Particle Segregation during Settling
Background
When powder is poured or conveyed from a transport line into a vessel, a dust cloud will be formed which naturally segregates in particle size due to the unique particle sizes and particle densities which exist in the dust mixture. This behavior is illustrated in the figure at right, adapted from NFPA 652, which highlights the presence of the residual deflagrable dust cloud which can form near the vessel entrance during this process.
The stratification will lead to higher concentrations of smaller particles near the inlet, whose explosibility characteristics will be unique from those of the bulk powder mixture. Given that smaller particles generally exhibit greater ignition sensitivity and explosion severity, the segregation is of serious importance and should be considered when developing a strategy for collecting and testing combustible dust samples.
To account for scenarios like this, the American Society for Testing and Materials (ASTM) does recommend that powder handlers test their dust samples for explosibility behavior with 95% of the sample having a particle diameter of 75 microns or less. The recommendation to reduce particle size by sieving or milling to meet this threshold assures that conservative data is obtained for the purpose of designing protection measures. However, there is no assurance that it's the right recommendation.
Analysis
The ASTM recommendation for reducing the particle size distribution is independent of the original sample size, and may be seem to be aggressive, but the rationale can be easily understood by looking at the t-x diagram below.
The plot depicts the time-dependent settling trajectories for particles of different sizes, based on a simple force balance considering gravity, drag force, and buoyance force.
The calculations were done for properties of flour with a bulk particle density of 1470 kg/m3.
Although the calculations only report what occurs during the first second, it's evident that particle size has a substantial influence on particle velocity and ultimately where the particle resides. In fact, for the 10 micron particle size, it reaches its terminal velocity of 4 mm/s before it can travel a distance equivalent to its diameter. If the vessel has a 10 meter drop to the powder bed surface, it would take approximately 40 minutes to settle out at this rate. Given the additional susceptibility of these light particles to gas flows in a vessel, which may aid in keeping the particles airborne, it's easy to see why a persistent dust cloud will be present.
The analysis here is simple to conduct, but it certainly has some shortcomings.
For example, we know that particle shape, velocity of the continuous phase (especially for low Stokes number particles), intraparticle adhesion, and interparticle effects which influence the drag coefficient (see here for a unique approach for accounting for this effect) are all factors which must be considered in a real-world vessel.
Nevertheless, this illustrates some of the basic physics which are relevant within the vessel, and is a good conceptual tool for rationalizing the ASTM testing recommendations.
One of our primary interests at the Dust Center is to build on these conceptual models to develop simple analysis tools that can be used to model dust cloud behavior and composition within industrial-scale vessels.