Strongly nonlinear waves in capillary electrophoresis

TL;DR

This paper investigates strongly nonlinear wave behavior in capillary electrophoresis, revealing how high sample concentrations lead to complex wave evolution beyond weakly nonlinear models, using numerical methods for analysis.

Contribution

It extends previous weakly nonlinear theory by numerically analyzing strongly nonlinear waves in capillary electrophoresis at high concentrations.

Findings

Numerical results agree with weakly nonlinear theory at low concentrations.

High concentrations cause qualitatively different wave evolution.

Nonlinear wave behavior deviates from Burgers' equation predictions at high concentrations.

Abstract

In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.