Divergence of Velocity Fields in Electrochemical Systems: Article No. 070535

Nitash Balsara, John Newman

Research output: Contribution to journalArticlepeer-review

5 Scopus Citations


The passage of current through electrochemical systems results in the development of concentration gradients in the electrolytic phase that can be modeled using concentrated solution theory. Application of this theory requires knowledge of three concentration-dependent transport coefficients, which are often taken to be conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity. The governing diffusion equation for molar concentration contains two additional terms - the thermodynamic factor which is related to activity of the electrolytic species and the solvent velocity. The main advance in this paper is the derivation of an expression for the divergence of the solvent velocity. Solving this equation requires knowledge of the partial molar volume of the electrolyte. Analogous expressions are derived for the mass average and molar average velocities. These velocities occur naturally in the diffusion equation if concentration is expressed as weight fraction and mole fraction of the electrolytic species, respectively.
Original languageAmerican English
Number of pages3
JournalJournal of the Electrochemical Society
Issue number7
StatePublished - 2022

NREL Publication Number

  • NREL/JA-5700-84105


  • diffusion
  • molar ratio
  • partial differential equations
  • solvents
  • velocity


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