We are interested in sources of inhaled particulate exposure; a ubiquitous source is the dust generated by falling powders. There are two mechanisms for dust generation: aerosol that results intrinsically from the falling powder stream; aerosol that results from the “splash” of the powder as it impacts a surface. Modeling the first process is the subject of a forthcoming article. The current article presents the results of a simple model for this second “splash” process. We argue that dust generated by this “splash” process derives from the aerodynamic resuspension of particles previously deposited on the surface; the aerodynamic forces are associated with the decelerating powder agglomerates.

Resuspension has been actively studied for some time—for a review, see Ferro (2022). Most resuspension studies focus on overcoming the adhesive forces binding the particles to the substrate (John 1995). However, Cleaver and Yates (1973) investigated the role of turbulent flow at the surface in particle detachment. Our interest is in the bulk aerodynamics leading to detachment and in the subsequent evolution of the aerosol dust cloud.

We first review (Section 1.2) real world sources of dust exposure and its measurement; we then focus (Section 1.3) on falling powders and distinguish (Section 1.4) the splash process; Section 1.5 defines our model of a descending pellet (representing an agglomerate) impacting a surface covered with a monolayer of primary particles. Section 2 summarizes our numerical methods. Section 3 discusses our results. Section 4 places our results in the context of the previous work by Shields on the (hydrodynamic) resuspension (of sediment) due to turbulent parallel flow.

Industrial powder handling represents a primary source of dust. Processes like powder spilling (Sutter, Johnston, and Mishima 1982), pouring (Heitbrink, Baron, and Willeke 1992), and conveying (Baker et al. 1986; Cheng 1973) can all lead to the generation of dust in occupational environments. Grinding and milling operations can also contribute to dust generation (Pensis et al. 2010). Conveyor transferring and the loading and unloading of bulk materials, like ore and agricultural products, can lead to dust generation (Chen et al. 2012; Shaw et al. 1998).

Dust can adversely affect human health. Silicosis, asbestosis, lung cancer, and heart disease are all related to dust exposure (Donaldson and Seaton 2012). Size and surface chemistry contribute to the toxicity of inhaled powders (Duffin et al. 2002, 2007). The health hazards associated with exposure to nanoparticles are of current interest (Trout and Schulte 2010). Increased production and use of nanomaterials presage increased occupational exposure to dust from these materials (Evans et al. 2010; Kuhlbusch et al. 2011; Peters et al. 2008).

A free-falling powder is a common source of airborne dust, often occurring during a materials transfer process, or an accidental spill. Manual powder handling operations, such as silo or bag filling from a hopper, bag emptying, powder weigh-out, and powder transfer from a conveyor, all involve free-falling powders. The mechanisms of dust generation from free falling powders are not well understood.

Dustiness quantifies the ability of a finely divided solid (a powder) to become airborne as a dust aerosol when the powder is subjected to a mechanical or aerodynamical stimulus (Liden 2006; Plinke et al. 1995). Various dustiness measurement methods have been developed (BOHS 1985; Hamelmann and Schmidt 2003, 2004, 2005). Three types of dustiness testing methods are commonly used: the rotating drum method, the free-falling powder method, and the Venturi method. For a comprehensive review of dustiness test methods, see Evans (2024). Field evaluations of worker dust exposure do not always correlate with dustiness test results (Brouwer et al. 2006; Heitbrink, Todd, and Fischbach 1989; Heitbrink et al. 1990; Ribalta et al. 2019).

Several historical dustiness test configurations utilize the falling powder geometry. Falling powder test systems can be of the single drop type, where a powder sample is dropped as a single bolus and impacts onto a solid surface, or the continuous falling type, where a continuous stream of powder winnows down a test chamber. Continuous falling methods tend to be more consistent than single drop methods (BOHS 1988); nonetheless, the majority of falling powder configurations are single-drop type.

Powell and Russell (1933) described a single-drop test with passive dust sampling to quantify coal and coke dust release; ASTM D547-41 (1980) standardized this test method. BOHS (1985) described a scaled down version with active particle samplers. Lundgren (1986) and Lundgren and Rangaraj (1986) similarly used active sampling. In a classical study, Andreasen, Hofman-Bang, and Rasmussen (1939) used the single drop technique to compare the dustiness of a wide range of materials against a lycopodium reference standard.

The Roaches Dust Particle Apparatus was developed to test dyestuffs (Berger-Schuun et al. 1989) and was later evaluated by Lyons and Mark (1992). A single bolus of test powder falls into a quiescent chamber and impacts onto a base surface. In the Palas Dustview II version, the aerosol is optically monitored. O’Shaughnessy, Kang, and Ellickson (2012) described a low mass variant of this test.

Burdett et al. (2000) describe a single drop test configuration with optical extinction detection, standardized as DIN 55992-2 (1999). The test powder falls down a column; a gentle cross flow of air transports the dusty aerosol to size selective particle collection foams (CEN 1993; ISO 1995; Vincent et al. 1999). Splashing of the falling test powder from the impaction plate introduces variability. The Carr dispersibility test (ASTM 2021) measures the aerosolized dust as that gravimetric fraction of the dropped bolus that does not deposit on a collection surface at the base of the chamber.

Wells and Alexander (1978) described a continuous pour configuration. Dust is measured from air drawn horizontally across the falling powder. In the MRI (Midwest Research Institute) pouring device (Cowherd, Grelinger, and Wong 1989), a powder falls onto a powder covered receiving surface; a rotating, vibrating stainless-steel sample cup ensures a continuous stream of powder. EN15051-3 (CEN 2013) and EN17199-3 (CEN 2019) standardize a continuously metered falling powder test, performed against a slow countercurrent of upward moving air (Dahmann, Hartfiel, and Mocklinghoff 1997).

Computational Fluid Dynamics (CFD) has previously been used to study various dustiness testers. Dubey, Ghia, and Turkevich (2017) used CFD to investigate injection and sampling in the Venturi dustiness tester (VDT). The aerosolization within the VDT injection tube has also been investigated with CFD (Palakurthi 2017; Palakurthi, Ghia, and Turkevich 2017, 2022; Sharma 2021; Sharma, Ghia, and Turkevich 2020a, 2020b). Chen et al. (2021) and Chen, Jog, and Turkevich (2023) used CFD to investigate dust behavior in the standard (EN15051-2) and high-speed (Heubach) rotating drums. Schulz et al. (2019) used CFD-DEM to investigate the dustiness of bulk material handling in high-speed rotation drums as well as in the Palas Dust View apparatus. Chen et al. (2023) used CFD to study surface dust aerosolization by a turbulent parallel jet. Ansart et al. (2009, 2011) and Ansart, de Ryck, and Dodds (2009) used an Euler-Euler multiphase model to investigate the intrinsic dust generation from a continuous falling powder.

Heitbrink (1990) and coworkers (Heitbrink, Baron, and Willeke 1992) emphasized the additional dust generated by the “splash” of the powder from the substrate. A single bolus of powder fell either onto a flat plate or into a water-filled beaker. The difference in aerosol concentration caused by changing the impact surface was assumed to be the aerosol caused by processes that occur when the powder hits the flat plate. Two fine aluminum oxide powders were studied. Comparable contributions to the aerosol were generated from the powder as it falls and from the impact. The impact aerosol was enhanced in ultra-fines compared with the aerosol aerodynamically generated from the falling powder (Heitbrink 1990).

The Ibaseta-Biscans experiment (2007) was inspired by the MRI test (Cowherd et al. 1989). The powder was released from an invertible beaker; aerosol concentration and size distributions were measured at various heights. Two nanostructured powders were studied: anatase TiO₂ and fumed SiO₂. Aerosol was produced by two mechanisms: dust generation from the falling powder and dust generation after impact on the chamber floor. Most of the aerosol was generated during the impact against the solid surface and then was upwardly convected. Once the aerosol was uniform in the chamber, the aerosol concentration decreased homogeneously via settling. We have visualized the second “splash” process in our laboratory.

A nominally 3μm calcium carbonate powder (Dust Chaser Fluorescent Leak Detector Powder from W. H. Kingsmill, Ltd., Burlington, ON, Canada: 75% calcium carbonate, 25% resin: 1,3-isobenzofurandiole polymer with 2,2-bis(hydroxymethyl)-1,3 propanediol to incorporate pink fluorescent pigment) is poured from a glass beaker, at a height of ~0.5m, onto a Plexiglas tray (with rim). The pouring powder is illuminated with UV light (100 LED Scorpion Master with peak λ=390nm); the pouring process is recorded with a Camcorder (Hitachi DZ-BD10HA) at 30fps. The powder stream is intermittent (rather than continuous), reflecting cohesive agglomeration of the powder; the falling aggregates appear brightly illuminated (Figure 1a).

After 0.3s, a fainter dust cloud (presumably consisting of smaller particles) rises from, and bounded by, the rim of, the Plexiglas tray (Figure 1b). The particle size distribution (SEM analysis conducted by Maxxam, Bureau Veritas, Kennesaw, GA) of the original powder contains a significant submicron fraction (33.2% with l<1μm) in addition to the larger particles (41.2% with 1μm < l < 2μm; 15.6% with 2μm < l < 3μm; 6.3% with 3μm < l < 5μm; 2.9% with 5μm < l < 10μm; 0.8% with l > 10μm).

A falling powder generates dust via two processes: (a) dust generation directly by the falling powder (air-particle interaction—upper part of figure), and (b) dust generation resulting from powder agglomerates impacting the bottom surface (lower part of figure) (Figure 2).

In the first process, the falling powder entrains flow in the surrounding air (CEN 2013). The velocity gradient, between the falling powder and the quiescent air, transfers kinetic energy from the powder into air motion. The resultant air flow is complicated and is the subject of a future study.

In the second process, when agglomerated powder impacts the bottom surface, the accompanying air flow resuspends individual particles that had previously been deposited on the surface (Andreasen, Hofman-Bang, and Rasmussen 1939; BOHS 1985; Cawley and Leith 1993; Cowherd, Grelinger, and Wong 1989; Hammond 1980; Heitbrink, Baron, and Willeke 1992; Plinke, Leith, Boundy, et al. 1994; Plinke, Maus, and Leith 1992; Plinke et al. 1991). The present article reports the results of simulations of this second process. Plinke, Leith, Goodman, et al. (1994) studied the impaction force of falling powder agglomerates on the substrate.

Individual primary particles falling onto the bottom of the chamber do not contribute to the splash aerosol; they merely sediment at their Stokes terminal velocity. Large particle agglomerates falling to the bottom, or the collective motion of the dense particle stream impacting the bottom surface, generate strong vorticity in the vicinity of the bottom surface, which suspends previously deposited particles.

Our simulations study the aerodynamic dust generation resulting from the impact of the falling powder with the bottom surface. Falling agglomerates, or the collective motion of the falling powder, are modeled as a falling pellet disk. The pellet remains intact in this simulation. The powder hill at the base of the powder stream is modeled as a layer of particles. In our simulations, this layer of particles is released slightly above the bottom surface within 0.1s after the powder pellet impact. A result of our simulations is that the backflow generated by the falling disk (vortex shedding) is much more efficient than that from an impinging piston whose backflow at the surface merely derives from the displaced air ahead of the piston. A schematic of these simplifications is shown in the online supplemental information (SI, Section S-1).

The model geometry is inspired by the Heitbrink experiments (Heitbrink, Baron, and Willeke 1992). The test chamber is a column of 75cm in height with a square 12 × 12cm base. The standard pellet in the simulations is a cylindrical disk of 4mm radius and 3mm thickness. The size of the pellet is clearly much larger than a typical agglomerate; however, we argue (see the SI—Section S-6) that the physics of the splash process is relatively insensitive to the size of the pellet. For specificity, the powder and pellet are modeled as silica, with density ρ = 2000kg/m³; the pellet has a mass of 3.0144 × 10⁻⁴ kg. It is released from the top of the test chamber; for numerical stability of the simulation, the release is gradually ramped up, with the full gravitational acceleration only achieved after Δt=0.25s. Physically, the orientation of a falling disk would be unstable, with the disk tumbling (Field et al. 1997; Zhong, Chen, and Lee 2011; Zhong et al. 2013); in our simulations, the disk is constrained to fall with its flat always oriented horizontally, i.e., parallel to the bottom surface. Again, for numerical stability of the simulation, the pellet disk is not allowed to impact the bottom of the test chamber, but rather, the fall of the disk is halted 1mm above the bottom of the test chamber. Halting the pellet descent just before impact also isolates the aerodynamic resuspension mechanism (studied here) from other forces between the pellet and the particles that are to be resuspended.

The final velocity of the pellet is 3.64m/s, achieved at Δt~0.515s from release. The final velocity is reduced by 10% due to the ramping up of gravity; similarly, the impact time is delayed by 32% due to the ramping up of gravity. Only the final impact velocity is relevant for the dust cloud generation. This final velocity is only ¼ of the estimated terminal velocity (balancing gravitational acceleration against Stokes drag). For a discussion of the terminal velocity of disk-shaped particles, see Zhou et al. (2022). Since all velocities are low, the air is treated as incompressible. The Reynolds number for this final air flow around the pellet is Re ~ 1860. For 40 < Re < 105, the flow pattern is expected to be symmetric about the central axis of the disk, with a recirculation zone behind the disk. For Re ~ 105, the wake behind the disk is expected to lose axial symmetry, with long thin thread-like wakes extending behind a pair of recirculation zones (Natarajan and Acrivos 1993; Zhong and Lee 2012). Periodic vortex shedding is expected to occur for Re > 118 (Bearman and Takamoto 1988; Fabre, Auguste, and Magnaudet 2008; Miau et al. 1997; Shenoy and Kleinstreuer 2008; Zhong and Lee 2012). Vortex generation behind accelerating and decelerating disks has also been studied (Sallet 1975; Steiner et al. 2023; Taylor 1953; Yang, Jia, and Yin 2012).

Spherical particles are uniformly distributed as a monolayer at the bottom of the chamber and are released at Δt=0.6s after the release of the disk at the top, i.e., within 0.1s after the disk is stopped at the bottom. Releasing the particles just above the substrate deliberately neglects particle-substrate interactions (the focus of traditional resuspension studies, which emphasize overcoming the adhesion forces to the substrate). There are no particle-particle interactions and no particle agglomeration or break-up. Particle collisions with the chamber wall are treated as elastic. The simulations are athermal. The simulations are thus designed to isolate and highlight the role of aerodynamics in the resuspension process.

We have used STAR-CCM+ (2023) as the CFD simulation software in this study. STAR-CCM+ can easily track massive particle trajectories. For a general discussion of modeling dilute particle-laden flows, see Chen and Wood (1985), Crowe (1998), Curtis and van Wachem (2004), Schwarzkopf, Crowe, and Dutta (2009), Tsuji, Morikawa, and Shiomi (1984), and Zhang and Reese (2001).

The domain is the Heitbrink chamber (75 × 12 × 12cm). Unstructured grids (Ferziger, Peric, and Street 2019) were generated within STAR-CCM+; the basic cell is a 3mm cube (‘trimmed cell’) in the bulk of the domain and flattened rectangular prisms at the disk boundary surface. Near the bottom surface (5 × 12 × 12cm), the grid is 50% refined (refined cell is a 1.5cm cube). The central column (75 × 5 × 5cm) is also 50% refined. The total cell count is 1,131,386. The falling disk is treated as a moving part. The refined grid in the central cylinder rigidly moves with the falling disk. A schematic of the grid geometry is given in the SI (Section SM-2).

We first discuss the air flow generated by the falling pellet disk (R=4mm, t=3mm). As the disk falls, it induces air motion within the chamber (SI Figure S-5). After Δt~0.3s, Re > 100, and vortices are shed behind the disk; the flow behind the disk is asymmetric and unstable. Air ahead of the disk is quiescent. The disk “impacts” the bottom of the chamber at t=0.54s. Particles will be released at 0.6s. As the pellet impacts, the edges of the disk are regions of high vorticity (SI Figure S-6). Radial and upward air flow has the potential to loft particles up from the surface and aerosolize a dust cloud.

Figure 3 shows the vertical velocity, v_y, on the central midplane (z=0) just before (t=0.5s—panel a) and just after impact (t=0.6s—panel b); height axis is left-to-right (the top of the chamber is at left; the base of the chamber is at right); cross-plane distance is front-to-back. We are particularly interested in the air flow induced at the base of the chamber, which will be instrumental in lofting dust from the monolayer. Before impact, the downward vertical velocity is confined to the wake immediately behind the disk (there is negligible flow ahead of the disk, arguing against the importance of piston-like flow driving dust dispersion); a small region of upward velocity exists just outside the disk, presumably from the attached vortex ring around the disk. Upon impact, the region of upward velocity extends from the disk radius outwards all the way toward the chamber walls. A full time sequence of the evolution of the vertical velocity is given in the SI (Figure S-7).

Figure 4 shows the out-of-plane vorticity magnitude, |ω_z|, on the central midplane (z=0) just before (t=0.5s—panel a) and just after impact (t=0.6s—panel b); height axis is left-to-right (the top of the chamber is at left; the base of the chamber is at right); cross-plane distance is front-to-back. Again, we are interested in the air flow induced at the base of the chamber, which will be instrumental in lofting dust from the monolayer. Before impact, there is large positive/negative vorticity on the right/left of the disk, indicative of the vortex ring attached to the disk; again, vorticity is confined to the wake behind the pellet. Upon impact, the vorticity dissipates radially. We interpret this behavior as the detachment of the bound trailing vortex ring upon deceleration of the pellet. A full sequence of the out-of-plane vorticity, ω_z is given in the SI (Figure S-8).

In this section, we discuss the dust cloud generated by the impact of the standard pellet disk (R=4mm, t=3mm) on a monolayer of 1 μm silica particles. The dust cloud develops with time, as shown in Figure 5. The pellet has impacted at t=0.54s (before the first panel). The wake behind the decelerated disk evinces the residual motion (velocities depicted with the color scale) due to previous vortex shedding; this persists for long time (it is still apparent at t=20s). At the bottom of the chamber, the lofted particle dust cloud is indicated in dark blue. Due to the small particle size (d=1μm), the dust cloud does not settle with time. Note the scale: the chamber height is 75cm; the apparent dust cloud height is of the order of several cm.

Pictures showing the temporal evolution of dustiness, average height, and radius of the dust cloud are given in the SI (Section S-5). For the purposes of the simulation, dustiness is operationally defined as the fraction of particles that are lofted above y=5mm. Figure S-9 displays the dustiness as a function of time. Within 0.5s of impact, 14% of the monolayer has been aerosolized (note that the magnitude of this fraction is somewhat arbitrary, as it would be reduced for a chamber of larger base size). This time for aerosolization is comparable to what we observed (0.3s) in our visualization of the splash process (Figure 1). Due to their small size, the particles remain suspended for the duration of the simulation (40s). The persistence of the splash dust cloud is consistent with our observation (Figure 1).

Figure S-10 displays the height of the dust cloud. The maximum height (height of the highest particle) is ~20 times the average height (averaging the height over all particles). This indicates that the dust cloud density decreases with height, as expected. It also indicates that the dust cloud is not vertically well-mixed over its entire height. The constancy of that ratio suggests that the structure of the dust cloud does not change with time. The lack of vertical mixing is consistent with our observation (Figure 1).

Figure S-11 displays the average radius of the dust cloud (averaging the radial location over all particles). Within 0.5s, the extent of the dust cloud quickly expands to 4.5cm, which is an order of magnitude larger than the disk radius, and seems to be limited by the confining walls of the chamber; we cannot measure the intrinsic radius (with no confining chamber walls) of the dust cloud in these simulations. The small undulation for 2s < t < 6s suggests that while the cloud is initially propelled outward, it undergoes a minor retraction during this time interval (possibly driven by the motion of the vortex ring detaching from the fallen disk). The simulation lateral extent (4.5cm) is larger than that of our visualization (Figure 1), but our experimental dust cloud may be more confined due to the retaining wall of the Plexiglas tray into which the powder falls.

The average dust cloud height and radius may be combined to monitor the trajectory of the dust cloud centroid (note that this is not the center of mass, which would be located at r=0, above the pellet). Figure 6 displays the trajectory of the centroid for 0.6s < t < 10s. The dust cloud starts near the floor (r=2.6cm, h=9mm) at t=0.6s and is propelled outward and lofted (r=43cm, h=7.3cm) at t=10s. At intermediate times (t~2s), there is a slight retraction in radius with no additional lofting, and then lofting recommences with an additional expansion; at later times (t>8s) there is a slight retraction as lofting continues but is considerably slowed.

We have also conducted simulations where the initial monolayer of particles does not cover the entire floor of the chamber but rather is confined to a sequence of annuli around the pellet impact point. This allows a calculation of dustiness as a function of radial distance from the impacting disk (Figure 7). Note that this dustiness “profile” does not give information on the structure of the dust cloud; rather, it represents the probability of resuspension as a function of distance from the impacting disk. As expected, aerosolization is complete (dustiness ~ 1) near the impacting disk; the probability decreases to ~0.5 at ~5 times the radius of the disk; the probability effectively vanishes at ~10 times the radius of the disk. This dustiness profile is time-independent, reflecting the lack of settling of the dust cloud of 1μm particles.

We also can follow the centroid trajectory of the cloud resuspended from each of these annular monolayers (Figure S-12). Each annulus, once resuspended, is propelled radially outward as lofting progresses. Each annulus experiences a retraction (2s < t < 4s) before it resumes expansion and lofting. For t > 4s, the trajectories of all but the outermost annulus coincide, suggesting radial mixing of the particles originating from these different annuli.

We have also monitored the number of particles aerosolized to different height slabs (0–0.5, 0.5–5, 5–10, 10–15, 15–20, 20–25cm). Inverting the measured average particle radius within each height slab permits a determination of the dust cloud profile (Figure 8). For small times (t=1s), the dust profile monotonically decreases away from the fallen pellet. At t=2.5s, the extrema of the cloud are propelled outward; at t=5s, intermediate heights are retracted inward. For t > 10s, the dust profile returns to being monotonic, as the lofting proceeds. For 20s < t < 40s, lofting has stabilized with the cloud retracting inward somewhat.

The model is relatively insensitive to variations in pellet radius and thickness (SI—Section S-6).

We now study changes in the dust cloud as the size of the particle in the monolayer is changed. Dustiness (the fraction of particles that have been lofted above 5mm height in the chamber) depends upon particle diameter (Figure 9). While the initial lofting of the dust cloud is independent of powder particle size, at longer times, gravitational settling reduces the particle population in the dust cloud. Gravitational settling is apparent at d=5μm; for d=7.5μm, the dust cloud settles over the timescale of the experiment (t=40s).

The depletion of particles from the dust cloud also affects the height of the dust cloud. We monitor this change by looking at the cloud centroid trajectories for powders of different particle diameters (Figure 10). For particles with d<5μm, the trajectories are identical to those of the 1μm dust cloud; for particles with d>15μm, gravitational settling precludes significant lofting; dust clouds for the intermediate particle sizes exhibit erratic cross-over between the small and large particle clouds.

Taking vertical sections, we may track the change in the temporal dust cloud profile as a function of particle size (Figure 11). Cloud height begins to decrease at d=5μm and is significant at d=10μm. The radial cloud retraction (t~5s) is apparent for clouds with d<7.5μm.