The nonlinear electromigration of analytes into confined spaces

Zhen Chen, Sandip Ghosal*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider the problem of electromigration of a sample ion (analyte) within a uniform background electrolyte when the confining channel undergoes a sudden contraction. One example of such a situation arises in microfluidics in the electrokinetic injection of the analyte into a micro-capillary from a reservoir of much larger size. Here, the sample concentration propagates as a wavedriven by the electric field. The dynamics is governed by the Nerst-Planck-Poisson system of equations for ionic transport. A reduced one-dimensional nonlinear equation, describing the evolution of the sample concentration, is derived. We integrate this equation numerically to obtain the evolution of the wave shape and determine how the injected mass depends on the sample concentration in the reservoir. It is shown that due to the nonlinear coupling of the ionic concentrations and the electric field, the concentration of the injected sample could be substantially less than the concentration of the sample in the reservoir.

Original languageEnglish (US)
Pages (from-to)3139-3152
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2146
StatePublished - Oct 8 2012


  • Electrokinetic injection
  • Electromigration dispersion
  • Nonlinearwaves

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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