The mathematical model developed by Reneker et al. [J. Appl. Phys. 87, 4531 (2000)] and Yarin et al. [J. Appl. Phys. 89(5), 3018–3026 (2001)] for modeling filament formation in electrospinning is combined in this work with the structure generation algorithm of Venkateshan et al. [Mater. Des. 96, 27–35 (2016)] to simulate the effects of electrospinning parameters on microstructural properties (i.e., fiber diameter, thickness, and porosity) of the resulting electrospun materials. The model is calibrated using the experimental data obtained from electrospinning polystyrene (PS) fibers. 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 PS concentration, on the thickness and porosity of the resulting fibrous materials. For instance, it was shown that increasing the voltage or decreasing the NCD in electrospinning polystyrene results in mats with thicker fibers but smaller dimensionless thickness (or lower porosities), in agreement with experimental observations reported in the literature. In addition to serving as a characterization tool for the electrospun materials, the computational model developed in this work can be used to create accurate representations of the surface morphology or the internal geometry of fibrous materials used in a variety of applications, such as particle filtration or droplet separation.

This work is the first to report a study aimed at generating 3D virtual geometries that represent the microstructure of an electrospun fibrous mat comprised curly fibers. Polycaprolactone (PCL) mats are considered in our study as an example of such fibrous structures. We started with simulating the formation of PCL filaments and observed good agreement between the predicted and measured fiber diameters. In the absence of quantitative information about the shape of a curly PCL fiber, we treated these fibers as arrays of beads arranged on epitrochoid profiles. We then used the fiber deposition diameter and velocity in a mass-spring-damper (MSD) model to generate 3D fibrous geometries comprised hundreds of such curly fibers. The damping and spring constants in the MSD model were obtained through calibration with experimental data reported for single electrospun PCL nanofibers. The size of the epitrochoid-like fibers was obtained empirically through matching the average thickness of the resulting mats with those measured experimentally. With the calibrated code, we studied the effects of electrospinning conditions on the porosity of PCL nanofiber mats. It was found that increasing the voltage or decreasing the needle-to-collector distance results in PCL mats with thicker fibers, and consequently, lower porosities.

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