Drift-diffusion in electrochemistry: Thresholds for boundary flux and discontinuous optical generation

S. Carl*, J. W. Jerome

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider an extension of the classical drift-diffusion model, which incorporates thermodynamic switching rules for generation and boundary flux. The motivation is the important case of the splitting of water molecules upon photonic irradiation of a semiconductor electrode located in an electrochemical cell. The solid state electrode forms the spatial domain of the model. The rules are motivated by the fact that the valence band of the semiconductor, which supplies positive charge to solution, has to be located at a lower energy level than the electrochemical potential of O 2 evolution in solution, and the conduction band, which supplies electrons to solution, has to be positioned at a higher energy level than the electrochemical potential of H 2 evolution. This defines thresholds in terms of electrochemical potentials before boundary flux is activated. The optical generation rate is affected, due to the increased carrier relaxation time, when these thresholds are crossed, and may be discontinuous. We thus consider a self-consistent model, in which ‘switching’ occurs only in principal variables. The steady-state model is considered, and trapping regions are derived for the solutions.

Original languageEnglish (US)
Pages (from-to)915-931
Number of pages17
JournalInternational Journal of Phytoremediation
Issue number9
StatePublished - Sep 2004


  • 35J55
  • 35R05
  • 49J40
  • AMS Subject Classifications: 35B05
  • Discontinuous elliptic system
  • Discontinuous switching
  • Drift-diffusion
  • Semiconductor
  • System of variational inequalities
  • Trapping region

ASJC Scopus subject areas

  • Environmental Chemistry
  • Pollution
  • Plant Science


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