Theory of solitary waves in electrophoresis

A theoretical study about the generation of solitary waves (SW) in electrophoresis and capillary electrophoresis is performed. Two models that use velocity terms in Fick's first law and absorption and decaying terms in Fick's second law are presented. These models give the time evolution of the band or zone shape in electrophoresis and capillary electrophoresis in the presence of electromagnetic radiation. In particular, the effect of electrophoretic mobility changes of the analytes due to radiation excitation is included in the present models. The analytes are represented either by three-level or four-level systems. It is shown that the resulting system of coupled nonlinear partial differential equations governing the spatial motion of these bands over time exhibits SW solutions for some values of the equation parameters. We analyze the conditions in which these SWs, which propagate with constant velocity, constant area, constant standard deviation, and without change of form, are generated. The results of the present models are compared with those from a previous two-level model (Phys. Rev. Lett. 1995, 75, 1210-1213). The velocities of these SWs are calculated analytically. The time evolution of their standard deviations is shown. The numerical integration of a two-component electrophoresis run shows higher resolutions under some conditions. The expected practical difficulties which may be encountered when observing this phenomenon are discussed. Some practical difficulties that are likely to limit its useful application in electrophoresis and capillary electrophoresis are mentioned.