Electrospinning has been the focus of countless studies for the past decades for applications, including but not limited to, filtration, tissue engineering, and catalysis. Electrospinning is a one-step process for producing nano- and/or micro-fibrous materials with diameters ranging typically from 50 to 5000 nm. The simulation algorithm presented here is based on a novel mass-spring-damper (MSD) approach devised to incorporate the mechanical properties of the fibers in predicting the formation and morphology of the electrospun fibers as they travel from the needle toward the collector, and as they deposit on the substrate. This work is the first to develop a physics-based (in contrast to the previously-developed geometry-based) computational model to generate 3-D virtual geometries that realistically resemble the microstructure of an electrospun fibrous material with embedded particles, and to report on the filtration performance of the resulting composite media. In addition, this work presents a detailed analysis on the effects of electrospinning conditions on the microstructural properties (i.e. fiber diameter, thickness, and porosity) of polystyrene and polycaprolactone fibrous materials. For instance, it was observed that porosity of a PS electrospun material increases with increasing the needle-to-collector distance, or reducing the concentration of PS solution. The computational tool developed in this work allows one to study the effects of electrospinning parameters such as voltage, needle-to-collector distance (NCD), or polymer concentration, on thickness and porosity of the resulting fibrous materials. Using our MSD formulations, a new approach is also developed to model formation and growth of dust-cakes comprised of non-overlapping non-spherical particles, for the first time. This new simulation approach can be used to study the morphology of a dust-cake and how it impacts, for instance, the filtration efficiency of a dust-loaded filter, among many other applications.