Aim. To consider the viscoelastic properties of an electrorheological fluid consisting of silicon dioxide particles in polydimethylsiloxane at different values of electric field strength.
Methodology. The frequency dependences of dynamic modules were approximated using the equations of the structural rheological model. The values of the coefficients of the equations were determined for different values of the field strength.
Results. The possibility of using the equations of the structural model to describe the frequency dependence of the loss modulus and the storage modulus is shown. The relationship between the coefficients of the rheological equations and the magnitude of the applied electric field is established. The relationship between the nature of the rheological curves and the structure of dispersion in the electric field is shown.
Research implications. Equations are proposed that are capable of approximating experimental data in individual sections of the frequency dependence of dynamic modules for an electrorheological fluid. A relationship is established between the calculated coefficients of rheological equations and the structure of the substance

Aim. Creation of algorithms for calculating and controlling a dispersed flow with a streamlined body in application to the problems of heat and mass transfer control and drag reduction in heavy precipitation conditions.
Methodology. Known physical laws, integration methods and analysis of studies by other authors are used.
Results. In this paper, a method for calculating the parameters of interaction of a flow with a solid body, the properties of the coating of which affect the processes of its flow, is developed. Parametric studies are carried out, optimal shapes of bodies in two-phase media at large values of the Stokes number are shown.
Research implications. The results can be used in designing the shapes of streamlined bodies moving in aerosol media, in particular when a flying vehicle move through clouds and media with precipitation

Aim. The aim of this work was to develop an algorithm for determining the density of incident mass, momentum and energy flows on a body of complex shape, flown around by a highly rarefied gas.
Methodology. The work uses methods of the molecular-kinetic theory of gases, aimed at determining the macroscopic characteristics of a rarefied gas flow. The work is based on the numerical solution of integrals of the Maxwell distribution function.
Results. An algorithm has been developed and tested on a model simulating a device (solar battery panel, antenna, etc.) installed on the surface of a spacecraft body.
Research implications. The developed algorithm can be used in problems related to determining the distribution of mass, momentum and energy flow densities over the surface of objects flown around by a highly rarefied gas medium, and in problems related to determining the characteristics of a spacecraft's own external atmosphere.

Aim: to find statistical distributions of molecules and their pairs in a shock-compressed gas mixture based on the modified Tamm-Mott-Smith method.
Methodology. Theoretical methods of mathematical physics were used.
Results. It is shown that the single-particle modified Tamm-Mott-Smith statistical distribution for a shock-compressed gas mixture is essentially four-modal. This makes it possible to satisfy both the conditions of conservation of mass, momentum and energy fluxes inside the shock wave front, and to significantly simplify the systems of moment equations used in numerical calculations. Analytical representations are obtained for all types of distribution functions of pairs of molecules in a shock compressed binary mixture of gases.
Research implications. The obtained analytical results are essential for clarifying the question of the need to take into account translational disequilibrium in determining the velocity coefficients of energetically activated inelastic collisions inside shock wave fronts

Aim is refinement of the calculation of the diffracted light field from flat objects within the framework of the classical Kirchhoff’s approach. This implies the derivation of analytical formulas taking into account the cubic terms of the phase expansion and subsequent analysis of the limit transitions.
Methodology. By obtaining the analytical formulas for diffracted fields, the method of “stationary phase” was applied.
Results. The formulas for the diffracted field with taking into account the cubic term of the phase expansion are obtained, from which obtains the well known formulas of diffraction of light in a private manner.
Research implications. The theoretical significance of the proposed methodology is the limiting transition to special cases, based on one general problem. Thus, from the problem of light diffraction by a slit, as a special case, appears the problem of light diffraction from a half-plane. By rotating the coordinate system, you can combine the angle of incidence of light with the angle of rotation, in results obtains the same formulas as for normal incidence. The use of symmetry elements of an object, analysis of limit transitions, and choose of a successful observation point allows, in a number of cases, to solve complex diffraction tasks. The given technique of calculation can be used in practical lessons on electrodynamics for determination of diffracted field from various objects