In some of the discussions I've mentioned above and also in some of these articles, they say statements such as "small droplets disperse easily" and "large droplets settle quickly". This is acceptable because broadly speaking it is true and it is okay for a wider audience not involved in the field. The devil is in the detail though. The reality is that it is much more complicated then this when the air is moving quite quickly (turbulent motion). You can't really say these statements anymore in this case because how the droplets disperse now additionally now depends on characteristics of the moving air. Or more specifically velocity fluctuations (momentum) imparted (transferred) to the droplets by the air.
Typically if the air is turbulent, the best way to describe this is as a superposition (an addition of sorts) of lots of different air movements, all of different shapes and sizes, all on top of one another. Think of it like a forest with trees (large scales), flowers (small scales) plants (medium scales) all on top of each other. It is a bit like that but the key difference is that the scales in the fluid are all entangled with eachother. One way to describe the large scales is called the "integral scale". Broadly speaking it measures very large distance air motion. If you are in a room, it will describe the characteristics of really large air motion which spans the entire room. But within this room, within the large scale air motion, don't forget we also have tiny air motions. These tiny, small motions we call "Kolmogorov scales".
The reason these two scales (Integral and Kolmogorov) are important is because they influence greatly how droplets disperse. We use a non-dimensional number (like how biologists use this R number) to describe, qualitatively how droplets move. This is called the Stokes number. It is a measure of how much intertia, i.e. resistance, that the droplet has to any momentum which is imparted onto it. Effectively it is calculated by a characteristic of the droplet divided by a characteristic of the gas. But unfortunately, we don't really know what is the best scale of the gas to use, is it either the Integral scale or the Kolmogorov scale. Whilst there is some agreement as to how to characterise the droplet, it is made complicated because sprays and clouds of droplets have different sizes, so ideally we want a single number describing the entire cloud, and not a number describing just one droplet in the cloud.
When the Stokes number is really small, we can then say, qualitatively, "small droplets disperse easily". This is the reason why we can do Particle Image Velocimetry, a technique used to measure either gas velocity or droplet velocity. You cannot measure size. Think of this like small dust grains moving with the wind.
When the Stokes number is very large, we can say "droplets settle quickly", or better still, they follow ballistic trajectories. This simply means they just basically ignore much of the surrounding air motion. Think of this like a cricket ball moving through a very light wind.
However, when the Stokes number ~ 1, the droplets behave in a strange way. They begin to form clusters in the flow. This is the same as clustering you get in machine learning. In essence, you get regions in the air flow where there are many droplets (clusters) and region in the air flow where there are few (voids). It is called "preferential concentration" in my field. Unfortunately we don't know the mechanisms as to why this occur though some have been proposed. The relevant point here is that there is experimental and simulation evidence to suggest that when the droplets form clusters, their settling velocity, i.e. how quickly the droplets settle, is enhanced! It could be that these droplets, when they get close together, just form a "super" droplet of sorts. I have no idea what the consequences of this effect are for evaporation. This preferential concentration effect is known to also enhance collisions, at least from what we can understand in CFD (computational fluid dynamics) simulations and its influence on the formation of rain in clouds is hotly debated.
So if you know the Stokes number, you can, at least qualitiatively, have some indication on how the droplets disperse. So what Stokes numbers do you have? If the air is very strong, the Kolmogorov scales get smaller. So if you study the dispersion of the droplets using those scales, you could in theory say all the droplets disperse easily.The majority of papers I've read use Kolmogorov scales rather than integral. But again I stress, it is very difficult to first, produce this Stokes number and secondly to try and get a representative Stokes number of the entire spray or cloud.
Unfortuately, if the droplets have initially a large moving velocity, another parameter must be considered as well. This is called the "settling parameter" although I don't see many authors use it at all. The need to use settling parameter is important because a large amount of energy or momentum is transferred to the droplets during sneezing/coughing. Therefore, at least initially, these droplets may ignore all the surrounding air simply because they are moving so quickly, they don't really have time to react to any of the motion. When the settling parameter, described in this way, is unity, the settling velocity of the droplets is enhanced as well! This is called the "crossing trajectories effect" and was described in part in the 1950's I believe. When the velocity of the droplet decays to a situation where they become well correlated with the air motion, you don't really need the settling parameter anymore because it is a function of the Stokes number in this case. Note that a lot of professors believe you only really need the Stokes number, so my understanding here is somewhat limited.
Again note that the settling parameter and Stokes number only give a qualitative indication of what happens. They can't tell you exactly where the droplets will go, just give an indication of roughly how they will disperse. To track exactly where the droplets go requires experiments or simulations.
There has been a lot of work in engineering in studies of particles or droplets in "simple idealised turbulence" i.e. turbulence you typically only get in laboratory, but less fundamental studies in turbulent flows you encounter in nature and engineering. However, a lot of work comes from combustion, studying spray ignition in engines and how the spray behaves in that flow environment but this isn't my field. A lot of simulations have been carried out in cloud physics as I mentioned above. The problem is that whilst we want to believe all turbulent flows are the same, there is some belief that they are not. So a flow in the pipe must be treated differently to the flow of air in your room etc. We just don't know if turbulent flows have any universal properties which are true for all engineering and natural applications. So just because when you sneeze in a room the droplets behave one way, it may be different if you sneeze outdoors where the air motion is different.
The reason why you need to be careful with CFD is that the methods used, RANS and LES don't simulate all the flow using the Navier Stokes (NS) equations of motion for fluid dynamics. Note that the NS equations are simply Newton's second law applied to moving fluids. RANS actually uses an averaged Navier stokes equation and this requires turbulence modelling - i.e. adhoc "best guess" methods - to fix the averaged equations so that they can be simulated. No one knows if the various turbulence models are valid but it is cheap to run and can give results which give "the overall picture" for air flows without droplets. LES does simulate some of the equations, but it cuts of at a certain point and simply models the rest - it claims beyond that point the flow behaves in a way described by a model. Guess where that model is - the Kolmogorov scales, so it isn't clear that you can use LES for problems with droplets because it isn't clear if the models really describe the Kolmogorov scales accurately or not. DNS (Direct Numerical Simulation) simulates all the details of the flow and is in theory the best simulation. But it has a very high computational cost. I'm not sure what they've done in the video, I am skeptical they managed to do DNS but you never know.
Even if you manage to get a DNS you still have to consider how you describe the small droplets. The majority of simulations just say the droplets are "points", so that they don't have an appreciable size. The majority of simulations ignore any "back influence" of the droplets on the air flow. So in other words, if the air flow causes droplets to move, the droplets themselves may change locally the air flow! There may also be collisions between droplets, irrespective of the clustering phenomenon I described above which are ignored and local flow distortions caused by the droplets. If you read the spoiler below, these collisions can lead to droplets of different sizes, which of course may be important. Finally, if the droplets are larger than the Kolmogorov scale air motions, their dynamics is different and there are very few simulations which look at these droplets - most focus on particles/droplets smaller than the Kolmogorov scale. Also note that if the particles or droplets have a density smaller than the density of the surrounding air, the dynamics are different as well.
You may ask why not carry out experiments and brute force our way through this. Laser experiments are quite difficult to carry out. The laser must be aligned with its internal/external optics. If a camera is used, it may need to be synced with the laser. 3D experiments in multiphase flows are exceedingly rare. Tracking individual droplets, in particular their collisions, is generally difficult. So whilst there are some good experiments, they are lagging behind considerably to where we need to be. Couple this with the issues with CFD and this is why particle/droplet dispersion in turbulence is a pretty tricky problem.
Note I've also ignored temperature affects, called thermophoresis and turbulence intensity (the air motion is stronger in one location than another) affects, called turbophoresis. I've not studied these effects but they can also influence particle/droplet dispersion. Note also I don't have a background in simulations, so some of that knowledge may be out of date. Note that for the benefit of this discussion, solid particles disperse in the same way as liquid droplets, with the exception of the discussion on collision outcomes.
