How Viruses Survive in Aerosol Droplets

Viruses like flu and SARS-CoV-2 (the cause of COVID) spread across the air in aerosol particles, often of order a micrometre across. To do this the virus needs to survive intact the rather violent process whereby a tiny droplet breaks off from a liquid. In this case the liquid mucus lining our throat and lungs. Violent here includes some rather fast, metres per second, flows as the droplet breaks off from the liquid and rounds up into a sphere. I estimated the shear stresses involved in this process in an earlier blog post as

shear stress in boundary layer σ=η×shear rate∼(η2Γ3ρdD5)1/4∼104Pa      d=1 μm\text{shear stress in boundary layer~} \sigma = \eta \times \text{shear rate} \sim \left(\frac{\eta^2\Gamma^3}{\rho d_D^5}\right)^{1/4}\sim 10^4\text{Pa}~~~~~~d=1~\mu\text{m}

where η is the viscosity (saliva is only a bit more viscous than water, at around 1 mPa s), Γ is the surface tension (about 0.05 N/m), ρ is the mass density (1000 kg/m3) and dD is the droplet diameter.

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Training a toy neural net

I am no expert but as I understand it, a lot of LLMs like Anthropic’s Claude, and image generators like Stable Diffusion, are built on neural nets. And a lot of these neural nets are trained via backpropagation. I want to understand a little more about this, and maybe teach a simple example in my Python course – although this may be a little advanced for first year physicists. So first I need to teach myself a little about both how a neural net works and backpropagation works.

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Breaking off droplets without breaking the virus inside the droplets

A respiratory virus like flu or SARS-CoV-2 (the cause of COVID-19) begins its journey to infect a new person by leaving the mucus-covered throat or lungs of an infected person, and becoming airborne in tiny droplets*. The infected person then breathes out these droplets containing their cargo of airborne infectious virus. This process of the virus leaving the liquid lining our lungs, throat and mouth, in small airborne droplets – an aerosol – is poorly understood. Viewing tiny, perhaps a micrometre across, droplets deep in our lungs, is impossible. But the formation of these aerosols obeys the same physics* as the formation of another aerosol – sea spray – shown in the image** above.

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Diffusing towards a cute kitten

The image sequence above shows AI generation by a so-called diffusion model, specifically runwayml/stable-diffusion-v1-5 (obtained from Hugging Face). the Google Colab notebook that generated it is here. The final image – usually the only one you see – is on the far right. On the far left is an image that is near the start of the image-generation process. Image generation starts with just noise, along with the prompt to specify what you want the image to be: “a cute British short hair kitten, looking directly at you”. Then an iterative procedure is applied, in this case 48 times, to somehow subtract the noise to leave the kitten.

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“Physics” as an LLM understands it

Large Language Models like OpenAI’s ChatGPT, Google’s Gemini, Anthropic’s Claude etc work with words but under their bonnets it is all maths. In particular the meaning of a word is encoded in a vector: a line of numbers, which allows the LLM to do vector maths on it to produce more words: its answer to your question.

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How dangerous do masks get?

Masks exist to filter out harmful viruses and bacteria from the air the wearer is breathing. This protects the wearer, and if the mask wearer is infected, it protects others in the same room. Masks are air filters worn on the face and air filters are typically meshes of tiny fibres – illustrated in the rather shonky AI image above. They work by the virus-containing droplets in the air sticking to the fibres inside the filter, and so not going through the mask.

But then what happens to the virus-containing droplets stuck to fibres inside the filter material? There is understandable concern that the mask could be contaminated by these droplets, and that perhaps later infectious virus could be dislodged from the mask and go on to infect someone.

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Cool evaporating droplets

The evaporation of water droplets is a lot more complex than you’d think or hope. One reason is that small water droplets, at least in not very humid air, evaporate so fast that the evaporation cools them. This is just like when you blow on hot coffee to cool it, you increase the evaporation rate and this cools the coffee. Evaporation takes energy, called latent heat levap, which for water is large. At room temperature the latent heat is a bit less than 10−19 J per water molecule that evaporates. Calculations by Hardy et al. find that it can cool an evaporating water droplet by more than 10 C.

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Infectious disease superspreaders on ships

At the moment two ships are in the news for infectious disease outbreaks, the MV Hondius for an outbreak of the Andes strain of hantavirus (ANDV) and the Ambition for a norovirus outbreak. This outbreak on the Handius has resulted in three deaths to date. These are just two of a long line of plague ships, including the Diamond Princess during the early stages of the COVID pandemic. Viewed from one way, this is perhaps unsurprising: large cruise ships squeeze several thousand passengers and crew into a confined space that looks a perfect place to transmit disease from one person to another. But I am bit surprised both that the companies that run these ships don’t seem to be doing anything to stop these regular bursts of bad PR, and that potential passengers are not put off by the risk of boarding a potential plague ship.

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Predicting next year’s CO2 levels with simple machine learning

Due to us burning oil, coal, gas etc etc, the amount of CO2 in Earth’s atmosphere is increasing, and has been for well over a century. This is now well documented. Some of the first measurements were made by Charles David Keeling on the Muana Loa volcano*. He started in March 1958, and the measuring continues to this day. Katherine Bourzac has written a fascinating article about the history of these measurements, which with a couple of interruptions have continued to this day, almost 70 years of data. The data** is here:

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