Mathematical Modeling of Cryochemical Formation of Medicinal Substances in Nanoforms. The Role of Temperature and Dimensional Parameters

Abstract

The work is aimed at creating a mathematical model of cryochemical synthesis of nanoforms of pharmaceutical substances. The therapeutic efficacy of pharmaceutical substances largely depends on the size and morphology of the particles. Reducing the particle size of pharmaceutical substances to nanoscale makes it possible to obtain highly effective drugs, which makes it possible to use smaller doses of drugs and, thus, reduce side effects and toxicity. Cryochemical synthesis is one of the most powerful methods for obtaining nanoforms of medicament. The method, which is completely new, is based on sublimation or evaporation of the initial pharmaceutical substance under high vacuum conditions and the introduction of the resulting vapors into an inert gas stream, followed by low-temperature condensation of the flow of molecules of the substance from the gas phase on the cooled surface. The first step in the mathematical modeling of cryochemical synthesis processes is the calculation of the temperature field in the carrier gas flow interacting with the cooled surface. For this purpose, a stationary equation of thermal conductivity with mass transfer is used for the one-dimensional case. We prove existence and uniqueness theorems of the solution. Analytical solutions of the equation for Dirichlet, Neumann and Robin boundary conditions are found.