Adjusting a commonly used respirator pressure drop equation for use with modern respirators

Millions of workers in the United States require the use of a respirator while at work. Occupational inhalation hazards have the potential to cause respiratory diseases. Wearing a FFR (filtering facepiece respirator) are commonly used respirators that can help protect workers against inhalation hazards. When choosing a respirator, an important parameter is pressure drop. Pressure drop relates to the collective effort of individual fibers in a respirator resisting airflow and affects comfort and breathability of a respirator. There are many models to predict pressure drop. A commonly used pressure drop equation developed by Davies in 1952 is: Δp = (ηULf(α))/(df2), f(α) = 64α1.5 (1 + 56α3) when 0.006 < α < 0.3. The equation can be rearranged to back calculate an effective diameter rather than measuring the individual fibers themselves but may be larger than the actual fiber diameter. Given modern advancements in respirators this study has two specific aims: 1) To determine the key physical characteristics of filter media associated with modern respirators and 2) To evaluate the accuracy of a commonly used model to predict the pressure drop caused by inflowing air through modern respirator filter material. This study used 10 FFR models. The average pressure drop for 3 filter samples of each respirator type filter was measured at 4.7 cm/s and 10.5 cm/s. A total of 100 filter fiber diameters for each respirator were counted using photos from a SEM (scanning electron microscope). A median measured fiber diameter for each respirator was calculated. Three different effective diameter equations were used for each respirator: the Davies model, a model based on fiber diameter distribution, and an adjustment of the Davies model based on study results. Pressure drop values between the various FFRs varied, indicating not all respirators are created equal. When placing the data in a pressure drop model, the respirators did not align with the expected curve from the commonly used model. The commonly used equation was adjusted to Δp = (ηULf(α))/(df2), f(α) = 4α1.5 (1 + 56α3) when 0.006 < α < 0.3 by changing constant, 64, to 4 by minimizing the RMSE (root mean square error) between measured and modeled data. The respirator filter data from this study aligned better with the curve of the adjusted equation. The adjusted equation provided a more accurate prediction of fiber diameter compared to the other to effective diameter equations.