Computational Fluid Dynamics Studies of a Flow Reactor: Free

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Computational Fluid Dynamics Studies of a Flow Reactor: Free Energies of Clusters of Sulfuric Acid with NH or Dimethyl Amine 3

David R. Hanson, Imanuel Bier, Baradan Panta, Coty N. Jen, and Peter H. McMurry J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 28 Apr 2017 Downloaded from http://pubs.acs.org on May 1, 2017

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The Journal of Physical Chemistry

Computational Fluid Dynamics Studies of a Flow Reactor: Free Energies of Clusters of Sulfuric Acid with NH 3 or Dimethyl Amine D. R. Hanson*, I. Bier, B. Panta, Augsburg College, Minneapolis, MN C. N. Jen, Univ. of California, Berkeley P. H. McMurry, Univ. of Minnesota, Minneapolis, MN * [email protected]

Abstract Computational fluid dynamics simulations (CFD) of a flow reactor provided 3D spatial distributions of its temperature and flow profiles and abundances of sulfuric acid, nitrogeneous base and the acid-base clusters formed from them. Clusters were simulated via their kinetic formation and decomposition involving sulfuric acid and base molecules. Temperature and flow profiles and the base and sulfuric acid distributions are characterized and the latter is compared to mass spectrometer measurements. Concentrations of simulated clusters of sulfuric acid with either NH3 or dimethylamine were compared to experimentally measured particle concentrations. Cluster thermodynamics were adjusted to better the agreement between simulated and experimental results. Free energies of acid-base clusters derived here are also compared to recent quantum chemistry calculations. Sensitivities to the thermodynamics were explored with a 2D laminar flow simulation and the abundance of large clusters was most sensitive to the thermodynamics of the smallest cluster, consisting of 1 base and 1 acid. Comparisons of this model to the computational fluid dynamics models provide verification of the implemented cluster chemistry. A box model was used to calculate nucleation rates for the conditions of other experimental work, and to provide predictions of nucleation for typical atmospheric conditions.

1. Introduction Nucleation of sulfuric acid with ammonia (NH3) and/or dimethylamine (DMA) is believed to contribute significantly to particle formation rates observed in the atmosphere 1-4. Laboratory studies 5, 6 provide rates and mechanisms of particle formation that can help ascertain these processes in the real atmosphere. Good knowledge of laboratory experimental conditions facilitates application of their results to the atmosphere and enables comparisons with laboratory results. One approach is to use estimates of the free energies of small molecular clusters to predict particle formation rates for the conditions of H2SO4-amine experiments such as those of Almeida et al.5, Erupe et al. 7 and Berndt8 et al. Previous work comparing measurements with models have used thermodynamics-based approaches. An amine-sulfuric acid nucleation rate scheme that adjusted decomposition rates of a few clusters of amines and sulfuric acid to match measurements has been presented by Chen et al.4 (nucleation rates in a chamber and 1 ACS Paragon Plus Environment


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atmosphere) and Jen et al.9 (acid dimer measurements in a flow reactor.) The latter paper stressed the importance of the initial clustering reaction of acid a with base b forming a1b1, a pathway also indicated as important in theoretical studies10, 11. Nucleation rates based on theoretical free energies for acid-base clusters have been presented5, 10, 11 for both the NH3-H2SO4 and DMA-H2SO4 systems. These calculated rates were compared to measurements5, 12 albeit with large uncertainties in the former. Cluster thermodynamics can also provide a point of comparison between experimental results and quantum chemical calculations13-17. Exploring free energies using sophisticated statistical methods18 has been described recently and this technique was used to evaluate ion-cluster evaporation rates. Described here are computational fluid dynamics (CFD) simulations of particle formation in a flow reactor. The simulations have many tens of acid-base clusters that form and decompose along specific pathways, and these model results are compared to experimental data. This comparison was done previously for nucleation in the binary system, H2SO4-H2O19, 20, where simulated clusters containing up to either 12 or 24 H2SO4 molecules gave particle formation rates that agreed with observations thus verifying, at least in that circumstance, the free energies of the H2SO4-H2O clusters. Also, comparison of simulated and measured H2SO4 at the exit of the flow reactor constrained [H2SO4]; knowledge of [H2SO4] within the reactor is very important for accurate free energies. The experimental data to be matched by the CFD models is from Glasoe et al.6, the number densities of particles produced in a cylindrical flow reactor. Specifically, Glasoe et al.'s particle data for sulfuric acid with ammonia or dimethylamine were simulated with CFD.

The CFD results contain information on reactant

abundances as well as the abundance of particles produced by a given set of cluster thermodynamics. This work builds upon the models and the simulation techniques presented in Panta et al.19 The models presented here differ from the Panta et al. models mainly by increasing the number of grid cells of the computational mesh and incorporating second-order solvers to improve numerical accuracy, and the incorporation of free energies for clusters containing up to 6 acid and 3 base molecules. A number of models are described in this work. The main 3D model incorporates the primary features of the experiment that most affect particle concentrations. A more detailed 3D model with showerhead (SH) inlets, 3D-SH, is described in the Supplement that predicts sulfuric acid concentrations throughout the flow reactor based upon its vapor pressure and the flow rate over a bulk liquid reservoir. To verify the H2SO4 levels in the 3D CFD models, measurements of experimental [H2SO4] taken using a chemical ionization mass spectrometer9 were compared to the simulated [H2SO4] of both 3D models. In addition to these 3D CFD models, a chemical kinetics module was employed in both a box (or zero-D) model and a 2 dimensional laminar flow reactor (2D-LFR) simulation. These models are less computationally intensive than the 3D models, and thereby provide an efficient means to explore the effects of changes in cluster energetics and for expanding the size of 2 ACS Paragon Plus Environment

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the clusters. They also facilitate application of the present results to the atmosphere and to the conditions of other experiments. Table 1 lists the main features of these models.

Table 1. Overview of the principal models presented here. sLpm is L min-1 for standard conditions: T=273 K and P=1 atm. Model Features Isothermal Objects a H2SO4 at the inlet b c 3D88 cm length, Plug flow inlet for acid, two inlets, three walls 315 pptv at 307 K main sidearm for base 3D-SHd

165 cm length, showerheads (SH) for acid entrained flow and 6 sLpm balance, sidearm port for base

three SHs, base sidearmse, three wallsc

partial pressure of 5x10-8 atm in 0.3 sLpm N2(g)

2D-LFR

155 cm length, radial flow velocity profile fixed for FDLf

isothermal, typ. 300 K

~160 pptv at 300 K

acid source from OH+SO2, base injected at fixed rate, 1st-order wall loss for all species

isothermal

kOH of 2x104 cm-3 s-1

0D or Box

(a) Objects that can have temperatures set separately thus significantly affect flow patterns. (b) Sulfuric acid level to mimic a 0.3 sLpm 7 -3 N2 flow over a ~96% H2SO4 liquid; for the Box model, OH production rate kOH that yields a steady state [H2SO4] = 1x10 cm . (c) Gas temperature incoming flow set to mixing region wall temperature, 307 K, sidearm wall and gas temperatures set to transition region temperature, 298 K. (d) DMA_I is the only thermodynamic scheme implemented in 3D-SH. (e) Two sidearms included: only one has flow. (f) Fully Developed Laminar: indicated as 2D-LFR.

2. Details of the 3-D CFD, 2D-flow reactor, and 0D/Box Models. 2.1 Overview of 3D model and transport properties Depicted in the left side of Fig. 1 is the geometry of the main 3D fluid dynamics model. It is similar to that presented in Panta et al. (see their section 2.3.3 and SI section 5) where the top 88 cm of the flow reactor is simulated. In this model, the nitrogen flow carrying H2SO4 and water vapor enter the reactor via a plug-flow inlet. Experimentally, however, these gases are introduced separately via showerhead inlets, thus a 3D model with detailed geometries for the showerhead inlets was developed (3D-SH) and it is depicted on the right hand side of Fig. 1. The results of the main 3D model are presented throughout the text unless noted otherwise. The 3D-SH model provides additional spatial information on H2SO4 and cluster abundances and these results are discussed primarily in the supplement. The CFD simulations21 were performed with a commercial product and utilized second-order solvers for energy, momentum, pressure, the H2SO4 and base monomers, and all clusters. Cluster concentrations solved to second-order were subject to spurious chemistry in some cells which was eliminated by increasing the mesh density at specific regions where an artifact had developed. See the supplemental information for detailed comparisons of different models and solvers.

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The 3D models were run to steady state such that cluster concentrations changed very little (< 3%) for an increment of 100 iterations. Multiple processers (16 or 32) were implemented allowing for high spatial resolution (~2x106 cells vs. 1.3x105 in Panta et al.) Sharp edges and angles were smoothed in the main 3D model, notably at the end of the base addition inlet. As in Panta et al., all clusters and monomers were lost efficiently on the flow reactor wall (no evaporation). The 3D-SH model had approximately 5x106 cells and it extended over the entire length of the flow reactor, about 1.65 m (did not include the mass spectrometer sampling section). The kinetic scheme implemented in these models has reactions of clusters with up to 3 base molecules and 6 acid molecules with free energies that determine base and H2SO4 evaporation rates assuming gas-kinetic forward rates. Simulations of the binary system (H2SO4 and water only with zero sidearm flow) were also performed to compare the main 3D model’s velocity profiles, temperatures, and clusters to those of the 2D model of Panta et al. Reactions of H2SO4 with the largest clusters were also implemented for some runs to verify that the assumptions of the kinetic scheme do not lead to errors. 2.2 Detailed Cluster Chemistry. The present cluster chemistry derives from that developed in Panta et al. where H2SO4 and base molecules interact with clusters but water molecules are not tracked. Clusters in all likelihood contain water in the experiments conducted at ~28% relative humidity. In effect, our chemical model assumes pseudo-equilibrium with respect to water which is reasonable due to its high abundance (as done previously22-25). However, water molecules can affect the free energies of clusters which should be taken into account if relative humidity effects are explored (which was not done in the Glasoe et al. experiments.) Note that current quantum chemical results14, 33 indicate that water has a relatively small effect on the energies of these types of clusters compared to the effect on energies due to the choice of theoretical method.13-17 An important element of the simulations is that they are focused on experimental results where acid abundances were larger than DMA abundances. Therefore, the simulations primarily included clusters with 6 or fewer H2SO4 molecules and 3 or fewer base molecules. This may affect the legitimacy of extrapolating the H2SO4-DMA thermodynamics to those of other experiments where base exceeds acid (discussed in section 5.3.1.) Also, see sections 2.3.3 and 2.4 for a discussion of cluster sizes and section 4.6 for results of simulations including clusters with more base molecules. Cluster chemistry is incorporated via forward and backward reactions such as ai-1bj + a1b0 ↔ aibj

(R1)

where a and b indicate H2SO4 and base molecules respectively, and the subscripts indicate their number in the clusters. Similar reactions are included for the addition and loss of the base monomer, a0b1. The ratio of the 4 ACS Paragon Plus Environment

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forward and backward rate coefficients is equal to the equilibrium constant which is directly related to the standard Gibbs energy change of the reaction; for R1, this energy is denoted ∆aG0(i,j) indicating an acid is added and the product cluster is indexed. Figure 2 shows the reaction scheme and example nomenclature for the free energies of adding H2SO4 (a1b0) and base (a0b1). Also, the addition and loss of a1b1 (the diagonal arrows in Fig. 2) and a2b1 from a few clusters were included in most runs (i.e., some coagulation processes were included). These two clusters are among the most abundant for many sets of conditions. The formation rate for each cluster is determined by the forward rate coefficient, kf, which is taken to be the gas-kinetic collision rate coefficient19, 26. The size dependence of kf upon H2SO4 is taken into account using the bulk density of ~ 60 wt % H2SO4, however, we do not consider the sensitivity of kf to temperature, T, because of the small range of T encountered in the reactor. This approach regarding the H2SO4 and T dependence for kf is similar to that in Panta et al.19 The same forward rate coefficient was used for the addition of an H2SO4 and a base molecule as a simplification. The dependence of kf on base content was assumed to be a 5% increase in kf for each additional base. The reverse rate coefficients, kr = Afexp(-Ea/RT), are highly T-dependent through the activation energy, Ea, over RT in the exponential term and depend on the stepwise changes in the standard entropy in the Af term. The enthalpy of adding an H2SO4 or a base, i.e., the respective stepwise enthalpy change ∆ a/bH0(i,j), is taken to be -Ea for that step. Free energies of clusters are the dominating factors in their kinetics. Several groups have calculated free energies for ammonia-H2SO4 and dimethylamine-H2SO4 clusters using quantum chemical3, 13-17, 27 methods and these provided a starting point for cluster energetics in this study. Ranges of the standard enthalpies of cluster formation (from the monomers, ∆H0) and the Gibbs free energies of formation of the clusters (also called total free energy of a cluster, ∆G0) were explored in the simulations. The Ortega et al.13 thermodynamics for NH3-H2SO4 and DMA-H2SO4 covers the widest range of clusters considered here and was thus used to guide the present thermodynamic schemes. The Panta et al.19 thermodynamics were used for the H2SO4 clusters without base, i.e., aib0. 17

15

Energetics were developed

14

considering (i) calculations of Bork et al. , Nadykto et al. Depalma et al. and recently Myllys et al.16, for the (H2SO4)n(DMA)n n=1,2 clusters, (ii) the bulk thermodynamics of H2SO4-base mixtures28 and (iii) comparison of simulations with experiment. We arrived at four sets of thermodynamics - denoted NH3_I, NH3_II, DMA_I and DMA_II - that were used in the main 3D model to predict particle number densities. Of these four, NH3_I remained close to the NH3-H2SO4 scheme of Ortega et al., while the others deviated significantly from the Ortega et al. thermodynamics. Figure 3 shows the standard free energy changes for addition of an acid molecule for DMA_I and the Ortega et al. DMA-H2SO4 scheme. Rationale for the development of the thermodynamics, values 5 ACS Paragon Plus Environment


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for ∆G0 for all the schemes, and evaporation rate comparisons are presented in the Supplement (S4). As noted above, the thermodynamics developed here also reflect the possible influence of water on the thermodynamics of the clusters of interest. This may be important for NH3-H2SO4 clusters as they were demonstrated in quantum calculations to take up water14,33 which influenced33 nucleation rates. Diffusion coefficients for dimethylamine in N2 were calculated29, 30 with molecular parameters estimated from critical point parameters (section 2.7 and Appendix A of Reid et al.31) and the 296 K value is 0.11 atm cm2 s. The value used for ammonia in N2 is 0.22 atm cm2 s-1 at 298 K.32 The diffusion coefficients of the ammonia

1

and amine containing (H2SO4)i clusters were taken to be the kinetic theory values of (H2SO4)i-water clusters19, 26 with no effect for added base molecules (it is uncertain how to apply the information33 that exists on how water molecules are displaced by base molecules.) Other important fluid dynamics parameters were those used in Panta et al.19 (of particular note is the coupled relative humidity, RH, and temperature dependency for the diffusivity of H2SO4.) 2.3 Cluster truncation and Np 2.3.1 Comparison of simulated and experimental results.

In the implemented chemical scheme, clusters with 6 H2SO4 or 3 base molecules do not add further H2SO4 or base molecules, respectively, thus cluster chemistry was ‘truncated’ at either 6 H2SO4 or 3 base molecules. Because the largest possible clusters - the accumulation clusters - are relatively small there are two main concerns: the proper comparison of simulated cluster abundances to particle number densities, Np, and the effects of truncation on the simulated clusters. For example, i ≥ 7 in R1 were not included thus the potential stabilization (i.e., decreased evaporation rates) of clusters at larger sizes might be missed. For the binary system, described in Panta et al.19, truncation’s effect on the abundance of the accumulation clusters was found to be small if the accumulation clusters were at least two molecules larger than the cluster where growth just exceeds evaporation (the critical or crucial cluster).

Quantitative comparison of the

concentration of accumulation clusters containing up to 24 acid molecules to the concentration of smaller accumulation clusters confirmed that truncation only has a small effect on calculated Np. Glasoe et al.6 used the term ‘crucial’ cluster to describe the smallest stable clusters: where growth exceeds evaporation. This was to delineate these clusters from the term ‘critical cluster’ that originated in the onecomponent liquid drop model (classical nucleation theory) where free energies are taken to be continuous functions. For the DMA experiments simulated here, the experimental power dependencies, which can be related to the crucial cluster composition,34 were found to be 2-to-3 acid molecules and 2 DMA molecules. This indicates that the accumulation clusters in the DMA-H2SO4 thermodynamic schemes presented here are sufficiently large that the truncation of the simulation at the cluster boundary has little effect on the production rate of accumulating clusters. 6 ACS Paragon Plus Environment

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The model-predicted abundance of new particles, Np, was taken to be proportional to the sum of the acid pentamers and hexamers (5 and 6 acid containing clusters summed over base content: SA5 and SA6, respectively) at the center of the reactor near its exit. This metric for Np is supported by the following arguments. (i) The simulated SA5 and SA6 are beyond the size of the smallest stable cluster (a4b2 for NH3 and a3,2b2 for DMA, Glasoe et al.) (ii) Clusters with 5 H2SO4 molecules need to be included if evaporation of H2SO4 from the truncation clusters (SA6) is fast enough to cause a buildup of 5 acid clusters. The a5,6b1 clusters are probably not stable enough to be considered particles yet their abundance is low so that it makes little difference in practice. The proportionality factor to get predicted Np from the centerline sum of SA5 and SA6 is prescribed by two factors: the averaging that occurs in the experiment (i.e. the particle detector flow entrains a significant amount of flow off the centerline stream) and the loss of particles as they travel to the sampling region, at an X of ~1.65 m. The averaging is calculated using a mixing-cup treatment35 for the 2 L/min particle sampling flow which is centered in the reactor (the radial distributions of velocity and a10b2,3, see next section, at X = 0.85 m were used.) This leads to a factor of 0.6. The loss of particles from X = 0.85 m to 1.65 m is taken from the 2D simulations of Panta et al.19 who report a loss of about 20 % over this distance. The overall proportionality factor is about 0.5. 2.3.2 Potential biases introduced by limited cluster size.

Truncating clusters can introduce biases of potential significance: (i) monomer losses may be underestimated because they do not react with a subset of the accumulation clusters and (ii) particles are kept small thus their diffusion and evaporation rates may be artificially enhanced. The monomer loss and diffusion biases are probably small over a large range of the simulation and measurement conditions because: (i) monomer loss is dominated by loss to the wall or loss to small clusters for nearly all the measurements and (ii) diffusion losses of the accumulation clusters is estimated to be less than 20 % by considering the first-order diffusion-limited wall loss rate coefficient of 0.016 s-1 36 for the a6b3 cluster and assuming a 10 s transport time. Artificially high evaporation rates due to limited cluster size is likely not important for the DMA-H2SO4 system but this cannot be established for the NH3-H2SO4 system. It is worthwhile to more fully assess these effects. Issues of truncation were partially addressed by performing additional 3D simulations that incorporated clusters up to 20 acid molecules. To ease the computational load, acid evaporation was suppressed and only one base reaction was included, a rapid loss of a base molecule from the a10b3 cluster so that only aib2 clusters for i > 10 were required. Discussed in section 4.6 are results obtained for 10, 14 and 20 H2SO4 molecules as the accumulation size. The next section discusses models that have extended cluster chemistry, up to sizes of 8 acid and 8 base molecules. These are useful for assessing whether evaporation rates in truncated systems are important. 2.4. Box and 2D flow reactor models 7 ACS Paragon Plus Environment


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A chemistry module was developed with rate coefficients identical to those in the 3D main model and it was deployed in both a 0-dimensional (box) model and a 2D flow reactor (2D-LFR) model run under isothermal conditions. See the Supplement for a detailed discussion of how the chemistry was calculated in each time step. The 2D model was used in sensitivity studies to explore how adjustments to the cluster free energies affect particle number densities. Since flow and temperature are prescribed and far fewer cells are needed in a 2D geometry, these simulations ran quickly. This also allows for extending the acid-base cluster chemistry to larger clusters, up to 8 acid and 8 base molecules and the effects of the truncation cluster’s evaporation rates can be addressed. Rate coefficients for clusters larger than a6b3 relied on extrapolations of the free energy schemes. For the 2D-LFR simulations, diffusion coefficients for individual clusters are those used in 3D-main, and cluster loss to the walls occurs through diffusion. For the box model, a first-order wall loss rate coefficient that depends on the square root of the species’ diffusion coefficient was assumed for all species 37. For monomer acid, this loss coefficient was typically 0.002-0.0005 s-1. The simulations were run for times sufficient to achieve steady-state in cluster concentrations. A box model result could be readily cast into a nucleation rate by multiplying the accumulation cluster concentration by its first-order loss rate coefficient. The box model has the option of including coagulation of the truncation clusters. This was crudely taken into account by using a pseudo-sectional model where SA8 (the sum of [a8bj] over j) along with SA16, SA24, SA32, SA40 and SA48 all reacted together with a coagulation rate coefficient of 1x10-9 cm3 s-1. This coagulation scheme was used to signal when these reactions resulted in a significant decrease in SA8 clusters in the box model. Nucleation rates are presented only if SA8 coagulation reactions were 30 % or less of the SA8 wall loss. Except for the highest nucleation rates (> 100 cm-3 s-1), coagulation effects were less than ten percent (and 15 to 30 % for the three highest nucleation rates reported here, S2.4).

3. 3D-main model characteristics 3.1 Relating experimental [H2SO4] to modeled [H2SO4] It is very important for the correctness of the thermodynamics that modeled [H2SO4] accurately represents the experimental [H2SO4]. In this section, we compare measured to modeled [H2SO4] to develop a criteria for the amount of H2SO4 to input in the model to match a given experimental condition. New measurements of the [H2SO4] at the exit of the reactor are presented in the Supplement. The experimental H2SO4 is determined by the sulfuric acid laden N2 flow, QB4. This flow passes over a concentrated H2SO4 solution and becomes saturated in H2SO4 vapor. To establish the relation between an experimental level of H2SO4 and that set at the input of the simulation, we use simulated H2SO4 profiles. Since 3D-main does not extend to the mass spectrometer detection region, results from a 2D model (slightly modified from Panta et al.19) were used to relate [H2SO4] at axial position X = 8 ACS Paragon Plus Environment

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0.85 m and [H2SO4] at X = 1.75 m. This results in an overall relation between the mixing ratio, [H2SO4]0, in the inlet of the main 3D model and experimental QB4 values: [H2SO4]0/(1050 pptv) = QB4/(1 sLpm). The model profile also gives the [H2SO4] at X=0.5 m and on-axis, where nucleation rates are close to peak, and this is 0.63 of the initial mixing ratio. For a QB4 = 0.2 sLpm, the [H2SO4] where particles are formed at the highest rates in the model, at X = 0.5 m and on axis, is ~3.3x109 cm-3. See the supplement section 1.2.1 for details. The 3D-SH model was also used to provide values of [H2SO4] at the mass spectrometer detection region. Remarkably, these simulations provide [H2SO4] that is comparable to that detailed above (and in S1.2.1) not only by simulating losses but also by prescribing the amount of H2SO4 flowing through the QB4 showerhead based on the vapor pressure of H2SO4 over a bulk ~96 wt. % sulfuric acid solution. These simulations are presented in detail in the supplement, S1.4. 3.2 Binary 3D simulation Results from the main 3D model with the sidearm flow turned off were compared to 2D simulations of the binary system presented by Panta et al.

Good agreement in axial velocity, temperature and H2SO4

concentrations were found throughout the reactor (plots of axial velocity and temperature are shown in the Supplement), e.g., the median difference between on-axis H2SO4 concentrations was 0.2 %. The binary system clusters up to the hexamer were also modeled as in the 2D model (i.e., using identical rate coefficients and using the first-order solver) and cluster concentrations in the two models agreed to within 10% with a median deviation of 1.6 and 3% for the tetramer and hexamer, respectively. These results indicate that the main 3D model has flows, heat and mass transfer nearly identical to those of the 2D simulation of Panta et al. 3.3. Summary of additional characteristics More CFD model characteristics and a number of simulation issues are presented in the Supplement. These include a verification of the implementation of the kinetic schemes (S2.2.1. Fluent 2D vs. 2D-FR), discussion of the 1st- and 2nd-order solvers (S1.1.2), description of nucleation zone conditions (S1.2), sensitivities of model results to experimental conditions (S1.3), and descriptions of mysterious but negligible base concentrations upstream of the addition port (S1.5).

4. Model Results. 4.1 Base addition and cluster formation As in the experiment, base addition was accomplished in the 3D simulations by including base in the sidearm flow at a specified mole fraction. Contour plots for the addition of DMA at 4 pptv (No-Loss Mixing ratio, NLM: the base abundance calculated assuming full dilution by the main flow with no loss to the wall) and an acid content of 210 pptv at the main inlet are shown along with axial velocity in Figure 4. The axial velocity plot (Fig. 4a) shows that there is still a semi-buoyant zone (dark blue region indicate negative X velocities) but it is smaller 9 ACS Paragon Plus Environment


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than it was without a sidearm flow. There is never a zero radial velocity and this region is flushed out. H2SO4 in Fig. 4b is relatively constant over a large region of the nucleation zone. In Fig. 4c, however, dilution and loss lead to large gradients in [base] as it mixes into the main flow. The acid abundance in this simulation is comparable to the experimental setup when QB4, was set to ~0.2 sLpm. Figures 4d-g are contour plots for the most abundant H2SO4 dimer, a2b1, and the most abundant H2SO4 trimer, tetramer and hexamer (a3b1, a4b2 and a6b3, respectively.) Cluster formation begins upon interaction of the two vapors and proceeds quickly through H2SO4 dimers and trimers, which appear at significant levels within a few cm of the base addition port. Mass accumulates at the H2SO4 hexamer, which appears at its largest number density about 15 cm downstream of the base addition port. Clusters are abundant in the buoyant zone, upper cross hair (Fig. 4b), but because flow through this region is a small fraction of the total flow, clusters originating here are diluted. Another consequence of the formation of the clusters in the region of slow flow is a long exposure to relatively high monomer abundances, enhancing the prospects for cluster growth. Cluster formation in the H2SO4-DMA system is efficient at the elevated temperatures (> 296 K) of the gas during mixing. For example, the a6b3 cluster abundance maximum contour in Fig. 4g extends over a region where the temperature ranges from 303.5 to 300 K. Gas spends about 5 s in this region, depending upon which streamline is considered. Additional details of this region are presented in the Supplement. 4.2 NH3 - H2SO4 particle formation Figure 5 shows experimental and simulated particle numbers for the ammonia - sulfuric acid system. Unless otherwise specified all simulated concentrations are those of 3D-main, on-axis and 3 cm from the model’s exit (Z = 0, Y = 0, X = 0.85 m). For the results presented in Fig. 5, NH3 was varied while [H2SO4] was held constant at a level given by QB4 = 0.3 STP L/min. The appropriate [H2SO4]0 in the model is 315 pptv for this QB4 (flow rate over a sulfuric acid reservoir.) The simulated results using scheme NH3_II have a power dependency on NH3 of 1.9 which is close to the experimental power dependency of ~1.6. When H2SO4 was varied at constant NH3, simulated Np had power dependencies on H2SO4 of 3.3 using scheme NH3_II (see Supplement.) Simulated results using NH3_I lie about a factor of 30 below the experimental data (Fig. 5b) and have a larger dependence on both NH3 (2.5) and H2SO4 (4.1) than exhibited by NH3_II. Notably, the dependence on H2SO4 is in decent agreement with the experimental power dependency on H2SO4 of ~4 (see supplement). However, since the simulated Np using NH3_II better agrees with measured Np, the NH3_II thermodynamics phenomenologically represents particles formed in the Glasoe et al.6 NH3-H2SO4 data set. The dependence on H2SO4 however, is notably in worse agreement with the measurements than is the H2SO4-dependence using NH3_I. Finding thermodynamics that mimics the experimental data over its full range has not been successful. For both schemes for example, the predicted NH3 dependence is larger than experimental while the predicted 10 ACS Paragon Plus Environment

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H2SO4 dependence is too small for most conditions. We are exploring thermodynamics that better captures the experimental particle abundances over the whole range of data. The NH3_II thermodynamic scheme has H2SO4 evaporation rates

Computational Fluid Dynamics Studies of a Flow Reactor: Free

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