Analytical study of the velocity and pressure of the electrovortex flow in hemispherical bowl in a Stokes approximation

Abstract

Abstract The problem of an electrovortex flow in a hemispherical bowl with an internal electrode is considered. In the framework of the Stokes approximation, analytical expressions for the velocity and pressure fields are obtained. Two types of boundary conditions were used: non-leakage on the entire boundary (with no-slip condition on the free surface and partly slip on the electrodes) and an approximate adhesion condition on the electrodes. The non-leakage condition corresponds to the homogeneous Dirichlet boundary condition for the vector potential and the vorticity on the entire boundary. An approximate adhesion condition is posed using the Thom difference approximation. The analytical expressions for the velocity and pressure fields are written uniformly for both types of boundary conditions.