Modeling and Characterization of a Particle-Into- Liquid Sampler (PILS) ∗
2.4 PILS Model
until it impacts onto the droplet impactor plate is estimated to be 3.6 s; this time will vary between different designs based on the plumbing length between the inlet and the droplet impactor (combined 3 m in this design with tube IDs varying between 0.35 and 1.65 cm).
The time for each syringe to complete a full round-trip (downward stroke followed by an upward stroke) is measured to be 46 and 230 s using 50 and 250 μL syringes, respectively. The last liquid parcel to enter a syringe at the end of a downward stroke exits the syringe at the beginning of the next upward stroke, which results in very little time spent in the syringe. As will be shown later, model predictions show that there is a minimum time delay of 301 s and 304-313 s to overcome a step change in concentration for the original and modified PILS (assuming a 66 s debubbler liquid residence time), respectively; the time delays for the modified PILS are used here as a time-offset to intercompare with DMA measurements. The time-offset can be reduced by lowering the debubbler residence time; this involves optimizing the ratio between the flow rate of the wash-flow at the top of the droplet impactor and the speed of the syringes aspirating liquid from the debubbler.
measurements of concentration in vials to back-calculate the actual mass concentrations in the sampled aerosol and to properly adjust the PILS measurements for instrument time response. Both models are also used to simulate sample behavior in the original PILS, with the only difference being that the syringes were not considered.
The important flow elements of the modified PILS are the impactors, the plumbing leading to the condensation chamber, the condensation chamber itself, and the plumbing leading from the droplet impactor to the dispensing needle, which includes the debubbler and two syringes (Figure 2.2). During sample transport within the instrument, plumbing-related particle losses can occur by gravitational settling, diffusional deposition, turbulent inertial deposition, and inertial deposition at bends and flow constrictions. The model considers these processes as a function of particle size for all stages up to the droplet impactor, at which point the masses in each particle size bin are added into a cumulative liquid parcel. Predictions can be used to assess the sensitivity of the droplet size distribution to different initial conditions for the air and water vapor streams.
2.4.1 Model Equations
The basic equations of the PILS model are given in Table 2.1 (Figure 2.2 indicates which equations are applied when modeling specific stages of the instrument).
Semi-volatile species in the sampled particles can evaporate as a result of the release of latent heat of condensation and convective heating of the air sample. Ma (2004) reports a 13 to 16% loss (by mass) of NH4+ based on PILS (original design) intercomparisons with filter samples obtained during four selected ground-based and airborne studies. For the
range of particle surface temperatures examined (25–130°C), NH4+ is the most volatile, followed by Cl-, and then NO3- (Figure 2.3). To estimate the volatilization of these three species during PILS operation, we calculate the quantity of particle-phase NH4+, Cl-, and NO3- that will be converted to the gas phase in the condensation chamber. It is assumed that before the sampled aerosol reaches the condensation chamber, the denuders remove all of the gas-phase species (NH3, HCl, HNO3). The general assumption is made for the equilibria represented in Figure 2.3 that ambient volatile species are in equilibrium between the gas and particle phase, which has been argued to be especially valid for sub- micrometer particles (Pilinis and Seinfeld, 1987; Zhang et al., 2002); however, this assumption has been shown not to hold under all ambient conditions (Hildemann et al., 1984; Quinn et al., 1992; Parmar et al., 2001; Trebs et al., 2005).
After the condensation chamber and the droplet impactor, the liquid sample travels through the debubbler, syringes, and 0.5 mm ID PEEK tubing prior to reaching the dispensing needle. Although no aerosol mass is expected to be lost in these final flow components, mixing occurs in the debubbler and syringes. It is assumed that each liquid parcel drawn into a mixing vessel immediately mixes with the bulk liquid volume and that the mass concentration of the effluent is equal to the uniform concentration inside the vessel.
2.4.2 Model Predictions
Since the PILS operates with an upstream impactor to remove super-micrometer particles, we examine theoretical losses for sub-micrometer particles in the plumbing up to the condensation chamber (Figure 2.4). Losses are predicted to decrease from 2.21 to
0.42% for particles with diameters ranging from 0.01 to 0.08 μm, respectively. Losses subsequently increase from 0.42 to 8.58% for diameters increasing from 0.08 to 1.0 μm, respectively. Diffusional losses dominate the total losses for the smaller particle range, ranging from 95 to 57% of the total losses, whereas inertial deposition dominates for the larger particle range, ranging from 43 to 98% of the total losses. Inertial deposition at bends, of which 12 are present in this modified PILS design, dominate the inertial losses.
Losses in the condensation chamber are predicted as a function of particle size entering the chamber (Figure 2.5). As the steam temperature increases, the supersaturation increases, resulting in larger final droplet diameters in the condensation chamber. The final droplet size is more sensitive to the supersaturation ratio achieved by having higher tip temperatures than to the initial particle size entering the condensation chamber. The value of the water condensation mass accommodation coefficient (α) is shown to have a significant impact on the predicted final size of the droplets; as this value increases, water vapor is more effectively scavenged during condensational growth.
There is considerable scatter in experimental measurements for this parameter; values ranging from 0.04 to 1 are applied in current cloud model studies (Kreidenweis et al., 2003). Weber et al. (2001) report that particles in the condenser reach final diameters of nominally 2 to 3 μm, while Orsini et al. (2003) measured a typical droplet size distribution from sampling room air and observed the range of droplet diameters to be between 1 and 5 μm (with the majority of the droplets between 2 and 3 μm). Sullivan et al. (2004) report that droplet diameters within the PILS can reach up to between 3 and 5 μm, which is consistent with previous studies. The droplet diameters reported in the three aforementioned studies, the two most recent of which used the same steam
condensation chamber as our PILS, are consistent with model predictions assuming an accommodation coefficient between 0.01 and 0.05 and a tip temperature of 100°C (Figure 2.5a).
Losses during the droplet growth stage are dominated by gravitational settling and inertial deposition in the main body of the condensation chamber and in the conical section at the end of the chamber (these regions are defined in Figure 2.2). The losses exceed 1 and 10% when droplets reach sizes of 3 and 8 μm, respectively (Figure 2.5a).
Figure 2.5b shows that losses in the conical section exceed those in the main body when droplets grow larger than 2 μm. These results emphasize the importance of keeping the PILS tip temperature close to 100°C to minimize the growth of larger droplets that are more effectively lost by deposition prior to reaching the droplet impactor.
Calculations indicate that volatilization effects are most sensitive to temperature and the acidity of the sampled particles. Figure 2.6 shows the amount of NH4+ expected to remain in the particle phase at the end of the condensation chamber as a function of temperature and acidity. Ammonium is the sole ion vulnerable to volatilization over the span of temperatures, acidity, and dilution factors shown, whereas Cl- and NO3- losses are predicted to be less than 1%. Ammonium losses are higher as the temperature increases and as the droplet acidity decreases.