question on particle diffusion in air - Page 1
Forum section: electronics / general

author: engineheat
author_rank: Frequent Contributor
timestamp: October 10, 2020, 03:07:08 am
content: Let's say there is a 10 feet wall between you and another person, and you are all located in a factory with vents at the ceilings (say, 30 ft above). Both of you are roughly 2-3 from the wall. If he takes an air blower and blow some dust-like particle (like corn starch or flour) such that there is a cloud of it around him. Say after a given time (like 1 min), will the density of the particle near your location be much less than at his location? Assuming the wall is sufficiently long.Without the wall, the particle density at your location shouldn't be too different than his location since the Euclidian distance between you and him aren't that far apart. I wonder how the existence of the wall affect the diffusion time that it takes for the density at your location to match his. Are there math equations for something like this?Thanks

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 10, 2020, 03:44:49 am
content: If the particles are properly suspended (an aerosol), then it will be the diffusion rate times the minimum straight-line length, to observe a significant increase in particle density. This is kinda-sorta the time constant, but I'm abusing units because diffusion is, well, diffusional, so you get square roots everywhere. (Specifically, distance traveled goes as sqrt(t).) (The minimum time to observe any given particle is somewhat less than the speed of sound -- there's always a nonzero possibility that all the air molecules hitting the particle, push it perfectly in one direction, and all the rest dodge perfectly out of the way. The chance of this is, of course, astronomically small; the point is it's not really meaningful to consider a minimum or maximum speed, but that you need to set some reasonable threshold and count time until it's reached.)Equilibrium density depends on surroundings, since if there is a large radius to disperse particles over, the density will be lower at a given radius, whereas if it's the end of a closed hallway the density will become uniform (as you can understand intuitively from smoke filling a closed room).If the particles tend to fall under gravity, then the lateral diffusion rate will go down, oh I don't know, maybe exponentially with distance?In either case, there should be a formula or table for diffusion rate versus particle size and density. Look that up.Obviously, this assumes perfectly still air, which isn't very interesting. Aerosol transport is utterly dominated by ventilation systems, even when the flow rate is imperceptible. In a real situation, true molecular diffusion is probably not the driving factor.In this regime, analysis is possible, but you have to know ahellof a lot more about the situation: the geometry of the environment (down to some scale factor, below which, smaller features can be approximated as a lossy boundary condition), the air currents, if the air is stratified (hot air all stuck to the ceiling?), etc.For example, if there's an infinite floor, an infinitely long 'divider' wall of given height, and a ceiling of given height, it might be that air currents prefer to move along the wall; or they tend to kick up and over, forming a vortex on the other side (which heavily mixes air on that side). Or if it's not a smooth wall, it has segments projecting off it (like a cubicle office does), those will kick up anything the main wall doesn't already, breaking the flow into many vortices.Or it might not happen at all: if the ventilation is strong enough and vertically oriented, the lateral distance a particle can fall is quite limited (even if it remains suspended in the air column, without being heavy enough to fall on its own). Combined with a very fine quality filter, this approach works very well indeed in clean rooms.Tim