Covid-19 response: engineering tips and guidelines from the point of view of fluid dynamics

In this page I collect information on topics that are related to protection from and spread of coronavirus. My point of view is that of a fluid dynamicist. My job at TU Delft is to study how fluid move and transport stuff, so I feel that if there is a way of contributing to the coronavirus crisis – besides of course rigorously following the govenment’s health recommendations –  is to analyse the methods of protection against coronavirus, and the flow physics of spread of the infection.

As many of you, I feel harmless in the face of the coronavirus crisis. But coronavirus spreads because of physical mechanisms, and if we can quantify these mechanisms we can at least reduce the probability that our actions will contribute to the spread of the infection.

This page is written by myself (Lorenzo Botto) and it is meant to be as objective as possible. I cite relevant work; when citations are not given this is typically because the conclusions follow common sense. All the text is a work in progress. The page contents have received very useful input from colleagues and students of TU Delft’s Process and Energy Department.

The document is structured along the three topics where fluid flow phenomena do play an importart role: filtration via masks, transmission of the infection via suspended aerosols, transmission of the infection via surfaces.


I would like to start with masks, because I see there is a lot of misinformation around these means of protection. Besides, while in the Western world masks for the general population are not recommended (understandably, since we just do not have enough masks in Europe and the US to cover the needs of the entire population) in Asian countries masks are generally recommended, so it is best to be prepared.

One of the motivations to write this section is that there is an increasing interest in self-made (“DIY”) masks, driven by the shortage of masks in the open market. If you really have to make your own face mask, please consider that making a properly functioning mask requires meeting several engineering constraints.

I was able to find information on the following aspects:

  •  DEFINITION: In the context of COVID-19, a mask is a device to protect the  persons around the wearer, and in some cases the wearer, from transmission of droplets of bodily fluids containing the virus.  When the mask serves purely to reduce spread from an infected person, but not to protect the wearer, one says that the mask is used as a “source control”.
  • Quality standards for the health service and the general public can be very different, so recommendations for the general public may be different from those valid for healthcare workers.
  • Face masks approved for use in hospitals or other healthcare environments with large potential exposure to coronavirus have passed quality controls that ensure that minimal requirements in terms of filtration performance are met.. Such quality controls may or may not apply to masks purchased in the open market.
  • Masks used by the health service can be broadly categorized in surgical masks and respirators.  These two categories differ in the level of protection against “biological aerosols”, which in the context of Covid-19 are the small droplets that carry the virus. Respirators offer a large protection against the penetration of the small droplets of bodily fluids that carry the virus (typically a filtration efficiency > 95%). Surgical masks have lower filtration efficiency and have mainly the function of protecting others from the wearer, but not the wearer. An excellent introduction to safety standards for respirators is this document by the company 3M (which is one of the world largest producers of masks). It indicates the different safety standards that effective respirators used in hospitals meet. Essentially, the masks that work in protecting the wearer against viruses follow the European standards FFP2 and FFP3 or their American equivalent N95. This class of respirators filter approximately 95% of the particles that pass through the filter (is it all the particles, or only the particle or a given size? I don’t know. If I find out, I will update the site with new info).
  •  The masks used by the general public range from surgical masks, to respirators, to simple cloth masks. Most masks you see around are surgical masks (and many of dubious quality and/or destined for industrial rather than sanitary use). Cloth masks made of woven fabric are ineffective in filtering small particles in the micron-size range (such as  smallest droplet nuclei), as their pore size is relatively large. So, be wary of cloth masks (besides cloth masks, T-shirts and scarves have been found only marginally effective as protective measures against virus penetration).
  • The fact that cloth masks are ineffective does not mean that one cannot use fabrics to make masks. Surgical masks do contain filtration fabrics, but these fabrics are non-woven. Non-woven means that the fibers do not follow a regular arrangement (as in most textiles for clothing), so the pore size can be made very small. Non-woven fabrics are widely used (vacuum cleaner filters and diapers are made of non-woven textiles) so a shortage of such fabrics is not expected.
A, B, C, D, E, F: microscopy images of cloth textiles . G, H, I: microscopy images of the external (G), intermediate (H) and internal (I) surface of a surgical mask. The scale bar in A is 500 microns. From H we can infer an average pore size roughly in the range of 1-10 microns. (reference: Neupane, Bhanu Bhakta, et al. “Optical microscopic study of surface morphology and filtering efficiency of face masks.” Peer J 7 (2019): e7142.)
Drop penetration in a textile. A woven medium acts as a sieve, producing droplets comparable in size to the distance between the yarns of the textile. (Zhang, Gannian, et al. “Droplet impact dynamics on textiles.” Soft matter 14.40 (2018): 8182-8190.)
  • The filtration efficiency is largely set by the density of the fibers mesh and by the thickness of the filtering layers (find here a PhD thesis discussing the details). High density (small pores) and thick layers give large filtration efficiency, but also a large pressure drop.  Finding the right balance between filtration efficiency and small pressure drop is an important consideration, particularly if the mask has to be worn for long times or the person wearing the mask has difficulty breathing (because of age or illness).
  •  Another factor that is often overlooked in the design of self-made masks is the possibility of flow leakage from the sides of the mask. Truly protective respirators used in medical environment are sealed on the sides against air leakages , so that all the respiratory flow has to pass trough the filter.  The air flow will follow the path of lowest resistance, so if the mask is not well sealed along the borders, contaminated air will pass through the leaks. Leakage brings about a tough engineering constraint. Filtration media with high filtration efficiency tend to produce substantial pressure drops, so leakage from the sides is most problematic when the filter is good!
Selfies of nurses and doctors after a day of work helping coronavirus patients in various hospitals in Italy. The deep marks on the faces illustrate in a dramatic way the difference between an air-tight mask that offers large protection against the virus versus the relatively comfortable masks typically used by the general population. The last figure is a FFP2 or FFP3 face mask.
  •  The droplet size distribution following coughing or sneezing varies quite substantially.  The blue line in the figure below, taken from a technical document by the company 3M, shows a typical droplet size distribution produced by a sneeze, against the filtration efficiency of 6 (properly used) N95 masks. The droplet diameter ranges from about 200 nanometers to 10 microns (I assume this is the lowest portion of the particle size distribution, as a sneeze clearly produces also much larger droplets, up to a millimetre). Naturally, the droplets most difficult to catch are the smallest ones (diameters of the order of a micron or smaller). Besides being difficult to be captured by filtration media, these droplets are also the lightest, and therefore tend to be suspended in turbulent air streams for long time.

    Filtration efficiency of 6 N95 respirators, and typical droplet size distribution following a sneeze.
  • Naturally, the droplets most difficult to catch are the smallest ones (diameters of the order of a micron or smaller). Besides being difficult to be captured by filtration media, these droplets are also the lightest, and therefore tend to be suspended in turbulent air streams for long times.
  •  I do not have access to an N95 or FFP2/FFP3 mask. However, I examined an EN143.2000 filter, which according to the guideline from the UK Health and Safety Executive on respiratory protective equipment has a level of protection (P3) comparable to an FFP2/FFP3 mask. This filter is made of made of 3 layer, where the fibrous non-woven filtering medium is sandwiched between an outer and an inner layer layers. One of these two layers (I cannot find which one is the outer layer and which one is the inner layer!) is very thin, almost optically transparent, slightly porous, and  flexible (rightmost layer in the figure below). It is made most likely of a plastic material.  I assume this layer has only a structural function. The inner layer is a made of compacted  fibers (possibly fiber glass). This is probably the main filtration layer. The remaining layer is composed of several sublayers, like porous paper folded several times onto itself. Each layers seem also to be made of compacted fibers.

    The internal structure of a EN143.2000 filter produced by 3M.
  •  So far I could not find information about the wetting properties of the filters. The EN143.200 filter I have access is partially hydrophobic (the macroscopic contact angle, probed by gently placing a water drop on it, is less than 90 degrees), but it is definitely not super-repellent to water.  Mild liquid repellency is expected, as hygroscopic filters would accumulate moisture from breath becoming progressively ineffective.

Key recommendations on self-made face masks

Masks could in principle be self-made, but it would be necessary to i) purchase adequate non-woven filtration media; and ii) pay particular attention to mask sealing. Non-woven filtration media is widely used in industry and to make air filters for houses and vacuum cleaners, so in principle finding suitable fabrics is possible. In any case, reuse of filters is generally not recommended. A washable support mask (3D printed or made of suitable air-impermeable material) with disposable filtration medium could be a solution if the whole mask (support + filter) is properly engineered to avoid leakage while ensuring a relatively comfortable use. The filtration medium should not adsorb water, otherwise the material will become engulfed with liquid and will lose efficacy with time. For a guideline, a good article discussing the efficacy of home-made mask is: Davies, Anna, et al. “Testing the efficacy of homemade masks: would they protect in an influenza pandemic?.” Disaster medicine and public health preparedness 7.4 (2013): 413-418.



A timely article published on March 17 2020 on the very reputable journal “The New England Journal of Medicine” reports that  COVID-19 survives on various solid surfaces (copper, cardboard, stainless steel, plastic) for relatively long time. No viable virus was observed on cardboard after 24 hours. Plastic surface gave the longest life time: no viable virus was observed after 72 hours (3 days).  The decay is approximately exponential, and the half-life time (i.e. the time required from the virus population to be reduced by half) depends on the material. The largest half-life times where for plastic (6.8 hours) and stainless steel (5.6 hours).

Decay of covid-19 content after nebulisation of virus-containing droplets on plastic.

An implication of the long permanence on surfaces of COVID-19 is that, while transmission via surfaces is known to be less effective that transmission via direct inhalation of virus-containing droplets from an infected individual, it is good to pay attention to those surfaces that are touched by many people. For example, it seems natural to me to practice thorough hygiene after touching shopping cart handles and pinpads in supermarkets.