I am interested in how viruses survive the drying of the droplet they are in. The surface of a droplet is a dangerous place for a virus, surfaces exert forces and these look large enough to tear a virus apart. So, how likely is it that a virus ends up at the surface? Early on in the evaporation the droplet’s mucus or saliva will be quite dilute and watery, so the virus will diffuse around in it, and due to evaporation the mucus/air interface will be moving, and so tend to sweep up any viruses in its path. So if there is no interaction between the surface of water and a virus, or any sort of attraction, it looks likely that the virus will contact and stick to the surface.
But it seems likely that the surface of mucus repels viruses. If this repulsion is many times the thermal energy, then the virus will not contact the surface unless it is pushed onto it. The moving mucus/air interface can provide this push. When a virus is just below a surface that is moving, then the virus has to move down to avoid the surface and when it does this it needs to push through the surrounding mucus. This pushing through the mucus creates a drag force that tends to cause the virus to fall back onto the surface.
The drag force on a sphere of radius R moving at a speed v relative to the surrounding fluid, with a surface z away, is
drag force = 6 π R η λ(z) v
with η the viscosity of the fluid and the function λ(z) taking account of the effect of the nearby surface. For a particle far from a surface, z >> R, λ = 1, while for the particle very near the surface λ ~ 1/(z – R), i.e., it diverges as particle moves into contact with the surface. When the particle is very near the surface the drag can be tens or hundreds of times larger than when the particle is far away.
Let’s look at some numbers. If we put the viscosity of water, η ~ 1 mPa s, and a reasonably fast evaporation speed of v = 1 μm/s, then for a virus 100 nm across far from surfacw, the force is around 0.001 pN. This looks small. Forces in solutions vary but in many cases they are of order the thermal energy ~ 10-21 J divided by a nanometre, which gives a force of 1 pN.
So the drag force on the particle is a thousand times smaller than typical forces on particles in solution. This force is so small it looks essentially irrelevant.
But during evaporation the proteins in mucus become more and more concentrated, as the water evaporates leaving these proteins behind. This increases the viscosity and viscosities can become much higher than that of water, orders of magnitude higher at say 1 Pa s, not water’s 1 mPa s. With a viscosity of 1 Pa s and close enough to the surface that λ is of order 10, the drag force is 10 pN. This could easily be enough to push the virus onto the surface.
I think the conclusion is that early on the evaporation, almost any repulsion between the mucus/air interface and a virus, should be enough to keep the virus away from the interface. But later on as the mucus may become so thick and mucus that viruses are pushed onto the surface, and potentially destroyed.
Chance & Necessity 