The University of Chicago and Argonne National Labs have a run down of fabrics for filtration at <300nm and >300nm ACS that is part of their larger ACS-published study here. I have been wearing a seven layer satin mask (+ one 400-thread cotton outer layer) for the last month and a bit. At least, when shopping at the supermarket.
Ignoring errors, the study says that 14% effectiveness for <300nm particles and 51% effectiveness for >300nm particles. My question is on the formula for predicting the effectiveness of the 2-6 layers of satin. I think the formula at >300nm for two layers is =1-(1-.51)*(1-.51). There are simplifications to that formula perhaps, but the tedious way I lay it out there make it clearer to my non-math head.
Thus, the results are as follows:
| | <300 nm | >300 nm |
|--------------------|---------|---------|
| Actual ACS 1 layer | 14% | 51% |
| Predicted 2 Layer | 26% | 76% |
| Predicted 3 Layer | 36% | 88% |
| Predicted 4 Layer | 45% | 94% |
| Predicted 5 Layer | 53% | 97% |
| Predicted 6 Layer | 60% | 99% |
Of course, the ±11 and ±2 errors would widen too, with predictions for multi-layer, and additional errors could exist for based on the gap (or not) between layers. Is my formula right though?
Off topic questions pre-empted: yes the mask is breathable - I sewed a "retainer" into it - but I wouldn't want to wear it outdoors in the summer. See https://cv-masks.github.io/ragmask-max.html. Note that pattern now talks about using spunbond NWPP instead of any other fabric - and no retainer.
The general formula for $n$ layers of fabric, if each layer filters out a proportion $p$ of the particles, is
$$ 1 - (1 - p)^n. $$
The raised $n$ is an exponent: $(1-p)^2 = (1-p)\times(1-p),$ $(1-p)^3 = (1-p)\times(1-p)\times(1-p),$ and so forth.
In particular, with $2$ layers and $p = 0.51$ the answer is
$$ 1 - (1 - 0.51)^2 = 1 - (1 - 0.51)\times(1 - 0.51). $$
So it seems you have exactly the right idea.
The numbers in the table agree with the formula, rounded to the nearest whole percentage. Presumably, "predicted" means they applied the formula without testing to see what actual results they got.