Photophoresis of a moderately large high-viscosity droplet in slip mode

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 radiation

Methods. 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.

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