Analytical expressions for predicting capture efficiency of bimodal fibrous filters

In this work, a series of numerical simulations are formulated for studying the performance (collection efficiency and pressure drop) of filter media with bimodal diameter distributions. While there are numerous analytical expressions available for predicting performance of filters made up of fibers with a unimodal fiber diameter distribution, there are practically no simple relations for bimodal filters. In this paper, we report on the influence of the fiber diameter dissimilarity and the number (mass) fraction of each component on the performance of a bimodal filter. Our simulation results are utilized to establish a unimodal equivalent diameter for the bimodal media, thereby taking advantage of the existing expressions of unimodal filters for capture efficiency prediction. Our results indicate that the cube root relation of Tafreshi, Rahman, Jaganathan, Wang, and Pourdeyhimi (2009) offers the closest predictions for the range of particle diameters, coarse fiber number (mass) fractions, fiber diameter ratios, and solid volume fractions (SVF) considered in this work. Our study revealed that the figure of merit (FOM) of bimodal filters increases with increasing fiber diameter ratios for Brownian particles (dp<100 nm), and decreases when challenged with larger particles. It has also been shown that when increasing the ratio of coarse fibers to fine fibers, FOM increases for Brownian particles, and decreases for larger particles.