MATHEMATICAL MODEL FOR DETERMINE OF THE MESH BUBBLE POINT PORE DIAMETER

Abstract

The article presents mathematical models for determining the bubble point diameter of the pores of meshes with micron sizes square cells of plain and full twill weaving. Analyzed are mathematical models developed by a number of researchers to determine the bubble point pore diameter of the meshes and their point pore pressure. The analysis of the mathematical models showed that they were developed on the basis of a number of assumptions that, to varying degrees, take into account the spatial shape of the mesh cells and the physicochemical processes when the free surface through the mesh. This undoubtedly affects the accuracy of analytical calculations that are based on the use of these models. In the presented work, mathematical models have been developed that take into account the complex spatial shape of the wires from which the mesh is made. Mathematical models have been developed for plain and twill weaving meshes. When developing mathematical models, it was assumed that the free surface is formed on a hole with elliptical edges. In this case, it is assumed that the points of contact of the free surface of a plain weave mesh correspond to the most distant points of the projection of the mesh cell. For full twill meshes, taking into account the structure of their weaving, it is assumed that the free surface is formed on two adjacent cells. The influence of the contact angle between the mesh surface and the working fluid was taken into account by analyzing the spatial shape of the mesh wires. The developed models make it possible to take into account the effect of liquids with a contact angle from zero to 90 degrees. Simplified mathematical models of the meshes have also been developed for the case of perfect wetting of the mesh surface with a liquid, when the contact angle is zero. The obtained mathematical models can be used in the design of capillary phase separators of liquid acquisition devices in zero gravity of spacecraft, as well as in the calculation of capillary devices of various technical systems, such as heat exchangers, gas-liquid mixers, chemical reactors, bubble filters, etc.