Playing with the Argonne/Chicago fabric filtration data

Mid 2021 update: High thread count cotton and/or multi-layer polyester satin isn't a good choice for high filtration masks. They're not breathable enough at mid filtration performance. And additional layering to get to hight filtration still only decreases breathability further. With that they get hot and uncomfortable as well as giving your chest muscles a good workout.

Disclaimer: There has been some critisizm that Konda et al 2020 (this study out of Chicago Uni and Argonne National Labs) had air flowing at too low a rate, which wouldn't map to real world cloth face mask usage. High flow of air through the measuring equipment would yield lower protection percentages. Also that the Chiffon they ultimately picked isn't a standard chiffon at all as it incorporates spandex/lycra.

As of 2018, we now know that "droplets and droplet nuclei" are the particle sizes to worry about for influenza-like illnesses. Not particle sizes smaller - see Defining the sizes of airborne particles that mediate influenza transmission in ferrets). The WHO uses "droplets and droplet nuclei" but doesn't qualify that. Others like Prather et al: Reducing transmission of SARS-CoV-2 talk of aerosols but doesn't stipulate actual sizes. We need a canonical way of describing the infecting particle sizes. Also we need to standardize on nano meters (nm), OR micro meters (μm) OR microns.

Using Konda et al's data for further Silk calculations

For silk, at 1.2 CFM, Konda et al (Aerosol Filtration Efficiency of Common Fabrics Used in Respiratory Cloth Masks) tested 1, 2 and 4 layers of silk. I reverse engineered the data from the pertinent graph, and used a formula for calculating filtration for layers of fabric based on the filtration numbers for one layer

Particle size μm	6 calc'd	5 calc'd	4 calc'd	3 calc'd	4 actual	2 calc'd	2 actual	1 actual
0.8	0.98	0.96	0.93	0.86	0.84	0.73	0.60	0.48
1.5	0.99	0.98	0.95	0.90	0.86	0.78	0.63	0.53
2.5	0.99	0.98	0.96	0.91	0.88	0.80	0.65	0.55
3.5	0.99	0.99	0.97	0.92	0.89	0.82	0.67	0.57
5	1.00	0.99	0.97	0.93	0.92	0.83	0.70	0.59

The formula is (percentages as 0.0 to 1.0 numbers):

=1-(POWER(1-<LAYER_1_FIGURE>,<LAYER_COUNT>))

I had help here from David K via math.stackexchange.com/questions/3698080 

The resulting graph for that looks off though - calculated values do not match actuals for 2 & 4 layers:

Correcting the calculation formula

Spreadsheet with "correction factor" of 0.67 for each additional layer that affects calculated cells:

Particle size μm	6 calc'd	5 calc'd	4 calc'd	3 calc'd	4 actual	2 calc'd	2 actual	1 actual
0.8	0.93	0.90	0.84	0.74	0.84	0.60	0.60	0.48
1.5	0.95	0.92	0.87	0.79	0.86	0.64	0.63	0.53
2.5	0.96	0.93	0.89	0.80	0.88	0.66	0.65	0.55
3.5	0.97	0.94	0.90	0.82	0.89	0.68	0.67	0.57
5	0.97	0.95	0.91	0.83	0.92	0.70	0.70	0.59

And here's the graph for that:

And it is clearer that the calculated values for 2 and 4 layers of silk are much closer to the actual values. I've no idea why this needs a correction factor. It could be because of the layers being clamped in the Chicago/Argonne test rig, and that if they were not clamped they'd be a better filter in combination. I've no idea though.

Thus we can now predict what five or six layers of silk that Konda et al tested would yield in terms of filtration for droplet and droplet nuclei.

Fabric Practicalities & Breathability

Silk isn't washable at high temperatures so it is unclear how long lived it would be. We do have 3D patterns that are a tight enough fit onto the face to not worry about the edge-air leakage. Some of those 3D patterns include features to boost breathability which is a challenge for cloth masks that are multi-layer

Formal FFP1/FFP2 Specs

From the FFP1/2/3 page on wikipedia:

Class[4]	Filter penetration limit (at 95 L/min air flow)	Inward leakage	Typical Elastic Band
FFP1	Filters at least 80% of airborne particles	<22%	Yellow
FFP2	Filters at least 94% of airborne particles	<8%	Blue or White
FFP3	Filters at least 99% of airborne particles	<2%	Red

So this hypothetical five layer silk mask would approach FFP2 grade, and a hypothetical six layer silk mask would reach that spec.

Note: N95 is slightly better than FFP2.

Testing Chiffon and Satin (the polyester kind)

Konda et al didn't test Satin at 1.2 CFM, but they did at 3.2 CFM. Satin figures look to be at about 90% of chiffon figures at that CFM.  Chiffon (1 & 2 layers) was presented in the same 1.2 CFM graph as the 1, 2 & 4 layers of silk (above). Thus, if we thing the 90% performance of satin is proportional at 1.2 CFM too, we can estimate satin performance based on the chiffon at 1.2 CFM:

Particle size μm	3 layer satin calc'd	3 layer chiffon calc'd	1 layer satin estimated	2 layer chiffon calculated	2 layer chiffon actual	1 layer chiffon actual
0.8	0.91	0.94	0.585	0.85	0.85	0.65
1.5	0.93	0.96	0.63	0.88	0.88	0.7
2.5	0.95	0.97	0.6615	0.90	0.9	0.735
3.5	0.95	0.97	0.675	0.91	0.92	0.75
5	0.96	0.98	0.693	0.92	0.94	0.77

And from there, use the formula to calculate more layer permutations.

Then a graph:

The correction factor to get measured and calculated two layers of chiffon to match changed from 0.67 to 0.94 - maybe smushed layers don't reduce the filtration as much for polyester derivatives (as they do for silk).

So it looks like three layers of the fancy chiffon that was sourced for this study will get you slightly better than N95 specs (droplets and droplet nuclei)

And it looks like three layers of the satin that was sourced for this study will get you slightly worse than N95 specs (droplets and droplet nuclei).

Granted, there are lots of hacks to arrive at those figures, and I'm really not qualified certify the results. I've asked for additional multi-layer tests (and source data), but didn't hear back.

So for some months I have been making cloth masks with a thinner still satin, and that'd need more than three layers to make the same spec.

Takeaway: What to make though, for an N95 spec?

As indicated in the study, picking one layer of 600-thread cotton (Wamsutta brand) and 1 layer of regular satin, you'll reach N95 specs for droplet and droplet nuclei. No need for a filter pocket. 

Konda et al picked 600-thread Wamsutta cotton and chiffon but their particular stretch-chiffon was not regular or highly available form of that.