Thanks to all.
Bobshouse, your analogy got me to thinking about this a little differently. The more I looked into it, the more complicated it got. The following is what I learned so far. It is still a gross over-simplification and probably still contains errors but I haven't time to go any further just yet.
Efficiency is the ratio of some desired or useful result divided by the total possible result.
Efficiency = amount of useful work / total possible work
Filter efficiency is the ratio of particles, of the specified size (or possibly sometimes larger), trapped by a filter divided by the total number of particles, of the specified size (or larger?), found in the air upstream of the filter.
A micron (μm, or micrometre or micrometer) is one millionth of a metre (meter). There are 25,400 microns to an inch.
We are not given any indication of which testing standard was used to obtain the ResMed filter efficiency values nor exactly what the given specifications mean. We don't for example, know whether the ratings apply to 7 and 0.5 micron
mean diameter particles (which includes smaller and larger) or to
particles of those diameters and larger, nor what mix of particle sizes.
HEPA filters are all rated for particles of
0.3 micron mean diameter. I have seen this expressed (on Wikipedia, incorrectly perhaps?) as
particles of mean diameter 0.3 micron or larger.
I am unsure which applies to the ResMed specifications.
A filter's efficiency of 88% at 7 microns should probably mean that it will stop 88% of particles 7 microns mean diameter but it could mean that it will stop 88% of particles of 7 microns or larger, a looser specification;
A filter's efficiency of 89.9% at 0.5 micron should probably mean that it will stop 89.9% of particles .5 micron mean diameter or it could mean that it will stop particles of 89.9% of particles 0.5 micron or larger.
Either way, this represents a significant difference between the two filters.
What follows is based on the (looser) specification of particle size, i.e.,
mean diameter or larger. I am not sure how to do the same for the tighter definition and I haven't the time to pursue it right now. I offer what follows for what it is worth and I am not sure what that is.
I calculate efficiencies of 0.0 for both filters for, i.e, neither filter catches: viruses, pesticides and coal flue gases.
The following particles seem to be caught, to varying degrees, by the finer filter (efficiency is given) and not the standard one (efficiency is 0.0).
0.5μm 7μm Particle
89.9% 0.0% liquid droplets
89.9% 0.0% anthrax
89.9% 0.0% Lead dust
89.9% 0.0% Spider web
82.6% 0.0% Paint pigments
78.9% 0.0% Tobacco smoke
71.9% 0.0% various combustion byproducts
46.3% 0.0% Oil smoke
41.3% 0.0% Smoldering or flaming cooking oil
The following particles are caught significantly better (more than three times as many) by the finer filter than the standard one. Both efficiencies are given.
0.5μm 7μm Particle
89.9% 27.8% Insecticide dust
86.3% 26.7% Radioactive fallout
The following particles are caught better by the finer filter than the standard one. Both efficiencies are given.
0.5μm 7μm Particle
89.9% 48.9% Mold
89.9% 52.8% Red blood cells
89.9% 66.0% Antiperspirant
88.7% 67.7% Face powder
89.9% 71.5% Iron dust
88.8% 72.6% Atmospheric dust
89.9% 76.4% Talcum dust
89.9% 77.2% Yeast cells
89.6% 78.1% Bacteria
89.9% 78.5% Spores
The following particles are caught marginally better by the finer filter than the standard one. Both efficiencies are given.
0.5μm 7μm Particle
89.9% 81.7% Textile dust
89.9% 81.8% Asbestos
89.9% 82.7% Coal dust
89.9% 84.4% Cement dust
89.9% 87.4% Metallurgical fumes & dust
89.9% 88.0% Mold spores
89.9% 88.0% Pollen
89.9% 88.0% Dust mites
89.9% 88.0% Beach sand
89.9% 88.0% Glass wool
To test a filter, particle counters measure the size and quantity of upstream particles per known volume of fluid, as well as the size and quantity of particles downstream of the filter. The number of particles trapped by the filter can then be computed as Particles Upstream - Particles Downstream.
Filter Efficiency = Particles Trapped / Particles Upstream = (Particles Upstream - Particles Downstream) / Particles Upstream
I have had to make some assumptions and ignore some variables:
- I have assumed here that the efficiencies refer to particles of the specified diameter and larger. The results are not applicable if the efficiencies refer to mean particle diameters.
- I have had to ignore the effects of actual operating conditions, e.g., flow surges and changes in temperature.
- I had to assume that the particle sizes are uniformly distributed throughout the entire size range. This is not realistic.
- I had to assume that a filter's efficiency is constant for all particle sizes. This is unrealistic. It seem reasonable that a filter should do better at stopping larger particles than smaller ones.
- I had to assume that a filter's efficiency is constant for all particle types. This is unrealistic. It seem reasonable that a filter might do better at stopping some particles than others, e.g., due to shape, stickiness.
As well, a filter's efficiency does not indicate its dirt-holding capacity, the total amount of contaminant that can be trapped by the filter throughout its life, nor does it indicate its stability or performance over time.
There may be other, implied, assumptions I haven't even discovered yet.
Having calculated all this, I am now left wondering whether it is of interest or use to anyone or was just an academic exercise.
Particle Diameter (microns)
min max Particle
0.5 5 Liquid droplets
1 5 Anthrax
2 2 Lead dust
2 3 Spider web
0.1 5 Paint pigments
0.01 4 Tobacco smoke
0 2.5 various combustion byproducts
0.03 1 Oil smoke
0.03 0.9 Smoldering or flaming cooking oil
0.5 10 Insecticide dust
0.1 10 Radioactive fallout
3 12 Mold
5 10 Red blood cells
6 10 Antiperspirant
0.1 30 Face powder
4 20 Iron dust
0.001 40 Atmospheric dust
0.5 50 Talcum dust
1 50 Yeast cells
0.3 60 Bacteria
3 40 Spores
6 20 Textile dust
0.7 90 Asbestos
1 100 Coal dust
3 100 Cement dust
0.1 1000 Metallurgical fumes & dust
10 30 Mold spores
10 1000 Pollen
100 300 Dust mites
100 10000 Beach sand
1000 1000 Glass wool
0.08 0.2 Coal flue gas
0.005 0.3 Viruses
0.001 0.001 Pesticides & herbicides
Sources
Filter Arrestance and Efficiency
Filter efficiency definition
Particle Sizes
I was just trying to put the filter and filtering capabablities into perspective. 
