One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

Gabitto, Jorge; Tsouris, Costas

doi:10.3390/colloids2010004

Title: One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

Abstract

Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transport equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.

Authors:

Gabitto, Jorge ^[1];

^[2]

Prairie View A&M Univ., Prairie View, TX (United State). Dept. of Chemical Engineering
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: 2018-01-19

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1422528

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Colloids and Interfaces

Additional Journal Information:: Journal Volume: 2; Journal Issue: 1; Journal ID: ISSN 2504-5377

Country of Publication:: United States

Language:: English

Subject:: 25 ENERGY STORAGE; 36 MATERIALS SCIENCE; CDI; volume average; porous media; two-equation models

Citation Formats


                    Gabitto, Jorge, and Tsouris, Costas. One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes.  United States: N. p., 2018. 
Web.  doi:10.3390/colloids2010004.

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                    Gabitto, Jorge, & Tsouris, Costas. One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes.  United States.  https://doi.org/10.3390/colloids2010004

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                    Gabitto, Jorge, and Tsouris, Costas. Fri .  
"One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes".  United States.  https://doi.org/10.3390/colloids2010004.  https://www.osti.gov/servlets/purl/1422528.

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@article{osti_1422528,

  title        = {One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes},

  author       = {Gabitto, Jorge and Tsouris, Costas},

  abstractNote = {Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transport equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.},

  doi          = {10.3390/colloids2010004},

  journal      = {Colloids and Interfaces},

  number       = 1,

  volume       = 2,

  place        = {United States},

  year         = {2018},

  month        = {1}

}

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Similar Records

Title: One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

Abstract

Citation Formats

Local thermal equilibrium: An application to packed bed catalytic reactor design journal, January 1986

Modeling the Capacitive Deionization Process in Dual-Porosity Electrodes journal, April 2016

Transport in chemically and mechanically heterogeneous porous media IV: large-scale mass equilibrium for solute transport with adsorption journal, September 1998

Effective diffusion and conduction in two-phase media: A unified approach journal, September 1983

Diffuse charge and Faradaic reactions in porous electrodes journal, June 2011

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Improved constraints for the principle of local thermal equilibrium journal, May 1991

The modelling of a textile dyeing process utilizing the method of volume averaging journal, October 2003

Volume Averaging Study of the Capacitive Deionization Process in Homogeneous Porous Media journal, May 2015

Dispersion in pulsed systems—II journal, January 1983

Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments journal, October 1995

Bulk and surface diffusion in porous media: An application of the surface-averaging theorem journal, January 1993

Desalting by Means of Porous Carbon Electrodes journal, January 1971

Nonlinear dynamics of capacitive charging and desalination by porous electrodes journal, March 2010

Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes journal, June 2012

Diffusive mass transfer between a microporous medium and an homogeneous fluid: Jump boundary conditions journal, March 2006

On the theorems for local volume averaging of multiphase systems journal, June 1977

Mesoporous Carbon for Capacitive Deionization of Saline Water journal, December 2011

Heat conduction in multiphase systems—I journal, January 1985

Multi-Scale Analysis of Effective Transport in Periodic Heterogeneous Media journal, April 1982

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes text, January 2009

Attractive forces in microporous carbon electrodes for capacitive deionization preprint, January 2013

Local thermal equilibrium: An application to packed bed catalytic reactor design
journal, January 1986

Modeling the Capacitive Deionization Process in Dual-Porosity Electrodes
journal, April 2016

Transport in chemically and mechanically heterogeneous porous media IV: large-scale mass equilibrium for solute transport with adsorption
journal, September 1998

Effective diffusion and conduction in two-phase media: A unified approach
journal, September 1983

Diffuse charge and Faradaic reactions in porous electrodes
journal, June 2011

Attractive forces in microporous carbon electrodes for capacitive deionization
journal, February 2014

Improved constraints for the principle of local thermal equilibrium
journal, May 1991

The modelling of a textile dyeing process utilizing the method of volume averaging
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journal, May 2015

Dispersion in pulsed systems—II
journal, January 1983

Local thermal equilibrium for transient heat conduction: theory and comparison with numerical experiments
journal, October 1995

Bulk and surface diffusion in porous media: An application of the surface-averaging theorem
journal, January 1993

Desalting by Means of Porous Carbon Electrodes
journal, January 1971

Nonlinear dynamics of capacitive charging and desalination by porous electrodes
journal, March 2010

Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes
journal, June 2012

Diffusive mass transfer between a microporous medium and an homogeneous fluid: Jump boundary conditions
journal, March 2006

On the theorems for local volume averaging of multiphase systems
journal, June 1977

Mesoporous Carbon for Capacitive Deionization of Saline Water
journal, December 2011

Heat conduction in multiphase systems—I
journal, January 1985

Multi-Scale Analysis of Effective Transport in Periodic Heterogeneous Media
journal, April 1982

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes
text, January 2009

Attractive forces in microporous carbon electrodes for capacitive deionization
preprint, January 2013