Modeling Aerosol Exposures

I have gotten very few requests for blog topics since issuing the offer some time ago.  One such request has come from Richard Quenneville who asks how one might model aerosol or airborne particulate exposure.

Aerosols are certainly different from vapors or gases and the differences significantly complicate any attempt to model their exposure.   Even relatively small aerosol particles (microns or tenths of microns) are much larger than the individual molecules that make up a gas or vapor.  This gives them different properties at least in the following areas:

• ·    They are typically more readily electrically charged especially if they are generated by sliding along a surface (e.g., dust from transporting powder in a pneumatic tube).  This charge can affect the size distribution and sampling of the aerosol.   
• ·     With or without electrical charge, aerosol particles are often susceptible to combining with one another in a mechanism known as agglomeration.  This process, of course, changes the size distribution of the aerosol.
• ·     Most important, because they have much more mass than vapor molecules they have a settling velocity which increases with increasing particle size and this, again, constantly changes the airborne size distribution of the aerosol with time.
• ·     Because of their mass, airborne particles do NOT always make it into sampling orifices thus biasing their measurement.

Assuming agglomeration is not happening in a time frame that is relevant to the potential exposure, one can estimate any time-interval concentration of any aerosol particle or size range of particles.   This is done by taking the average settling velocity of the particles in that size range and accounting for their loss from settling.   Typically is this done for particles from 2 meters in height settling to the floor.  If one is sure that the breathing zone remains at say 2 meters high you can calculate the concentration loss from the horizontal volume at 2 meters height to say, 1.8 meters.   If you do this over small enough time intervals you can estimate a time-weighted average of aerosol concentration for any time period dependent on the nature of the aerosol source.

This brings up another complication of dealing with aerosol.  Compared to vapors, predicting the “release” or generation rate of particulate into the air is highly problematic because it depends on many undefined or unmeasured factors such as inter-particle forces.  I have never been able to use first-principle models to predict this rate. Instead, we have had success experimentally determining this rate from simulating the mechanism of generation, measuring the resultant concentrations and back calculating the rate of generation.  I personally think this is what needs to happen for the exposure assessment of nanoparticles released to the air in various scenarios.

Please note, settling is dependent on the particle size distribution of the generated aerosol.  I have seen situations in plants that were literally “particle fountains” with particle size distributions with a significant portion of the particles were greater than 100 microns.  These particles hit the floor in a time frame of seconds which dramatically lowers the total aerosol mass/volume.   Particles on the other end of the spectrum, e.g., nanoparticles, are going to essentially remain airborne and not settle at an appreciable rate in most scenarios.

Finally, aerosol, especially insoluble aerosol, will deposit in the respiratory track based particle size.  At the current time we have some aerosol exposure limits specified in terms of total and respirable particulate.   These are defined mathematically by the ACGIH and these algorithms can be applied to the concentration in the above size intervals above to render the amount of aerosol that might be inhaled (inhalable mass concentration) or be able to reach the deep pulmonary regions of the lungs (respirable mass concentration).

The above analysis sounds daunting mathematically and indeed it is not simple; however, it is nothing that an Excel spreadsheet cannot handle with relative ease given the proper input of scenario specific dimensions, generation rate, initial particle size distribution, particle size interval-specific settling velocity and ACGIH algorithms.   Like all models it is not exact but, I believe it is accurate enough to be useful.