BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

Migration of nanoparticles across a polymer-polymer interface: theory and simulation

We proposed recently a theoretical description for hydrodynamic flows in inhomogeneous liquids in the vicinity of solid interfaces, consistent with current theoretical descriptions of the thermodynamical equilibrium of liquids in...

LASER REFRACTOGRAPHY – A NOVEL TECHNOLOGY OF LIQUIDS REFRACTOMETRY

This paper is devoted the base principles of the method of laser refractography and the results of its application in experimental visualization of optically inhomogeneous liquids. Laser refractography is a novel information-measurement technique based on the probing of fluid flows with a structured laser beams, digital recording of the refraction images obtained, and their computer processing with a view to reconstructing the parameters of the flows. Block diagrams of measuring laser systems are shown, and typical refracrograms are presented.