Mathematical optimization of filters used in N95 filtering facepiece respirators

The filter used in an N95 filtering facepiece respirator (FFR) has a collection efficiency and pressure drop that are primarily influenced by filter depth and solidity, as well as the average diameter and electrostatic charge of its fibers. A sensitivity analysis was performed to determine the influence of each property on particle collection efficiency at the most penetrating particle size (MPPS) and pressure drop using previously verified N95 FFR filter performance models. Collection efficiency was most influenced by changes in filter solidity and least influenced by fiber charge. Likewise, pressure drop was most influenced by fiber diameter, least influenced by changes in filter depth, and was not affected by fiber charge. Given the competing desire for low pressure drop and high collection efficiency, the use of a quality factor demonstrated that increasing filter charge and fiber diameter had a nearly equal positive association with overall filter efficacy. A filter optimization process was also conducted that employed a non-linear optimization routine to first determine the filter depth required to obtain a collection efficiency criterion of ≥ 95% collection efficiency at the MPPS for sets of fiber diameter and filter solidity values, and to determine the pressure drop resulting from each combination of the three property values while holding fiber charge constant. This analysis demonstrated that filters with low solidity, high fiber diameter, and high depth produce the lowest pressure drop. However, all combinations of filter properties within the ranges analyzed produced acceptable pressure drops, indicating that an upper limit on filter depth can be applied based on N95 FFR design constraints and still maintain a reasonable pressure drop. To aid filter design efforts, linear regression models were developed to first predict the filter depth needed to meet the efficiency criterion given known fiber diameter and filter solidity, and then to predict the pressure drop from those three properties.