Стационарная вращательно-симметричная конвекция при изотахофорезе в круговой цилиндрической области с недеформируемой свободной непроницаемой боковой поверхностью

Abstract

The results of a study of the isotachophoresis process convective stability are presented. Isotachophoresis is the method of separation of a multicomponent mixture to individual components by an external electric field. It is assumed that the process of isotachophoresis occur in an infinite vertical circular cylinder with free side boundaries. The problem of the stationary (monotonic, neutral) concentration gravitational convection occurrence is transform to the study of the solution stability for the problem linearized on the solution of the original problem corresponding to the mechanical equilibrium of the final stage of the isotachophoresis process, in which the zones of the individual components of the mixture move with the identical constant velocity in a stationary flow. It is indicated that the main contribution to the stability/instability of the equilibrium is made by concentration gradients in the vicinity of the boundaries between the zones of individual components. Due to the complexity of constructing an exact solution corresponding to mechanical equilibrium, the exact solution replaced by an asymptotic solution (piecewise constant concentration distribution), which, in turn, is an exact solution of the asymptotic version of the transport under action of an electric field component equations (diffusion-free model). The choice of piecewise constant mechanical equilibrium leads to concentration gradients in the form of delta functions and a linear boundary value problem with delta-like coefficients to determine the critical parameters of instability. An exact solution of the problem (a system of ordinary differential equations with boundary conditions) and, using the method of one-dimensional perturbations, an exact dispersion relation for determining critical parameters (in the case of vanishingly small diffusion) is constructed.