Electrostatic interaction of two charged spheroidal macroparticles is analyzed within the linearized Poisson-Botzmann model.Interparticle forces are calculated through finite-element method in the regimes of weak and moderate screening with constant surface potentials in the absence of external field. Keywords: linearized Poisson-Botzmann model, two charged macroparticles, spheroidal macroparticles, colloidal particles, dusty plasmas.

The Poisson–Boltzmann equation has been employed to consider the electrostatic interaction between two charged dielectric spherical particles in a solution of a symmetric electrolyte. The interaction forces between the particles of the same radius have been calculated by the finite element method under the condition of uniform charge distribution on their surfaces in the absence of an external field. The dependence of the electrostatic repulsion forces between the particles on the magnitude of the particle charges and the dielectric permittivities of the particle materials and the ambient medium has been analyzed.

The finite-element method has been employed to calculate the photophoresis velocity of solid aerosol particles, the sizes of which are much larger than the mean free path of molecules in a gas. The thermal electromagnetic radiation from the particle surface and the temperature dependences of the density, viscosity, and thermal conductivity of the gaseous medium and particle material have been taken into account. The photophoresis velocity has been numerically calculated for a number of axially symmetric particles moving along their rotation axes. Cylindrical particles, particles having a shape resulting from rhomb rotation around one of its diagonals, and spheroidal particles have been considered.

Еlectrostatic interaction of two charged spheroidal macroparticles is analyzed within the linearized Poisson–Botzmann model.Interparticle forces are calculated through finite-element method in the regimes of weak and moderate screening with constant surface potentials in the absence of external field.

Application of finite element method for calculation of electrostatic interaction force of two conducting bodies of spheroidal shape with preset charges on their surfaces in zero external field is considered.

The application of the discontinuous Galerkin method for calculating the temperature distribution in a solid-gas system is considered. Analysis is carried out with regard to a temperature jump at the gas-solid interface and the thermal conductivities of the solid and gas. The corresponding variant of the weak form of the Poisson equation is obtained.

The thermophoretic motion of a solid spherical aerosol particle directed normally to an infinite planar solid surface is analyzed. The solution is performed in a bispherical coordinate system with allowance for linear corrections in the Knudsen number. The finite thermal conductivity of a solid body is taken into account in the analysis.

The thermocapillary motion of a liquid drop immersed into another liquid near an infinite plane interface between two liquids is theoretically analyzed. The motion is considered under the conditions of a constant temperature gradient normal to the interface at infinity and small Reynolds and Peclet numbers. The problem is solved in bispherical coordinates. The analysis takes into consideration the thermal conductivity of the liquids and the thermocapillary motion of the liquids due to a nonuniform temperature distribution over the plane interface.

A problem concerning the free evaporation or condensation growth of a droplet near an infinite planar surface of the same liquid is solved. The behavior of the droplet is considered at vapor temperature and concentration gradients preset at an infinite distance from it. The boundary conditions take into account effects that are linear with respect to the Knudsen number. Equations are derived for the rate of variations in the radius of the droplet and the velocity of its steady motion induced by nonuniform temperature and concentration of the vapor. Dependences of the rate of variations in the radius and the velocity of the steady motion of the droplet on the distance from the planar surface are presented for a droplet 1 μm in radius suspended in air.

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.

The hydrodynamic interactions of freely evaporating or growing droplet (suspended in gaseous medium) in the supersaturated vapor with the droplet of nonvolatile substance or spherical solid particle are theoretically studied with allowance for effects that are linear with respect to the Knudsen number. The process of interaction between the volatile droplet and the infinite plane surface of nonvolatile liquid or solid is considered as a limiting case. Numerical estimates of the velocities of the steady motion of evaporating droplets of water and castor oil are reported. For the droplet of water and spherical solid particle, the effect of the heat conductivity of the latter on the velocity of particle motion is considered. Analogous estimates are obtained for a water droplet that evaporates near the infinite solid surface of castor oil or solid. The effects of the droplet size and the heat conductivity of wall on the rate of the evaporation of water droplet are analyzed.

A compact solution is obtained to the problem on the force of interaction between two conducting spheres with preset charges on their surfaces in zero external field. The derivation is based on exact solution of the problem of the potential distribution in the bispherical coordinate system. The expression for the force was derived by differentiating the potential energy of interaction between the spheres with respect to the distance between their centers. It is shown using numerical calculations that with decreasing distance between the spheres, the ratio of their charges for which the forces of interaction between the charges are zero tends to the ratio of the charges of contacting spheres. It follows hence that for any ratio of charges of the same polarity, which differs from the ratio of charges of the contacting spheres, there always exists a small distance between the spheres, at which they attract each other.

The pairwise hydrodynamic and electrostatic interaction between micrometer-sized water droplets at small distances between them due to their evaporation and the presence of an electric charge on at least one of them is considered. The velocities of the steady-state motion of charged water drops with radii of 1 and 10 µm evaporating in air are calculated. It is shown that at small distances between the drops the joint action of hydrodynamic attraction and polarization interaction, always of attraction type, favor the coalescence of the drops (or drops and solid particles), leading to the displacement of the maximum of the function of drop distribution over size to the region of greater sizes and the gravity sedimentation of large drops. At large distances between the drops, when the short-distance hydrodynamic and polarization attractive forces become smaller than the long-distance Coulomb repulsion forces between likely charged particles, this distance tends to increase. These phenomena give a microphysical explanation to the phenomenon of electrostatic blooming in optically dense smokes and mists.

The hydrodynamic interaction of a freely evaporating (or growing in a supersaturated solution) drop suspended in a gaseous medium with an infinitely large surface of a liquid or a solid is studied theoretically taking into account the effects linear in the Knudsen number. The results of numerical calculations of the velocity of a steady-state motion of a water drop evaporating or growing in air are considered. According to these results, the drop can move either to the wall or away from it. The direction of motion depends on the drop radius, the distance between the wall and the drop, and the thermal conductivity of the wall material.

The problem of the free evaporation of a droplet of moderately large size occurring near an infinite flat wall is solved. The cases in which the wall surface is impenetrable to an evaporating substance and vapor concentration remains unchanged at the surface are considered. The temperature of the wall surface is assumed to be constant and equal to the gas temperature at a large distance from the droplet. A set of algebraic equations is derived for molecular fluxes and the temperature and the concentration of gaseous components. Dependences of the evaporation rate of a water droplet suspended in air on its radius and distance from a wall are determined.

The effect of quadratic (in the Knudsen number) corrections to the motion of two interacting drops of the same size and of the same liquid due to their evaporation is estimated on the basis of an original modification of the approximate hydrodynamic reflection method and its generalization to thermal and diffusion fields. It is shown that the dependence of the velocity of thermophoretic motion of the drops on their spacing is virtually independent on the physicochemical characteristics of the liquid except for the evaporation heat. The conditions under which the corrections in the Knudsen number noticeably affect this dependence are determined.