MATHEMATICAL MODEL FOR MEASURING THE CONCENTRATION OF NANOPARTICLES IN A LIQUID DURING SEDIMENTATION

摘要

Expanding the application areas of polymer composite materials with dispersed filler requires the development of technologies providing the required mechanical characteristics. One of these methods is based on forming a thin polymer shell on the surfaces of particles. At the same time, it is impossible to take into account the mechanical characteristics of a thin polymer shell due to its ultra-small thickness. The mechanical properties of the polymer shell can be determined only by indirect methods, and prior information can improve the adequacy of the properties determination. The method, which allows reducing the requirements for composite sample preparation, is proposed. This method is based on the sedimentation approach. It is suggested to evaluate the sedimentation time (or velocity) by measuring the optical density of the solution, consisting of nanoparticles and polymer macromolecules. The nanoparticle and polymer macromolecules parameters are defined using sedimentation time. The mathematical model for simulation of the photo sedimentation velocity of particles in a solvent is developed. The model considers the sedimentation process under the influence of gravity, hydrostatic lift, and drag forces. The model takes into account also the influence of the Brownian motion of the solvent on the particle movements based on elastic collision as well as the effect of the inelastic collision of particles with each other. The particle concentration is estimated based on beam light scattering modeling. The results of the mathematical model investigation and the experimental results confirm the feasibility of the proposed method. The results and estimations allow both to determine the sedimentation time and to formulate the method requirements for measuring particles of various sizes and densities. The proposed approach can be used to create equipment for nanoparticle parameters (mass, density) measuring.