## Wednesday, February 3, 2021

### TWO FACE MASKS OR ONE?

TWO MASKS OR ONE? Douglas Winslow Cooper, Ph.D.

To prevent hazardous particles from being inhaled, some people choose to use two face masks rather than one. This short article will examine that choice.

Let Q be the total breathing rate for the person, as in liters/minute. It is the total of Q’ through the mask and Q” through the leaks in the seal to the face:

Q = Q’ + Q”

Let p be the pressure difference between the space inside the mask and that outside of it. The flow for these two paths is proportional approximately to p:

Q’ = k’ p

Q” = k” p

Q= (k’ + k”) p

Q’ = (k’/2) p

So, the total flow becomes

Q* = (k’/2 + k”) p*,

a reduction versus one mask, unless the breather breathes harder and increases the difference in p between the outside and the inside of the mask

To get the same flow as for a single mask, Q=Q*,

Q= (k’ + k”) p = (k’/2 + k”) p*

The mask user will need to increase the inhalation pressure difference

so (k’ + k”) p = (k’/2 + k”) p*

p*/p = (k’ + k”) / (k’/2 + k”)

This increase in the pressure difference will increase the leakage through the seal to the face, a leakage that brings in unfiltered air. Less air will flow through the mask and be filtered, but filtered better. Whether this is a net gain depends on the details.

Two limits are clear:

1. A second mask that is almost perfectly filtering the air but is almost not allowing any air to go through it will lead to (unfiltered) leakage almost exclusively.

In the limit, it blocks all flow except leakage, which is unfiltered, and it will accelerate fatigue of the breather.

2. A second mask that filters well but supplies almost no resistance to flow will not increase fatigue, will not increase leakage, and will filter the air better than a single mask. If the mask is a HEPA (high-efficiency particulate air) mask, it will have near-perfect filtration singly, and little or no improvement would be expected from two of them, as raising the air flow resistance will cause more leakage at the seals.

Thus, using one HEPA mask seems optimal.