The article describes obtaining polyacrylonitrile (PAN) nanofibers by electrospinning on a setup developed at the Mendeleev University of Chemical Technology of Russia (MUCTR). A technique for producing PAN-based carbon nanofibers (CNFs) and PAN-based CNFs modified with titanium oxide (TiO₂) is presented. The article presents a comprehensive study of the characteristics of PAN-based nanofibers and CNFs, including an analysis of the external structure of the fibers, the dependence of fiber diameters on the viscosity of the initial solutions, the effect of temperature treatment on the functional groups of PAN, elemental analysis, and flame-retardant properties. It was found that the fiber diameter and its external structure strongly depend on the viscosity of the initial solutions; an increase in viscosity leads to a linear increase in the fiber diameter. Preliminary temperature treatment at 250 °C helps stabilize PAN nanofibers and prevents their melting at the carbonization stage. The differential scanning calorimetry results allowed us to determine the presence of peaks for the initial PAN nanofibers, indicating an exothermic process in the temperature range of 290–320 °C. The peak height decreased with increasing TiO₂ concentration in the samples. For CNF samples of different compositions, the endothermic effect prevailed in the temperature range of 400–700 °C, indicating the possible flame-retardant properties of these materials. The limiting oxygen index (LOI) was calculated based on the thermogravimetric analysis results. The highest LOI values were obtained for CNFs based on PAN without adding TiO₂ nanoparticles and CNFs modified with TiO₂ (3 wt.%). The resulting CNF-based nonwovens can be recommended for use in heat-protective clothing, flame-retardant mattresses, and flame-retardant suits for the military.

The process of freezing (crystallization under cooling) is the preliminary preparation of samples for vacuum freeze drying. At this stage, the structure of the product is formed, which depends on the size of the resulting ice crystals. One of the most interesting and cost-effective ways to intensify the freezing stage and controlled nucleation is ultrasonic treatment. The effect of ultrasound with a power of 50 W and a frequency of 40000 Hz on the freezing kinetics and ice crystals size distribution were studied for polymers of various nature: sodium alginate, chitosan, polyvinyl alcohol, and a cross-linked polyelectrolyte complex of alginate-chitosan. Cryoscopic temperatures for these polymers were determined. A mathematical model for calculating the kinetics of freezing and size distribution of ice crystals was implemented in Python.

This article presents the results of a study on the rheological characteristics of in situ thermosensitive nasal gels based on poloxamer 407 (P407) and their effect on spray angle. The development of new drug delivery systems based on in situ thermosensitive gels can overcome several shortcomings of traditional nasal sprays associated with mucociliary clearance and low mucoadhesion. Using the cold method, samples based on P407 were prepared in pure form, in combination with poloxamer 188 (P188), and with the addition of several mucoadhesive polymers: chitosan, sodium alginate, and hydroxypropyl methylcellulose (HPMC). Analytical studies were carried out for all obtained samples, which showed that the gelling temperature (T_sol–gel) of compositions with P407 was inversely dependent on its concentration, decreasing from 32.71 °C to 24.63 °C. The addition of hydrophilic P188 increased T_sol–gel. The addition of mucoadhesive polymers had varying effects on T_sol–gel: chitosan and HPMC increased the temperature, while sodium alginate decreased it. The addition of mucoadhesive polymers significantly affected the viscosity of the formulations; for example, the addition of sodium alginate resulted in a fivefold increase, making the formulations unsuitable for spraying. A study of the spray angles of T_sol–gel samples in the range of 27–31 °C using the SprayVIEW measuring system revealed an inverse relationship between the viscosity of the formulations and the spray angle. A mathematical model of the solution droplet trajectory was presented, enabling the spray angle to be predicted depending on the formulation composition. The relative error of the computational experiments did not exceed 10%. This approach has the potential to reduce the number of full-scale experiments, and consequently their cost.

This paper presents modern methods of mathematical modeling, which are widely used in the development of new inhalation and intranasal drugs, including those necessary for the treatment of socially significant diseases, which include: tuberculosis, bronchial asthma, and mental and behavioral disorders. Based on the conducted studies, it was revealed that the methods of mathematical modeling used in the development of drugs are fragmented, and there is no single approach that would combine the existing methods. The results presented in the work should contribute to the development of a unified multiscale model as a new approach in mathematical modeling that contributes to the accelerated development and introduction to the market of new drugs with high bioavailability and the required therapeutic efficacy.

Freeze-drying is often used as a final stage to produce three-dimensional porous matrices for medicine. Because a pure solvent crystallizes first during freezing, it acts as a pore-forming agent. The size of the solvent crystals primarily depends on the cooling rate and the composition of the material to be frozen. Ultrasonic treatment also affects the size of crystals and can be used to control the structure of a porous matrix. This article describes the effect of ultrasound (40 kHz, 50 W) applied at the preliminary freezing stage of polysaccharide solutions (alginate, chitosan, alginate–chitosan and alginate–gelatin) on the finished matrix properties. The most attention was paid to the effect of ultrasound on the size and shape of crystals formed during freezing, which leads to a change in the porous structure of the matrices after solvent sublimation. As a result of changes in the microstructure, a number of differences in the vibrational spectra of the molecules and the values of pore volume, sorption capacity, permeability and degradation of matrices were identified. Such changes in the structure of materials, as well as the emerging directionality of pores, together can affect the process of cell cultivation in these polysaccharide matrices, which can be useful in solving problems of tissue engineering.

In order to carry out mathematical modeling of the drug particles or drop movement in the human respiratory system, an approach to reverse prototyping of the studied areas based on the medical data (computed tomography) results is presented. To adapt the computational grid, a mathematical model of airflow in channels of complex geometry (respiratory system) has been developed. Based on the data obtained, the results of computational experiments for a single-phase system are presented.