# How does a virus fall down in static air?

If we drop a virus from a height, in static air, will it fall to the ground like a lead ball, a balloon, or like a virus? How will it fall to the bottom? Like a Brownian particle? It will not float in the air, as its density is higher than air. But still it seems a light particle. If I blow the air in which it's immersed, I can blow it away. From all sides air molecules bump into it. Giving it random pushes. Can we say it's part of the air it's in and as such float in it?

If we imagine ourselves standing beside it, while it lays on a solid structure, and we push it over the edge, what effects the molecules have that fly around on all sides? Will I see it fall down between the speeding molecules, which only give random impulses to all sides of the virus?

• Very, very slowly. Dec 19, 2021 at 18:38

The smaller the particle, the less effect gravity has compared with the interactions of other particles. Viruses are tiny and would (by themselves) fall incredibly slowly in air. It would be bounced constantly in all directions. If the air were still, it would trend downward over time, but only on quite long timescales.

Virus transmission doesn't normally consider lone virus interactions with the air because lone virus particles seem to have low viability. Instead they need to remain within a water droplet. So it's the size of the water droplet that dominates the path through the air. Bigger droplets fall faster than smaller droplets.

• Some bodies happen to create unusually many tiny droplets when they open their mouths and speak or cough, thus the phenomenon where some people are covid superspreaders Dec 19, 2021 at 4:56
• Still, compared to the molecules constituting the air, the virus is a heavy compact structure. Why does it fall incredible slow? A tiny waterdroplet falls slower than a heavy one because of the mass and surface vary with the radius tripled and squared, so the droplet will fall sloweŕ if smaller (the air resistance needed to counter gravity gets smaller when the droplet gets smaller). If we treat the virus as a sphere with mass M and radius R, how slow is incredibly slow? Can we treat the air as continuous still? Dec 19, 2021 at 14:41
• @BowlOfRed can you supplement your answer with equations to quantify / back up what you are saying? For example, how does fall speed depend on mass and/or volume? What is a timescale which is "long" in this case? Dec 20, 2021 at 4:21
• If you live in a place where there's snow, compare to how a light precipitation (which we would call a light drizzle if it were rain) when it's slightly windy will end up looking more like mist. The snow will eventually reach the ground, but the turbulence will keep it in the air for a long time. Dec 20, 2021 at 11:22

Depending on the size of a particle, its motion in air under gravity can be modeled in two ways:

• Air pressure difference on the two sides of the particle. This gives a terminal velocity, which is the fastest speed the particle will fall relative to air.
• Brownian motion caused by the collisions from individual air molecules. Using the Stokes-Einstein relation, a drift speed due to gravity can be calculated.

In either case, if the air is moving faster upwards than the particle is moving downwards relative to air, the particle goes up. Typical average indoor air velocity is on the order of 0.1 m/s, though local velocities near heat sources or movement will be faster.

Individual viruses have a diameter varying from 20 to 300 nm and a density about twice that of water. Viruses remain infectious much better inside small water droplets called aerosol, which have a size varying from 100 nm to 10 µm.

The transition between these two types of movements can be described by the Knudsen number. In air, Brownian motion starts significantly affecting particle motion below a size of 1 µm.

In the graph below, I've drawn the two speeds up to this transition area. There is a large difference, and in reality this would be blended together over the transitional zone of a few decades of scale.

Aerosols fall in the transitional zone. What this means is that larger aerosol particles will fall at terminal velocity, while smaller ones and individual viruses follow Brownian motion. The latter results in much slower movement speeds and the particles thus remain suspended orders of magnitude longer. This page has some graphs for aerosols in particular.

• I'm inclined to accept this answer! As you self wrote, on these tiny scales it's the question indeed if the formula used is valid. Air is not continuous stuff, and the virus can fall freely between the air molecules, of which there are a lot of course. Dec 19, 2021 at 16:30
• It is not the size of the molecules but their mean free path, what makes a relevant length scale here. Hence, e.g., the Knudsen number. Dec 19, 2021 at 16:30
• @VladimirF Thanks, I've expanded the answer a bit. This question has quite a bit of depth :)
– jpa
Dec 19, 2021 at 18:54
• From a "why" standpoint, an evolutionary answer might point out that viruses that are larger will tend to fall to the ground and not produce infections. Viruses that are smaller have less room to pack in their genome.
– Dan
Dec 20, 2021 at 0:39
• @Elmore Hmm, mean free path is on the same scale as virus size, not orders of magnitude larger. But I agree that the sedimentation length is long compared to individual viruses - this analysis is thus better suited for the aerosols.
– jpa
Dec 20, 2021 at 5:47

More involved look: Particles movement and settling in fluids can be - to rather high accuracy - modeled through statistical mechanics. Namely, through Laplace-Perrin distribution

And sedimentation length:

This distribution describes how particles immersed in a fluid move stochastically around. Sedimentation length is how far a particle can travel through brownian motion by chance 1/e.

For virii, a fast glance at public documentation and papers gives estimates of mass and size to be m* = 1 femtogram, and diameter of 20nm.

Sedimentation length for virii is thus about 4.2*10^-7 m which is ~20 times larger than their diameter.

Roughly speaking we can say that if sedimentation length is much larger than the size of the particle itself, it stays suspended. This mean that if you arranged a number of virii at the floor, completely still, and a body of air filling the room, completely still too, but all at room temperature, after a while you could expect to encounter some of the virii near the ceiling.

In the real world there are always small disturbances in the air that ensure much larger particles stay suspended too. Also, in the real world we don't really consider free virii as the infectious agent, but small aerosols emitted by people breathing and speaking. The time they spend airborne is heavily dependent on diameter, and follow interesting size- and travel distance distributions.

• Hmm, according to wikipedia "At the length l_g above the reference point, the concentration of colloidal particles decreases by a factor of e.". Wouldn't that mean with a sedimentation length of 400 nm, the probability of finding a particle at the roof would be exp(-3m/400nm) = pretty much zero?
– jpa
Dec 20, 2021 at 6:47
• What about the force of gravity pulling the virus down? Is that contained in sedimentation length? Dec 20, 2021 at 9:50
• @Pathfinder Yes, air is a fluid. Both gases and liquids are fluids. Dec 20, 2021 at 10:24
• I'm with @jpa on this.. the sedimentation length is talking about particles with a high concentration such that concentration changes by a factor of e for every sedimentation length. So your concentration of virus near the floor should be $e^{\frac{3}{4.2*10^{-7}}} = 10^{194163}$ times the concentration at the ceiling. In practice this would mean that if the air happened to be completely still in a room, eventually the virus would settle such that having a single particle higher than a few centimeter above the ground would be astounding. However, the air isn't still, so not very applicable.
– Rick
Dec 20, 2021 at 18:14