Analysis of the electroconvective dissolution of a conducting solid sphere in a current-carrying liquid

A. I. Raichenko , A. A. Raichenko , E. S. Chernikova , A. A. Miroshnichenko

Abstract
The process of dissolution of a solid spherical inclusion in a conducting liquid carrying dirrect electric current has been investigated. All possible versions of conductivity of the solid inclusion (from the insulator to superconductor) have been considered. The normalized rate of dissolution (Sherwood number) caused by an electroconvective diffusion is a function of two arguments, R⁴μ₀μ_eJ₀²/(νD) (R is the inclusion radius, μ₀ (relative) permeability, J_0 the current density, viscosity, D diffusivity) and _i/_e (where lambda_i and λ_e are the conductivities of the inclusion and the liquid, respectively). For example, the Sherwood number at dissolution of an inclusion of WC in liquid Co at 1300°C and J₀ ≈ 10¹⁰ A/m2 is approximately 2. Figs. 4, tab. 1, refs 11.