DOI: 10.18503/1995-2732-2026-24-1-142-147
Abstract
Problem Statement (Relevance). The powder spraying is widely used in various industries. It allows to significantly increase the service life of the product, protect it from abrasive effects, and enhance its functional properties. Experimentally, it was found that reducing the size of the sprayed particles makes it possible to achieve a uniform coating. Therefore, it is necessary to develop appropriate mathematical formulas that make it possible to simulate the process of spraying extremely fine particles onto the surface. Objectives. The work is aimed at developing a mathematical approach that will allow simulating the process of spraying extremely fine particles onto the surface. Methods Applied. The authors have used a stereological formula for a Boolean model of a random set, probability theory, and Monte Carlo method. Originality.Using a stereological formula, an estimate of the average square area uncoated by round particles during spraying hass been obtained. Result. A mathematical model has been constructed of a set of points covered by spherical particles of radius sprayed onto the surface of a unit square r(m) at m∞. The dependence of the coating area on the radius of the sprayed particles and their number at a Poisson flow of a given intensity is determined. An estimate of the average square area uncoated by particles during spraying is obtained. A comparative analysis of the obtained estimate with the estimate of the average fraction of the uncoated area of the square calculated by the Monte Carlo method is carried out. Practical Relevance. The results obtained can be used in modeling the process of spraying extremely fine particles onto the surface of bioimplants. The model used can be applied to solve the percolation problem, namely, to determine the probability of connecting opposite sides of a square through dust-free channels, which is also a subject of research in technological processes.
Keywords
powder spraying, Monte Carlo method, Poisson flow, average uncoated area
The work was performed within the framework of the state assignment of the Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences No. 075-00459-25-00.
For citation
Tsitsiashvili G.Sh., Losev A.S., Chasovnikov D.R. Estimation of the Average Uncoated Surface Area During Powder Spraying. Vestnik Magnitogorskogo Gosudarstvennogo Tekhnicheskogo Universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2026, vol. 24, no. 1, pp. 142-147. https://doi.org/10.18503/1995-2732-2026-24-1-142-147
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