# Numerical Infeasibilities of Nanofibrous Mats Process Design
## 1 Introduction  
Electrospinning (ES) has been one of the most dynamically developing technologies over past decades [1]. A wide range of natural and synthetic nanofibrous mats have been successfully electrospun [2, 3]. ES contributes to the formation of polymeric fibers with a nano-scale diameter, that can mimic extracellular matrix [4]. Thanks to this feature, ES may be considered as a technology suitable for biomedical applications. [PERSON] and co-authors [5] presented in their work a problem associated with the mechanism of cell-biomaterial adhesion. For this purpose, they characterized electrospun poly-\(\varepsilon\)-caprolactone (PCL) scaffolds with an increasing concentration of self-assembling peptides (SAPs). [PERSON] and co-authors proposed the use of polycaprolactone electrospun structures in preclinical studies in relation to effective breast cancer therapy [6]. [PERSON] et al. drew attention to the latest trends in using ES to develop structures applicable in wound healing [7]. Some recent studies have focused on the use of electrospun materials in the filtration/purification processes [8], the flame retardant sector [9], and the solar industry [10]. Most studies have been content with an experimental method of material design. [PERSON] and [PERSON] conducted the experimental optimization of the electrospinning process of gamma-cyclodextrintrim/poly(ethylene oxide) aqueous solutions [11]. As a result, they obtained uniform fibers capable of removing aniline. Extensive experimental optimization has also been explored in the work [12]. The authors established the optimum conditions in which to fabricate hydrolyzed Polymer of Intrinsic Microporosity (PIM-1) structures of a high affinity in relation to cationic dyes (Methylylene Blue). [PERSON] and [PERSON] [13] proposed optimized processing parameters to produce fibers from starch-pullulian aqueous dispersions. Traditional methods used by engineers and scientists have been changed due to the appearance of powerful, high-performance computers. This general trend is reflected in numerical simulations, that together with experiment and theory, have become the central aspects of scientific discovery [14]. Today, a high-quality system design proceeds with the use of a computer. This approach may contribute to the growth of innovative solutions, new materials, and advanced technologies. In one study [15], the Artificial Neural Network model was used to predict the terminal diameter of ferrofluid-polyvinyl alcohol fibers. The model took into account variables such as voltage, flow rate, spinning distance and the (collector) rotation speed. [PERSON] and [PERSON] [16] presented the mathematical modeling strategy based on works [17, 18]; the simulation parameters were employed for a 6 wt % aqueous solution of poly (ethylene oxide). [PERSON] and [PERSON] [19] determined the fiber diameter of polyamide 6 based on numerical and experimental investigations. The proposed approach utilized Finite Extensible Non-linear Elastic-Chilcott and Rallison (FENE-CR) model; the authors examined the influence of initial polymer contribution. It is worth noting that a considered numerical approach allowed both the viscoelastic material behavior and fiber solidification to be captured. Mathematical models may significantly accelerate the design cycle and allow us to investigate the system's behavior. It is important to construct a model that reflects the considered tasks with appropriate accuracy. Some questions related to the solution procedure arise at this point. Therefore, to obtain numerical data that represent system behavior in different conditions and for a wide range of selected model parameters, it is desirable to perform numerous computer simulations. Then, based on the results obtained it is possible to focus on the detailed optimization of the received approximated solution. Nevertheless, in some instances for the chosen set of parameters the model cannot be solved. In this situation, we usually obtain the information about a calculation error.