The article solves a boundary value problem for a stationary system of equations of gas dynamics (a velocity-linearized system of Navier–Stokes equations, convective equations of heat and mass transfer), which allows us to study the motion of an evaporating spherical droplet in the field of electromagnetic radiation. Convective heat and mass transfer equations are solved by the method of spliced asymptotic expansions. The solution of the problem allows us to evaluate the effects of the reactive, thermodiffusion and Stephan effects on the rate of photophoresis of an evaporating droplet.

Thermophoretic motion of a spherical evaporating droplet in a viscous binary gas medium at arbitrary relative temperature differences in its vicinity is theoretically described in a quasistationary approximation at low Reynolds and Peclet numbers. A system of gas-dynamic equations is solved, including a velocity-linearized system of Navier–Stokes equations, as well as heat and mass transfer equations. The properties of a gaseous medium are described with account for the power-law dependence of the transfer (viscosity, diffusion, and thermal conductivity) and density coefficients on temperature. The resulting numerical estimates suggest that the dependences of the thermophoretic force and the velocity of the droplet on the average temperature of its surface are nonlinear.

Purpose of research. To obtain analytical expressions that allow calculating the strength and velocity of a moderately large, highly viscous droplet, taking into account the direct contribution of the evaporation coefficient, linear corrections by the Knudsen number and the reactive effect of a plane wave moving in the field of mono-chromatic radiationMethods. Methods of perturbation theory, gas kinetic methods, mathematical methods for solving linear partial differential equations with variable coefficients (the system of Stokes equations, Laplace and Poisson equations) were used.Results. In a quasi-stationary approximation, a theoretical description of the photophoretic motion of a moderately large evaporating highly viscous spherical droplet (there is no circulation of matter inside the droplet and interfacial surface tension forces) in a viscous binary gas mixture is carried out. A velocity-linearized system of Navi-Stokes equations and heat and mass transfer was solved. Expressions are obtained for the fields of mass velocity, pressure, temperature and the relative numerical concentration of the first component. The strength and speed of photophoresis of a highly viscous droplet was determined by integrating a stress tensor over the surface of the particle. Under boundary conditions on the surface of a highly viscous droplet, linear corrections in terms of the Knudsen number (isothermal, thermal and diffusion slips, temperature and concentration jumps, as well as sliding due to temperature inhomogeneity along the curved surface of the particle), the reactive effect and the contribution of the direct influence of the evaporation coefficient were taken into account. The contributions to the obtained formulas for the photophoresis of a moderately large highly viscous droplet are analyzed and the preliminary transitions to the results known in the literature (moderately large and large solid particles of spherical shape) are considered Conclusion. The obtained formulas based on the hydrodynamic method allow us to evaluate the effect of the direct contribution of the evaporation coefficient and linear corrections by the Knudsen number on the strength and speed of photophoresis of a moderately large evaporating highly viscous droplet in a binary gas mixture.

A theoretical description of the photophoretic motion in a viscous nonisothermal binary gas mixture of a large evaporating spherical droplet with significant relative temperature differences in its vicinity is carried out in the quasi-stationary approximation for small Reynolds and Pecle numbers. When describing the properties of a gaseous medium, a power-law type of dependence of the coefficients of molecular transport (viscosity, diffusion and thermal conductivity) and density on temperature was taken into account. Numerical estimates have shown the nonlinear nature of the dependence of the photophoretic force and velocity on the average temperature of the droplet surface.

For the first time, in the quasi-stationary Stokes approximation at low Reynolds and Peclet numbers, a theory has been constructed that takes into account the effect of convective heat transfer on the photophoresis of a heated large spherical aerosol particle using the method of matched asymptotic expansions. When solving gasdynamics equations, the power-law form of the dependences of the molecular transfer coefficients (viscosity, thermal conductivity) and density of the gaseous medium on temperature is taken into account.

Approximate solutions of stationary diffusion and thermal conductivity equations are obtained for the power-law dependence of the molecular transfer coefficients (thermal conductivity, diffusion) and the density of a binary viscous non-isothermal gas medium on temperature.

An approximate solution of a boundary value problem for the convective heat transfer equation is obtained by the method of matched asymptotic expansions for small Péclet and Reynolds numbers. When solving the stationary system of gasdynamic heat transfer equations including the system of Navier–Stokes equations linearized in the velocity, the convective heat transfer equation, and the Poisson equation, it is assumed that the temperature dependences of the viscosity, thermal conductivity, and density of a gaseous medium are power-law.

This paper describes a theoretical study of the steady motion of a large solid nonvolatile aerosol spherical particle, which contains thermal sources within itself, in a concentration gradient of binary gas mixture components. It is assumed that an average particle surface temperature significantly differs from the temperature of the binary gas mixture surrounding it. Equations of gas dynamics are solved taking into account the power-law dependence of the molecular transfer coefficients (viscosity, thermal conductivity, and diffusion) and the density of the gaseous medium on temperature. Under boundary conditions, diffusion and thermal slip are taken into account. Numerical estimates show that the diffusion and photophoretic forces and velocity substantially depend on the average particle surface temperature.

AbstractA theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

In the article, a motion of a large solid spherical aerosol particle in a single-component gas has been investigated. Mathematical modeling has been performed The obtained formulas allow determining the time of the particle transition into the final states, and also the distances travelled by the particle. The numerical evaluations solved with the use of these formulas demonstrate that for large initial Reynolds numbers the particle stopping distance can be significant. considering inertia, particle radius and resistance of the carrier gaseous medium to its motion.

A theory of photo- and thermophoresis of a heated medium-size spherical aerosol particle is proposed in the quasi-stationary Stokes approximation at relatively small Reynolds and Peclet numbers. Gas-dynamic equations are solved with allowance for power dependences of the molecular transport (viscosity and thermal conductivity) coefficients and density of the gas medium on temperature. Boundary conditions take into account effects that are linear with respect to the Knudsen number. Expressions for the total force and velocity are derived. It is shown than the above effects may substantially affect the motion of a heated particle.

Assuming that the fluid viscosity is an exponential-power function of temperature, a boundary value problem for the Navier–Stokes equations linearized with respect to velocity is solved and the uniqueness of the solution is proved. The problem of a nonuniformly heated spherical solid particle settling in fluid is considered as an application.

In the Stokes approximation at small Reynolds and Peclet numbers, we obtain a solution to the boundary-value problem of flow around of particles of spherical shape for stationary system of equations of a viscous non-isothermal fluid comprising a linearized by speed Navier–Stokes equation system and the equation of heat transfer given an exponential-power law of dependence of viscosity of fluid on temperature.

We obtain an analytical solution of a boundary value problem for a viscous incompressible nonisothermal fluid assuming an exponential–power law dependence of the fluid viscosity on temperature. A uniqueness theorem for the Navier–Stokes equation linearized with respect to the velocity is proved. We obtain expressions for the mass velocity components and pressure. The solution of the boundary value problem is sought in the form of an expansion in Legendre polynomials.

We obtain a solution to a boundary-value problem of a flow of spherical form particle for stationary system of equations of viscous non-isothermal gaseous medium including the Stokes equation, heat conductivity equation, and state equation with account taken of dependence of viscosity, heat conductivity, and density of gaseous medium on temperature.

The stationary motion of a large spherical aerosol particle in the external field of a temperature gradient in zero gravity is theoretically described using the Stokes approximation and the assumption that the average temperature of the particle surface differs considerably from the temperature of the surrounding gaseous medium. The gas dynamics equations are solved taking into account the power-law temperature dependence of the molecular transport coefficients (viscosity, thermal conductivity) and the density of the gaseous medium. Numerical estimates show that the dependence of the thermophoretic force and velocity on the average temperature of the particle surface is nonlinear.