Experimental investigation of a turbulent reacting plume

An experimental investigation has been made of a round, non-buoyant plume of nitric oxide, NO, in a turbulent grid flow of ozone, 03, using the Turbulent Smog Chamber at the University of Sydney. The measurements have been made at a resolution not previously reported in the literature. The reaction is conducted at non-equilibrium so there is significant interaction between turbulent mixing and chemical reaction. The plume has been characterized by a set of constant initial reactant concentration measurements consisting of radial profiles at various axial locations. Whole plume behaviour can thus be characterized and parameters are selected for a second set of fixed physical location measurements where the effects of varying the initial reactant concentrations are investigated. Careful experiment design and specially developed chemilurninescent analysers, which measure fluctuating concentrations of reactive scalars, ensure that spatial and temporal resolutions are adequate to measure the quantities of interest. Conserved scalar theory is used to define a conserved scalar from the measured reactive scalars and to define frozen, equilibrium and reaction dominated cases for the reactive scalars. Reactive scalar means and the mean reaction rate are bounded by frozen and equilibrium limits but this is not always the case for the reactant variances and covariances. The plume reactant statistics are closer to the equilibrium limit than those for the ambient reactant. The covariance term in the mean reaction rate is found to be negative and significant for all measurements made. The Toor closure was found to overestimate the mean reaction rate by 15 to 65%. Gradient model turbulent diffusivities had significant scatter and were not observed to be affected by reaction. The ratio of turbulent diffusivities for the conserved scalar mean and that for the r.m.s. was found to be approximately 1. Estimates of the ratio of the dissipation timescales of around 2 were found downstream. Estimates of the correlation coefficient between the conserved scalar and its dissipation (parallel to the mean flow) were found to be between 0.25 and the significant value of 0.5. Scalar dissipations for non-reactive and reactive scalars were found to be significantly different. Conditional statistics are found to be a useful way of investigating the reactive behaviour of the plume, effectively decoupling the interaction of chemical reaction and turbulent mixing. It is found that conditional reactive scalar means lack significant transverse dependence as has previously been found theoretically by Klimenko (1995). It is also found that conditional variance around the conditional reactive scalar means is relatively small, simplifying the closure for the conditional reaction rate. These properties are important for the Conditional Moment Closure (CMC) model for turbulent reacting flows recently proposed by Klimenko (1990) and Bilger (1993). Preliminary CMC model calculations are carried out for this flow using a simple model for the conditional scalar dissipation. Model predictions and measured conditional reactive scalar means compare favorably. The reaction dominated limit is found to indicate the maximum reactedness of a reactive scalar and is a limiting case of the CMC model. Conventional (unconditional) reactive scalar means obtained from the preliminary CMC predictions using the conserved scalar p.d.f. compare favorably with those found from experiment except where measuring position is relatively far upstream of the stoichiometric distance. Recommendations include applying a full CMC model to the flow and investigations both of the less significant terms in the conditional mean species equation and the small variation of the conditional mean with radius. Forms for the p.d.f.s, in addition to those found from experiments, could be useful for extending the CMC model to reactive flows in the atmosphere.

An experimental study of a reactive plume in grid turbulence

Experimental results for a reactive non-buoyant plume of nitric oxide (NO) in a turbulent grid flow doped with ozone (O3) are presented. The Damkohler number (Nd) for the experiment is of order unity indicating the turbulence and chemistry have similar timescales and both affect the chemical reaction rate. Continuous measurements of two components of velocity using hot-wire anemometry and the two reactants using chemiluminescent analysers have been made. A spatial resolution for the reactants of four Kolmogorov scales has been possible because of the novel design of the experiment. Measurements at this resolution for a reactive plume are not found in the literature. The experiment has been conducted relatively close to the grid in the region where self-similarity of the plume has not yet developed. Statistics of a conserved scalar, deduced from both reactive and non-reactive scalars by conserved scalar theory, are used to establish the mixing field of the plume, which is found to be consistent with theoretical considerations and with those found by other investigators in non-reative flows. Where appropriate the reactive species means and higher moments, probability density functions, joint statistics and spectra are compared with their respective frozen, equilibrium and reaction-dominated limits deduced from conserved scalar theory. The theoretical limits bracket reactive scalar statistics where this should be so according to conserved scalar theory. Both reactants approach their equilibrium limits with greater distance downstream. In the region of measurement, the plume reactant behaves as the reactant not in excess and the ambient reactant behaves as the reactant in excess. The reactant covariance lies outside its frozen and equilibrium limits for this value of Vd. The reaction rate closure of Toor (1969) is compared with the measured reaction rate. The gradient model is used to obtain turbulent diffusivities from turbulent fluxes. Diffusivity of a non-reactive scalar is found to be close to that measured in non-reactive flows by others.

Investigation of the airborne submicrometer particles emitted by dredging vessels using a plume capture method

This paper presents a method for investigating ship emissions, the plume capture and analysis system (PCAS), and its application in measuring airborne pollutant emission factors (EFs) and particle size distributions. The current investigation was conducted in situ, aboard two dredgers (Amity: a cutter suction dredger and Brisbane: a hopper suction dredger) but the PCAS is also capable of performing such measurements remotely at a distant point within the plume. EFs were measured relative to the fuel consumption using the fuel combustion derived plume CO2. All plume measurements were corrected by subtracting background concentrations sampled regularly from upwind of the stacks. Each measurement typically took 6 minutes to complete and during one day, 40 to 50 measurements were possible. The relationship between the EFs and plume sample dilution was examined to determine the plume dilution range over which the technique could deliver consistent results when measuring EFs for particle number (PN), NOx, SO2, and PM2.5 within a targeted dilution factor range of 50-1000 suitable for remote sampling. The EFs for NOx, SO2, and PM2.5 were found to be independent of dilution, for dilution factors within that range. The EF measurement for PN was corrected for coagulation losses by applying a time dependant particle loss correction to the particle number concentration data. For the Amity, the EF ranges were PN: 2.2 - 9.6 × 1015 (kg-fuel)-1; NOx: 35-72 g(NO2).(kg-fuel)-1, SO2 0.6 - 1.1 g(SO2).(kg-fuel)-1and PM2.5: 0.7 – 6.1 g(PM2.5).(kg-fuel)-1. For the Brisbane they were PN: 1.0 – 1.5 x 1016 (kg-fuel)-1, NOx: 3.4 – 8.0 g(NO2).(kg-fuel)-1, SO2: 1.3 – 1.7 g(SO2).(kg-fuel)-1 and PM2.5: 1.2 – 5.6 g(PM2.5).(kg-fuel)-1. The results are discussed in terms of the operating conditions of the vessels’ engines. Particle number emission factors as a function of size as well as the count median diameter (CMD), and geometric standard deviation of the size distributions are provided. The size distributions were found to be consistently uni-modal in the range below 500 nm, and this mode was within the accumulation mode range for both vessels. The representative CMDs for the various activities performed by the dredgers ranged from 94-131 nm in the case of the Amity, and 58-80 nm for the Brisbane. A strong inverse relationship between CMD and EF(PN) was observed.

Bio-inspired plume tracking algorithm for UAVS

There is an increased interest on the use of UAVs for environmental research and to track bush fire plumes, volcanic plumes or pollutant sources. The aim of this paper is to describe the theory and results of a bio-inspired plume tracking algorithm. A memory based and gradient based approach, were developed and compared. A method for generating sparse plumes was also developed. Results indicate the ability of the algorithms to track plumes in 2D and 3D.

Design and flight testing of a bio-inspired plume tracking algorithm for unmanned serial vehicles

There is an increased interest on the use of UAVs for environmental research such as tracking bush fires, volcanic eruptions, chemical accidents or pollution sources. The aim of this paper is to describe the theory and results of a bio-inspired plume tracking algorithm. A method for generating sparse plumes in a virtual environment was also developed. Results indicated the ability of the algorithms to track plumes in 2D and 3D. The system has been tested with hardware in the loop (HIL) simulations and in flight using a CO2 gas sensor mounted to a multi-rotor UAV. The UAV is controlled by the plume tracking algorithm running on the ground control station (GCS).

In search of a hidden long-term isolated sub-chondritic 142Nd/144Nd reservoir in the deep mantle : implications for the Nd isotope systematics of the Earth

Here we search for evidence of the existence of a sub-chondritic 142Nd/144Nd reservoir that balances the Nd isotope chemistry of the Earth relative to chondrites. If present, it may reside in the source region of deeply sourced mantle plume material. We suggest that lavas from Hawai’i with coupled elevations in 186Os/188Os and 187Os/188Os, from Iceland that represent mixing of upper mantle and lower mantle components, and from Gough with sub-chondritic 143Nd/144Nd and high 207Pb/206Pb, are favorable samples that could reflect mantle sources that have interacted with an Early-Enriched Reservoir (EER) with sub-chondritic 142Nd/144Nd. High-precision Nd isotope analyses of basalts from Hawai’i, Iceland and Gough demonstrate no discernable 142Nd/144Nd deviation from terrestrial standards. These data are consistent with previous high-precision Nd isotope analysis of recent mantle-derived samples and demonstrate that no mantle-derived material to date provides evidence for the existence of an EER in the mantle. We then evaluate mass balance in the Earth with respect to both 142Nd/144Nd and 143Nd/144Nd. The Nd isotope systematics of EERs are modeled for different sizes and timing of formation relative to ε143Nd estimates of the reservoirs in the μ142Nd = 0 Earth, where μ142Nd is ((measured 142Nd/144Nd/terrestrial standard 142Nd/144Nd)−1 * 10−6) and the μ142Nd = 0 Earth is the proportion of the silicate Earth with 142Nd/144Nd indistinguishable from the terrestrial standard. The models indicate that it is not possible to balance the Earth with respect to both 142Nd/144Nd and 143Nd/144Nd unless the μ142Nd = 0 Earth has a ε143Nd within error of the present-day Depleted Mid-ocean ridge basalt Mantle source (DMM). The 4567 Myr age 142Nd–143Nd isochron for the Earth intersects μ142Nd = 0 at ε143Nd of +8 ± 2 providing a minimum ε143Nd for the μ142Nd = 0 Earth. The high ε143Nd of the μ142Nd = 0 Earth is confirmed by the Nd isotope systematics of Archean mantle-derived rocks that consistently have positive ε143Nd. If the EER formed early after solar system formation (0–70 Ma) continental crust and DMM can be complementary reservoirs with respect to Nd isotopes, with no requirement for significant additional reservoirs. If the EER formed after 70 Ma then the μ142Nd = 0 Earth must have a bulk ε143Nd more radiogenic than DMM and additional high ε143Nd material is required to balance the Nd isotope systematics of the Earth.

Investigation into submicrometer particle and gaseous emissions from airport ground running procedures

Emissions from airport operations are of significant concern because of their potential impact on local air quality and human health. The currently limited scientific knowledge of aircraft emissions is an important issue worldwide, when considering air pollution associated with airport operation, and this is especially so for ultrafine particles. This limited knowledge is due to scientific complexities associated with measuring aircraft emissions during normal operations on the ground. In particular this type of research has required the development of novel sampling techniques which must take into account aircraft plume dispersion and dilution as well as the various particle dynamics that can affect the measurements of the aircraft engine plume from an operational aircraft. In order to address this scientific problem, a novel mobile emission measurement method called the Plume Capture and Analysis System (PCAS), was developed and tested. The PCAS permits the capture and analysis of aircraft exhaust during ground level operations including landing, taxiing, takeoff and idle. The PCAS uses a sampling bag to temporarily store a sample, providing sufficient time to utilize sensitive but slow instrumental techniques to be employed to measure gas and particle emissions simultaneously and to record detailed particle size distributions. The challenges in relation to the development of the technique include complexities associated with the assessment of the various particle loss and deposition mechanisms which are active during storage in the PCAS. Laboratory based assessment of the method showed that the bag sampling technique can be used to accurately measure particle emissions (e.g. particle number, mass and size distribution) from a moving aircraft or vehicle. Further assessment of the sensitivity of PCAS results to distance from the source and plume concentration was conducted in the airfield with taxiing aircraft. The results showed that the PCAS is a robust method capable of capturing the plume in only 10 seconds. The PCAS is able to account for aircraft plume dispersion and dilution at distances of 60 to 180 meters downwind of moving a aircraft along with particle deposition loss mechanisms during the measurements. Characterization of the plume in terms of particle number, mass (PM2.5), gaseous emissions and particle size distribution takes only 5 minutes allowing large numbers of tests to be completed in a short time. The results were broadly consistent and compared well with the available data. Comprehensive measurements and analyses of the aircraft plumes during various modes of the landing and takeoff (LTO) cycle (e.g. idle, taxi, landing and takeoff) were conducted at Brisbane Airport (BNE). Gaseous (NOx, CO2) emission factors, particle number and mass (PM2.5) emission factors and size distributions were determined for a range of Boeing and Airbus aircraft, as a function of aircraft type and engine thrust level. The scientific complexities including the analysis of the often multimodal particle size distributions to describe the contributions of different particle source processes during the various stages of aircraft operation were addressed through comprehensive data analysis and interpretation. The measurement results were used to develop an inventory of aircraft emissions at BNE, including all modes of the aircraft LTO cycle and ground running procedures (GRP). Measurements of the actual duration of aircraft activity in each mode of operation (time-in-mode) and compiling a comprehensive matrix of gas and particle emission rates as a function of aircraft type and engine thrust level for real world situations was crucial for developing the inventory. The significance of the resulting matrix of emission rates in this study lies in the estimate it provides of the annual particle emissions due to aircraft operations, especially in terms of particle number. In summary, this PhD thesis presents for the first time a comprehensive study of the particle and NOx emission factors and rates along with the particle size distributions from aircraft operations and provides a basis for estimating such emissions at other airports. This is a significant addition to the scientific knowledge in terms of particle emissions from aircraft operations, since the standard particle number emissions rates are not currently available for aircraft activities.

Ions in motor vehicle exhaust and their dispersion near busy roads

Measurements in the exhaust plume of a petrol-driven motor car showed that molecular cluster ions of both signs were present in approximately equal amounts. The emission rate increased sharply with engine speed while the charge symmetry remained unchanged. Measurements at the kerbside of nine motorways and five city roads showed that the mean total cluster ion concentration near city roads (603 cm-3) was about one-half of that near motorways (1211 cm-3) and about twice as high as that in the urban background (269 cm-3). Both positive and negative ion concentrations near a motorway showed a significant linear increase with traffic density (R2=0.3 at p<0.05) and correlated well with each other in real time (R2=0.87 at p<0.01). Heavy duty diesel vehicles comprised the main source of ions near busy roads. Measurements were conducted as a function of downwind distance from two motorways carrying around 120-150 vehicles per minute. Total traffic-related cluster ion concentrations decreased rapidly with distance, falling by one-half from the closest approach of 2m to 5m of the kerb. Measured concentrations decreased to background at about 15m from the kerb when the wind speed was 1.3 m s-1, this distance being greater at higher wind speed. The number and net charge concentrations of aerosol particles were also measured. Unlike particles that were carried downwind to distances of a few hundred metres, cluster ions emitted by motor vehicles were not present at more than a few tens of metres from the road.

Autonomous underwater vehicle trajectory design coupled with predictive ocean models : a case study

Data collection using Autonomous Underwater Vehicles (AUVs) is increasing in importance within the oceano- graphic research community. Contrary to traditional moored or static platforms, mobile sensors require intelligent planning strategies to manoeuvre through the ocean. However, the ability to navigate to high-value locations and collect data with specific scientific merit is worth the planning efforts. In this study, we examine the use of ocean model predictions to determine the locations to be visited by an AUV, and aid in planning the trajectory that the vehicle executes during the sampling mission. The objectives are: a) to provide near-real time, in situ measurements to a large-scale ocean model to increase the skill of future predictions, and b) to utilize ocean model predictions as a component in an end-to-end autonomous prediction and tasking system for aquatic, mobile sensor networks. We present an algorithm designed to generate paths for AUVs to track a dynamically evolving ocean feature utilizing ocean model predictions. This builds on previous work in this area by incorporating the predicted current velocities into the path planning to assist in solving the 3-D motion planning problem of steering an AUV between two selected locations. We present simulation results for tracking a fresh water plume by use of our algorithm. Additionally, we present experimental results from field trials that test the skill of the model used as well as the incorporation of the model predictions into an AUV trajectory planner. These results indicate a modest, but measurable, improvement in surfacing error when the model predictions are incorporated into the planner.

Experimental study of the concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller, which was placed in a glass-walled flume 0.4 m wide with a free surface depth of 0.15 m. The jet and scalar plume development were compared to that of a classical free round jet. Further, results pertaining to radial distribution, self similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration were presented and fitted with empirical correlations. Furthermore, propeller induced mixing and pollutant source concentration from a two-stroke engine were estimated.

Physical characteristics of small ions and their interaction with ultrafine particles in the urban environment

In recent years, the effect of ions and ultrafine particles on ambient air quality and human health has been well documented, however, knowledge about their sources, concentrations and interactions within different types of urban environments remains limited. This thesis presents the results of numerous field studies aimed at quantifying variations in ion concentration with distance from the source, as well as identifying the dynamics of the particle ionisation processes which lead to the formation of charged particles in the air. In order to select the most appropriate measurement instruments and locations for the studies, a literature review was also conducted on studies that reported ion and ultrafine particle emissions from different sources in a typical urban environment. The initial study involved laboratory experiments on the attachment of ions to aerosols, so as to gain a better understanding of the interaction between ions and particles. This study determined the efficiency of corona ions at charging and removing particles from the air, as a function of different particle number and ion concentrations. The results showed that particle number loss was directly proportional to particle charge concentration, and that higher small ion concentrations led to higher particle deposition rates in all size ranges investigated. Nanoparticles were also observed to decrease with increasing particle charge concentration, due to their higher Brownian mobility and subsequent attachment to charged particles. Given that corona discharge from high voltage powerlines is considered one of the major ion sources in urban areas, a detailed study was then conducted under three parallel overhead powerlines, with a steady wind blowing in a perpendicular direction to the lines. The results showed that large sections of the lines did not produce any corona at all, while strong positive emissions were observed from discrete components such as a particular set of spacers on one of the lines. Measurements were also conducted at eight upwind and downwind points perpendicular to the powerlines, spanning a total distance of about 160m. The maximum positive small and large ion concentrations, and DC electric field were observed at a point 20 m downwind from the lines, with median values of 4.4×103 cm-3, 1.3×103 cm-3 and 530 V m-1, respectively. It was estimated that, at this point, less than 7% of the total number of particles was charged. The electrical parameters decreased steadily with increasing downwind distance from the lines but remained significantly higher than background levels at the limit of the measurements. Moreover, vehicles are one of the most prevalent ion and particle emitting sources in urban environments, and therefore, experiments were also conducted behind a motor vehicle exhaust pipe and near busy motorways, with the aim of quantifying small ion and particle charge concentration, as well as their distribution as a function of distance from the source. The study found that approximately equal numbers of positive and negative ions were observed in the vehicle exhaust plume, as well as near motorways, of which heavy duty vehicles were believed to be the main contributor. In addition, cluster ion concentration was observed to decrease rapidly within the first 10-15 m from the road and ion-ion recombination and ion-aerosol attachment were the most likely cause of ion depletion, rather than dilution and turbulence related processes. In addition to the above-mentioned dominant ion sources, other sources also exist within urban environments where intensive human activities take place. In this part of the study, airborne concentrations of small ions, particles and net particle charge were measured at 32 different outdoor sites in and around Brisbane, Australia, which were classified into seven different groups as follows: park, woodland, city centre, residential, freeway, powerlines and power substation. Whilst the study confirmed that powerlines, power substations and freeways were the main ion sources in an urban environment, it also suggested that not all powerlines emitted ions, only those with discrete corona discharge points. In addition to the main ion sources, higher ion concentrations were also observed environments affected by vehicle traffic and human activities, such as the city centre and residential areas. A considerable number of ions were also observed in a woodland area and it is still unclear if they were emitted directly from the trees, or if they originated from some other local source. Overall, it was found that different types of environments had different types of ion sources, which could be classified as unipolar or bipolar particle sources, as well as ion sources that co-exist with particle sources. In general, fewer small ions were observed at sites with co-existing sources, however particle charge was often higher due to the effect of ion-particle attachment. In summary, this study quantified ion concentrations in typical urban environments, identified major charge sources in urban areas, and determined the spatial dispersion of ions as a function of distance from the source, as well as their controlling factors. The study also presented ion-aerosol attachment efficiencies under high ion concentration conditions, both in the laboratory and in real outdoor environments. The outcomes of these studies addressed the aims of this work and advanced understanding of the charge status of aerosols in the urban environment.

Investigation into the transport, behaviour and deposition of combustion aerosols from transport sources

The deterioration of air quality is a significant issue in large and growing cities. This work investigates particulate emissions from transport, the largest source of air pollution in cities today. Emitters such as busy roads and diesel trains are investigated, with specific reference to the evolution of particles over time and distance. Diesel trains are investigated as an alternative to road traffic in investigating evolutionary processes. Higher emissions and solitary sources mean that the emitted plume can be observed over time in a single location. These results represent the first investigation of the evolution of fine and ultrafine aerosol particles from this type of source. Aerosols near a busy road are investigated, with the result that a dependence of total number concentration on distance from the road is shown to be related to the fragmentation of nanoparticle clusters. Local meteorological conditions are also monitored and humidity is shown to vary with distance from the road in a nonmonotonic way. Particles from a busy road were also examined using a scanning electron microscope, with the intention of understanding the make up of the emitted aerosol plume. It was determined that due to significant surface behaviour post-deposition, this method of analysis could not directly classify airborne pollutants. Some interesting results were obtained however, particularly in terms of composite particles and the analysis of deposited patterns. This thesis introduces new work in terms of the analysis of diesel train particulate emissions, as well as adding further evidence towards the fragmentation process of aerosol evolution in both background concentrations and emitted aerosol plumes.

Tracking the magmatic evolution of island arc volcanism : insights from a high-precision Pb isotope record of Montserrat, Lesser Antilles

The volcanic succession on Montserrat provides an opportunity to examine the magmatic evolution of island arc volcanism over a ∼2.5 Ma period, extending from the andesites of the Silver Hills center, to the currently active Soufrière Hills volcano (February 2010). Here we present high-precision double-spike Pb isotope data, combined with trace element and Sr-Nd isotope data throughout this period of Montserrat's volcanic evolution. We demonstrate that each volcanic center; South Soufrière Hills, Soufrière Hills, Centre Hills and Silver Hills, can be clearly discriminated using trace element and isotopic parameters. Variations in these parameters suggest there have been systematic and episodic changes in the subduction input. The SSH center, in particular, has a greater slab fluid signature, as indicated by low Ce/Pb, but less sediment addition than the other volcanic centers, which have higher Th/Ce. Pb isotope data from Montserrat fall along two trends, the Silver Hills, Centre Hills and Soufrière Hills lie on a general trend of the Lesser Antilles volcanics, whereas SSH volcanics define a separate trend. The Soufrière Hills and SSH volcanic centers were erupted at approximately the same time, but retain distinctive isotopic signatures, suggesting that the SSH magmas have a different source to the other volcanic centers. We hypothesize that this rapid magmatic source change is controlled by the regional transtensional regime, which allowed the SSH magma to be extracted from a shallower source. The Pb isotopes indicate an interplay between subduction derived components and a MORB-like mantle wedge influenced by a Galapagos plume-like source.

The El Chichon stratospheric cloud : solid particulates and settling rates

Sampling of the El Chichón stratospheric cloud in early May and in late July, 1982, showed that a significant proportion of the cloud consisted of solid particles between 2 μm and 40 μm size. In addition, many particles may have been part of larger aggregates or clusters that ranged in size from < 10 μm to > 50 μm. The majority of individual grains were angular aluminosilicate glass shards with various amounts of smaller, adhering particles. Surface features on individual grains include sulfuric acid droplets and larger (0.5 μm to 1 μm) sulfate gel droplets with various amounts of Na, Mg, Ca and Fe. The sulfate gels probably formed by the interaction of sulfur-rich gases and solid particles within the cloud soon after eruption. Ca-sulfate laths may have formed by condensation within the plume during eruption, or alternatively, at a later stage by the reaction of sulfuric acid aerosols with ash fragments within the stratospheric cloud. A Wilson-Huang formulation for the settling rate of individual particles qualitatively agrees with the observed particle-size distribution for a period at least four months after injection of material into the stratosphere. This result emphasizes the importance of particle shape in controlling the settling rate of volcanic ash from the stratosphere.