| Popis: |
A mathematical model describing gravitational concentration convection under isotachophoresis, a method of separating a multicomponent mixture into individual components using an external electric field, is constructed. In the final stage of the isotachophoresis process, the mixture is divided into separate components, forming spatial zones whose boundaries move at the same velocity. The concentrations of substances in the zones are almost everywhere constant except in the small vicinity of the boundaries. In the process of separation, there is a strong spatial stratification of the liquid density. In the gravitational field, convective instability may occur, which can lead to the destruction of the boundary between the zones and the mixing of the separated components, reducing the resolution of the method. The convective mixing problem is reduced to finding critical values of parameters – characteristic of the diffusion coefficient, mobilities, concentration etc. Due to the fact that the size of individual zones, usually much more than the width of the boundary between the zones, it is sufficient to only study problem in the vicinity of the boundary between the two any zones. The exact formulation of the problem of hydrodynamic stability is proposed to replace the asymptotic model, the main features of which are as follows. First, the problem on the infinite axis is replaced by a problem in the domain in which the component concentrations differ significantly from the constants. Secondly, the transport mass equations are replaced by their analogues, which are valid in the vicinity of the boundary. In particular, the latter assumption allows us to replace the real distributions of the concentration of substances in the vicinity of the boundary, described by the Lerch function, by linear distributions. |
