The near field/far field (NF/FF) model is a contaminant dispersion construct that permits making airborne contaminant exposure estimates for an individual located close to an emission source. In the present analysis, chemical emission involves a constant mass rate of chemical application to surfaces, denoted I (mg/min), and an exponentially decreasing rate of emission of the chemical from the surfaces with rate constant α (min(-1)). The time-dependent emission rate function is: G(t), mg/min = I - I exp(- αt), where time t is in minutes. The exact time-dependent equations for the contaminant concentration in the NF and the FF are presented. These equations are used to revise a previous analysis of a study in which a penetrant liquid containing benzene was applied to parts on a work table in a test room. The previous analysis assumed that the benzene was applied as a bolus at the start of a 15-min use period, whereas the present analysis assumes the same total benzene mass was applied at a uniform rate over the 15-min use period, but with the same evaporation rate constant α. The new G(t) function leads to a lower 15-min time weighted average NF benzene concentration that better matches the experimental data. It is also shown that the exact equation for the NF concentration is well approximated by combining two well-mixed single-zone equations. The approximation method is mathematically simpler and obviates the need to derive the exact NF equation.
Keywords: Benzene exposure; mathematical modeling; near field/far field.