Zone electrophoresis. Numerical-analytical method for solving of applied problems in partial derivatives of first order

Abstract

Zone electrophoresis. Numerical-analytical method for solving of applied problems in partial derivatives of first order

Zhukov M. Yu, Shiryaeva E. V., Shchitov F. A.

Incoming article date: 25.11.2015

Numerical-analytical solution of the problem of multicomponent mixture fractionation under action an electric field is constructed. This problem is known as the problem of zonal electrophoresis which extensively used in chemistry, medicine, and biology. Problem is reduced to study of the Cauchy problem for systems of hyperbolic type quasilinear equations in partial derivatives of first order. The proposed method is based on a generalized hodograph method, which allows obtaining an analytical solution of the problem in implicit form. Explicit form of the solution is recovered using the transformation of the Cauchy problem for system of quasilinear hyperbolic equations to the Cauchy problem for a system of ordinary differential equations that are solved numerically.

Keywords: electrophoresis, hyperbolic conservation laws, generalized hodograph method