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Title: Uncoupling Electrokinetic Flow Solutions

Abstract

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. California Polytechnic State Univ. (CalPoly), San Luis Obispo, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1670757
Report Number(s):
SAND2020-8295J
Journal ID: ISSN 1874-8961; 689866
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Mathematical Geosciences
Additional Journal Information:
Journal Name: Mathematical Geosciences; Journal ID: ISSN 1874-8961
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES

Citation Formats

Kuhlman, Kristopher L., and Malama, Bwalya. Uncoupling Electrokinetic Flow Solutions. United States: N. p., 2020. Web. doi:10.1007/s11004-020-09889-8.
Kuhlman, Kristopher L., & Malama, Bwalya. Uncoupling Electrokinetic Flow Solutions. United States. doi:10.1007/s11004-020-09889-8.
Kuhlman, Kristopher L., and Malama, Bwalya. Tue . "Uncoupling Electrokinetic Flow Solutions". United States. doi:10.1007/s11004-020-09889-8.
@article{osti_1670757,
title = {Uncoupling Electrokinetic Flow Solutions},
author = {Kuhlman, Kristopher L. and Malama, Bwalya},
abstractNote = {The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.},
doi = {10.1007/s11004-020-09889-8},
journal = {Mathematical Geosciences},
issn = {1874-8961},
number = ,
volume = ,
place = {United States},
year = {2020},
month = {9}
}

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