Eruption dynamics are sensitive to ash aggregation, and aggregates are commonly found in eruptive deposits. While ash dispersal and associated hazards are sensitive to aggregation, few experiments have been conducted on this phenomena using natural materials across the diverse range of conditions expected in volcanic flows. We have isolated two regimes, wet and dry, in which aggregation occurs due to two different forces, electrostatic and hydrodynamic. Using a closed chamber to create a controlled atmosphere, we found that relative humidity, residence time, and kinetic energy are the three variables necessary to define wet and dry flow regimes. A series of process-based equations defining the behavior of ash particles have been developed. We propose an aggregation model that can be used for ash dispersal forecasts across a range of conditions in an eruptive plume.
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 The residence time of volcanic ash emitted into the atmosphere during explosive volcanic eruptions ultimately determines the extent and duration of airborne ash hazards [e.g., Ilyinskaya et al., 2011; Folch et al., 2010; Taddeucci et al., 2011]. One of the largest sources for uncertainty in determining ash residence time is our limited understanding of the mechanisms and rates of ash aggregation, the process by which ash particles adhere to each other in the atmosphere. While aggregation rates remain poorly understood, their presence is documented in many recent eruptions, and they are prominent in the depositional record [Brand and White, 2007; Branney and Brown, 2011; Brown et al., 2010; Scollo et al., 2007; Stevenson et al., 2012; Veitch and Woods, 2001]. Recent volcanic eruptions, including the eruption of Eyjafjallajökull in 2010, highlighted current gaps in our understanding and quantification of the aggregation mechanisms [Folch et al., 2009; Taddeucci et al., 2011; Folch et al., 2012]. Integrating new information on ash aggregation mechanisms into numerical models has been suggested as a critical factor needed to improve their accuracy [Scott and McGimsey, 1994; Veitch and Woods, 2001; Scollo et al., 2007; Folch et al., 2010; Textor et al., 2006b].
 Few experiments have been designed to study ash aggregation directly, and until recently [Van Eaton et al., 2012], either it has not been considered in models or water droplet coalescence has been used as a proxy for this behavior [Gilbert and Lane, 1994; James et al., 2002, 2003; Barsotti et al., 2008]. Models assuming liquid-coated ash cite the need for constraints on the efficiency of the process [Textor et al., 2006a; Costa et al., 2010]. In the limited parameter space that has been tested experimentally, droplet coalescence has been found to be an inaccurate proxy [Gilbert and Lane, 1994; Telling and Dufek, 2012]. Decreasing collision kinetic energy (CKE) has been found to increase the efficiency of both aggregation [Gilbert and Lane, 1994; Telling and Dufek, 2012] and droplet coalescence [Low and List, 1982]. However, droplet coalescence occurs at energies nearly 4 orders of magnitude below those found in particle aggregation [Beard et al., 2002; Telling and Dufek, 2012]. Gilbert et al. , James et al. [2002, 2003], and Telling and Dufek  have described particle aggregation behavior in a number of regimes. However, little work has been done to examine how atmospheric residence times might alter the efficiency of ash interactions despite the fact that Lautze et al.  and others have shown that ash is chemically and physically altered during transport in volcanic plumes. For accurate aggregation prediction, more information is needed about aggregation behavior in high residence time ash, water vapor rich flows, and a wider array of particle energies, all of which are expected to be encountered during explosive volcanic eruptions.
 Here we present experiments designed to investigate ash aggregation efficiency, the ratio of aggregating particles to the total number of particle collisions, across a range of conditions. In a controlled atmosphere, we examined the role of residence time, atmospheric pressure, and humidity on aggregation. Data were collected from two samples of ash and an ash proxy to further allow us to compare how composition might alter aggregation behavior. In the present work, we focus on processes occurring above the freezing point of water. The relationships derived from our results can be applied to volcanic plumes and pyroclastic density currents alike and fill a gap in our current understanding of aggregation processes.
 A controlled atmospheric chamber was designed to be evacuated from ambient conditions, at sea level, to 13 kPa, which corresponds to an altitude of roughly 16 km, and a range of relative humidities, 11–95%, likely encountered in volcanic plumes (auxiliary material). Particles, which were released from the top of the tank at varying speeds, collided with a fixed sample to examine variable impact energies. In order to create a uniform, stationary bed of particles, each target particle sample was adhered to a glass slide using thermal epoxy, and we ensured that a monolayer of ash particles was exposed at the surface to both treat the roughness effects of natural ash and also expose the surface for adsorption of water over time. A Phantom MIRO-4 high-speed camera was used to capture particle interactions at the bed at a rate of 2500 fps.
 Three particle samples were used in the experiments. A sample of ballotini (spherical silica) with a diameter between 90 and 150 µm was used as a proxy for ash. Samples from the Mount St. Helens, WA, 1980 eruption (dacite composition) and the Tungurahua, Ecuador, 2006 eruption (andesite composition) were also used to examine the potential effect of composition. These ash samples were both sieved to between 90 and 106 µm in diameter and had a roughness length on the order of nanometers up to a few micrometers [Delmelle et al., 2007; Carter et al., 2009; Ersoy, 2010]. The high-humidity experiments required a minimum humidity of 71%, the point at which Lathem et al.  predict monolayer water coverage to begin to form. Most high-humidity trials, however, occurred at greater than 90% humidity. Low pressures ranged from 13 kPa to 88 kPa, and multiple trials were conducted at roughly 17 kPa intervals. Variable ash residence time was examined by maintaining conditions in the tank between 1 and 150 min. Thirty to thirty-six trials were conducted on each of the samples.
 A random sample of 20 particles was chosen from every trial, which may include up to 100 particles, and the particles were analyzed manually. We analyzed larger samples (30, 40, and 50 particles) and confirmed that aggregation efficiency was not affected by the sample size of randomly chosen particles. The fall velocities for each particle were measured within 0.01 m/s using high-speed video and used to calculate an approximate CKE and the restitution coefficient, the velocity ratio of precollision and postcollision particles, and aggregation was recorded (effective restitution coefficient of zero). Overall, these experiments provided a robust data set considering ash aggregation efficiency as a function of residence time, atmospheric pressure, relative humidity, and CKE.
 The aggregation efficiencies of all three samples, SiO2, Mount St. Helens (MSH), and Tungurahua (Tu), were found to be sensitive to a range of pressure, relative humidity, residence time, and CKE conditions. While CKE is the dominant factor controlling aggregation efficiency [Telling and Dufek, 2012], we also found that high (>71%) relative humidity becomes important when particles interact for long periods of time with the atmosphere (Figure 1). The scatter in the data reflects that natural materials were used, each with variable shape and different contact angles during impact. We found a critical residence time by which aggregation efficiency increased by more than 60% over initial conditions for particles with identical CKE between approximately 50 min (MSH) and 110 min (Tu), when a film of water had developed on the fixed sample (auxiliary material). We confirmed the presence of the film by weighing the slides. The sample slides were each dried and weighed before being placed in the experiment at high relative humidity (>71%). Each slide was weighed at 10 min intervals, and a consistent weight increase of 0.1–0.2 ± 0.001 g per slide was observed by 50 min. The increase in weight, distributed over the surface of the slide, corresponds to a water layer with a depth on the scale of tens of micrometers. Since only the fixed sample developed a water layer, the interaction time required for two wetted particles to see a substantial increase in aggregation efficiency may be less than 50 min. In the low relative humidity condition, there is little difference between the long and short interaction time aggregation efficiencies (Figure 1). Decreasing atmospheric pressure enhanced CKE (and decreased aggregation efficiency) due to drag reduction on the particles but otherwise played no discernible role in the collision dynamics. In general, aggregation behavior for the different compositions showed no systematic variation.
 Electrostatic and wet aggregation processes both play a role in volcanic flows. The results of these experiments permit quantification of the flow regimes and conditions in which each is expected to dominate [Gilbert and Lane, 1994; Telling and Dufek, 2012]. In either regime, a balance of the inertial force of two colliding particles with the force required to arrest the collision can be used to predict whether a collision will produce an aggregation or a bounce event [Schmeeckle et al., 2001]. In the case of particles coated by a viscous fluid, the particles can be arrested by hydrodynamic forces [Davis et al., 1986; Schmeeckle et al., 2001; Matar et al., 2006]. However, such fluid forces are much weaker in the case of dry particle collisions where the working fluid is air and, in this case, electrostatic stopping forces need to be considered for the formation of particle aggregates.
 A film of water was observed at RH > 71% and interaction times longer than 50 min. We also noted a distinct change in the restitution coefficient behavior of the particles for these conditions. The data were split up into two categories—wet, which met these conditions, and dry, which did not. The abrupt change in aggregation and restitution coefficient behavior after a delay period is consistent with the interpretation of water layer growth over this time period exceeding the roughness scale of the ash particles.
 As an indicator of the importance of interstitial fluid during impact, we examined the ratio of the relative inertial timescale of a particle to the viscous fluid timescale (i.e., the Stokes number). The Stokes number is defined in equation ((1)), where m* is the reduced mass, u is the particle velocity, μ is the viscosity of the interstitial fluid at the point of collision, and r* is the reduced radius:
Below a given Stokes number, Stcr-a, all collisions are likely to produce aggregates, and above Stcr-b, all collisions are likely to result in a bounce. This range of critical Stokes numbers is dependent on the detailed geometry of the collision and the elastic properties of the material [Davis et al., 1986; Schmeeckle et al., 2001].
 The critical Stokes ranges for wet SiO2, MSH, and Tu, respectively, were found to be 13–61, 13–64, and 20–64. These values are on the same order as those in Davis et al. , a theoretical examination of critical Stokes number, and Schmeeckle et al. , which combined theoretical and experimental methods for larger particles immersed in fluid. However, in the dry sample, the Stokes numbers ranged from 120 to 4200 much beyond the range that permits explanation of aggregation due to hydrodynamic forces. As hydrodynamic theory is a poor indicator of particle aggregation for the dry particle case, a different relationship must be used to describe this scenario.
 The wet Stokes numbers are larger than unity, and this can in part be explained by variability in contact angle and shape [Schmeeckle et al., 2001]. Also, the viscous term appearing in the Stokes scaling is not the only force responsible for arresting the particle motion. The energy dissipated due to surface tension and fluid inertia in the film layer also contributes to lowering the restitution coefficient and promoting aggregation [Gollwitzer et al., 2012]. Including these terms, we calculate the restitution coefficient reduction relative to the dry restitution coefficient as a function of water layer thickness [Gollwitzer et al., 2012]. Figure 2a shows the ratio of the wet restitution coefficient relative to the dry coefficient (contour lines) as functions of the water layer thickness relative to the size of the ash particle and as a function of the Stokes number. The zero restitution coefficient line is equivalent to aggregation. A clear dampening effect can be seen in all three wet samples (Figure 2c).
 Electrostatic aggregation is the most likely mechanism to explain aggregation in the cases where particles are not covered by a water layer. As particles become charged through particle-particle collisions or during initial fragmentation [Gilbert et al., 1991; Gilbert and Lane, 1994], electrostatic bonds form, creating loosely bound aggregates. In this case, the arresting force is not viscous fluid in the space between the particles [Schmeeckle et al., 2001] but an electrostatic force. We define the ratio of inertial to electrostatic forces as the inertial-electrostatic (IE) ratio (equation ((2))), where δ is the distance between the two charges, m* is the reduced mass of the particles, u is the collisional velocity, k is Coulomb's constant, and q is the particle charge. The average charge density was estimated for the particles based on the range of charge estimates of Gilbert and Lane , James et al. , and Telling and Dufek . As the IE ratio approaches one or greater, aggregation efficiency should decay to zero (Figure 3).
5 Implications for Volcanic Modeling
 We can develop a process-based set of equations suitable for use in numerical modeling that defines the behavior of ash particles described in these experiments. One of the largest sources of variability for any given collision is the ash morphology and contact angle during collision. We propose describing this variability through a probability distribution,
where is a generic dissipation mechanism (either electrostatic or hydrodynamic) that can be described through a physical law and σdiss represents the variability arising from particle shape and uncertainty in evaluating the physical parameters. In the case of electrostatic aggregation, the dissipation is due to oppositely charged particles, Eelec, which is approximately 4 × 10−8 mJ, using estimates of charge density from James et al.  and Telling and Dufek . In the case of hydrodynamic aggregation, using the approach of Gollwitzer et al. , we calculate the dissipation is composed of the viscous dampening experienced by the particle due to the fluid, Evisc, 9 × 10−8 mJ, the kinetic energy change in the fluid due to the collision, Eacc, 4 × 10−8 mJ, and the surface energy change of the fluid, Eb, 8 × 10−7 mJ, using the characteristics of an average particle in our experiments (auxiliary material). Integrating this probability distribution for all dissipation energies that exceed the initial inertial energy of the particle, Ei, and incorporating the energy loss described by the initial restitution coefficient, e0, approximately 0.4, give the following set of equations for the aggregation fraction, Fagg, for the electrostatic,
and hydrodynamic cases
 The variance, σDiss, was varied systematically to obtain the best fit between the data and this model, while the energy components were calculated based on the physical properties of the ash and interstitial fluid using the approach of Gollwitzer et al.  (detailed information on computing these energies can be found in the auxiliary material). The variance for the electrostatic case is 7.4 × 10−11 and the variance for the hydrodynamic case is 6.9 × 10−10. These fits (Figures 1e and 1f) provide a probabilistic approach to calculating aggregation and can be incorporated into large-scale models of ash dispersal.
 We present a set of experiments that investigate the importance of CKE, atmospheric pressure, residence time, and relative humidity from 11 to 95% on the aggregation potential of volcanic ash and an ash proxy. CKE is the most diagnostic parameter for ash aggregation efficiency. Relative humidity was found to become important for particles that had long residence times in a high-humidity environment. In pyroclastic flows, these residence times may occur during propagation, in the recirculation region near the volcanic vent or in coignimbrite plumes [Brown et al., 2010]. In volcanic plumes, the residence time of fine to very fine ash can last from >30 min to >10 days, often in water vapor rich environments [Rose and Durant, 2011].
 The physics of wet aggregation, in high relative humidity, high residence time conditions, can be described accurately by hydrodynamic theory. Electrostatic ash aggregation is dominant in humidity regimes below 71% relative humidity and in fresh particles. For these cases, the inertial-electrostatic ratio was developed to describe aggregation efficiency. Probabilistic relationships were developed for the wet and dry cases to predict aggregation efficiency in terms of balancing the appropriate forces present during a collision. These equations can be incorporated into numerical models to improve hazards predictions and further our understanding of how pyroclastic density currents and volcanic plumes develop as they move away from the vent. Further work is required to develop a probabilistic relationship for ice-ash interactions.
 This work was supported in part by NSF grants 1144585 and 1150794. We would especially like to thank Calais, Porritt, and an anonymous reviewer for their help in improving the manuscript.
 The Editor thanks Lucy Porritt and an anonymous reviewer for their assistance in evaluating this paper.