Equations of flow multicomponent mixture of viscous incompressible fluid

Author(s):  A. S. Kravchuk, Dr., Prof., Belarusian State University, Minsk, Republic of Belarus, as-kravchuk7@yandex.ru

A. I. Kravchuk, candidate of Sciences, associate Professor, Belarusian State University, Minsk, Republic of Belarus

Issue:  Volume 50, № 3

Rubric:  Physics

Annotation:  Due to the fact that in the derivation of equations of mathematical physics using the standard method – derivation of the equations for the selected elementary volume of the medium, it allows using the method developed by the authors to generalize known equations to the case of composite media with volume fraction of the component. Implicitly used hypothesis that the volume fractions of the components are discrete random variable that describes the probability of the presence of one component of an inhomogeneous medium at a particular point with given coordinates at an elementary volume, as well as at geometric area as a whole. The constructed system of equations allows us to solve hydrodynamics problems, for example, for multi-component mixtures of mutually insoluble liquids

Keywords:  incompressible fluid; the viscosity, the volume fraction of the components; effective properties of a multicomponent mixture; the system of Euler equations for the average pressure, vectors of velocity and the mass forces; Navier-Stokes equations for the averaged pressure, viscosity, vectors of velocity and mass forces

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