03). The chemical of interest was dispensed by a 10 μL syringe (Hamilton Gas-Tight) at a 45° angle from the substrate by an x-y-z axis rack and pinion actuator (Edmund, K55-023). Experimental Procedure. The chemicals used in this study were Chemical Agent Standard Reference Material (CASARM, 98.0% purity) grade bis(2-chloroethyl) sulfide (distilled mustard, or HD) and high-performance liquid chromatography (HPLC) grade water (Sigma). 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
’ MATHEMATICAL MODEL AND METHOD OF ANALYSIS Mathematical Model for Evaporation. The mathematical 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 valid when gravitational forces can be neglected in the system. A droplet is often characterized by 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 = 0.083 and 0.176 for water and HD, respectively, indicating that the spherical cap assumption is valid for the present system. Extrand et al. developed an expression for the critical volume at which droplets will change from a sphericalcap shape to a shape distorted by gravity.23 According to this expression, the critical volume at 20 °C is 45 μL for the distortion 539
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Table 1. Boundary Conditions for COMSOL Impermeable Substrate Model moving boundary: Pagent,air
Figure 1. Simulation domain for COMSOL droplet shape-change model, depicting evaporation on an impermeable substrate. The drop size has been exaggerated for illustration purposes.
∇ Pa ¼
1 Da, air
∂Pa ∂t
0
0
Cagent ðr, zÞr dr dz
2
chamber boundary
insulation
no displacement
3
chamber boundary
insulation
no displacement
4
substrate surface
insulation
no displacement
5
liquidair interface
Pagent,air = Psat,air
z: hdrop(r) r: no displacement
ð4Þ ð5Þ
Assuming a constant drop radius, the height of the droplet is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hdrop ðrÞ ¼ ðR 2 r 2 Þ ðR HÞ ð6Þ where R drop R drop ð1 cos θÞ and H ¼ sin θ sin θ Therefore, the volume of the droplet is given by25 π 3 θ θ V ¼ Rdrop tan 3 þ tan2 6 2 2 R ¼
Or
Rdrop ¼
where Vdrop is the drop volume as specified by the experimental conditions and Fagent is the liquid density of the agent (dependent on environment temperature). At any given time during the simulation, the mass of agent in the air is given by a volume integral over the domain ¼ 2πMW
z: free displacement; r: no displacement
Vdrop ðtÞ ¼ mdrop ðtÞFagent
ð2Þ
ZH ZR chamber chamber air
axial symmetry
Accordingly, the drop’s volume is given by
where Pa is the partial pressure of agent in the air and Da,air is the diffusivity of agent in the air. The mathematical model is composed of a multiscale and multiphysics model that couples agent distribution within the air and a moving boundary condition, which describes the droplet shape’s evolution over time. The constant-base radius mode of evaporation was assumed for modeling. (This is a valid assumption for the substrate-agent pairs evaluated.) Because of symmetry in the system, an axisymmetric 2-D radial geometry was employed in the model. The system geometry and calculation mesh-point distribution is illustrated in Figure 1, and the boundary conditions for each component of the multiphysics model are given in Table 1. The saturation concentration of agent in the air (Psat,air) is given by the agent’s vapor pressure at the specified temperature, calculating using the Antoine equation.24 At time zero, the mass of agent on the surface of the substrate is given by
mair agent
radial symmetry
mdrop ðtÞ ¼ moagent mair agent
ð1Þ
moagent ¼ Vdrop Fagent
1
would not approach the air concentration saturation value (vapor pressure). The thermodynamic effects of evaporation were minimized by the thermal mass of the system and the temperature regulation of the environmental chamber. Whereas evaporative cooling may cause localized thermal fluctuations, the thermal mass of the system helps to maintain pseudoisothermal conditions. A mass balance of the system shows that at any given time the mass of the liquid droplet on the surface of the substrate is given by
of water on Al and 16 μL for the distortion of HD on glass, which further demonstrates the validity of the spherical cap geometry. The spherical cap geometry assumes an axisymmetric radial geometry for a droplet of volume, V, with the height at the center of the liquid given by H, a radius given by Rdrop, and the contact angle given by θ. At any distance r from the drop center (for r < Rdrop), the droplet height is given by h(r). On impermeable substrates, droplets evolve from their equilibrium shape due to evaporation into the air. Fick’s second law describes the change in agent distribution within the air as a function of time 2
drop shape
91=3 > > =
8 > >
θ θ > > > 3 tan2 ; :πtan 2 2
ð7Þ
ð8Þ
A rearrangement of eq 8 yields a third-order polynomial, with two complex roots and one real root. The real root gives the value of the contact angle θ ¼ 2 tan1 ½ðα þ βÞ1=3 ðα βÞ1=3
ð3Þ
ð9Þ
where
where Cair,agent is the concentration distribution of agent in the air, MW is the agent’s molecular weight, Hchamber is the height of the environmental chamber, and Rchamber is the radius of the environmental chamber. The environmental chamber did not provide a complete seal and only provided protection from forcedconvection mass transfer effects. To accommodate this experimental configuration, the internal volume of the simulated domain was set to 40 times the volume of the actual environmental chamber. The geometry was chosen to ensure that the chamber concentration
α¼
3V and β ¼ ð1 þ α2 Þ1=2 3 πRdrop
The unknown parameter for the simulation is Dagent,air, the diffusivity of agent into the air. The parameter estimation code predicts the drop volume as a function of time, based on a guessed value of Dagent,air. At a given time step, the model calculates the droplet contact angle (θ) based on the droplet volume (V) and radius (Rdrop). The droplet contact angle, radius, and height 540
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Figure 2. Sample profile images for water on aluminum substrates at 20 to 60 °C from 10 to 1000 s.
Figure 3. Profile images of HD on a glass substrate at 20, 40, and 50 °C.
characterize the surface area of the droplet that interacts with the air phase. The mass transport model requires a known, static, droplet radius throughout the material contamination period. The interaction area between the liquid contaminant and the substrate is mediated by the difference between the critical liquid surface tension and the critical surface energy of the substrate. The substrates chosen for the current study had surface energy values lower than the critical surface tension of the test liquids to minimize liquid spreading after the initial droplet shape equilibration period, which was obtained within seconds. These agentmaterial combinations provide systems where the model assumption of a constant contaminated area is maintained. The error term used for the goodness-of-fit optimization metric was the mean-square error of the predicted droplet volume over time compared with the experimentally calculated droplet volume. Prior to the parameter estimation procedure, data noisereduction filter techniques, such as the Robust Lowess smoothing filters, were applied to the data. The smoothing process establishes the average value for a set of neighboring response values, which helps remove any noise generated by the image analysis techniques. 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
