In-Situ Volume-Change Properties by Electro-Osmosis - Theory

Uncoupling electrokinetic flow solutions

“…We present an approach for exactly solving certain fully coupled electrokinetic problems, which should also be applicable to other coupled physics problems with symmetric governing equations and boundary conditions. As was shown in the examples, these problems can already be solved using fully coupled numerical models (e.g., Figure 4) or sometimes approximately using analytical solutions with only oneway coupling (Banerjee and Mitchell 1980, Shapiro and Probstein 1993, Reppert and Morgan 2002, Malama et al 2009ab, Malama 2014). The uncoupling approach presented here allows solving the fully coupled problem (i.e., considering both streaming potential and electroosmosis) using simpler numerical or analytical models as computational building blocks.…”

“…Writing the governing equations in the one-way coupled form (i.e., including effects of streaming potential, but not including electroosmosis -or vice-versa) results in a degenerate system of equations which cannot be decoupled using the eigenvalue approach. This oneway coupling approach, although common (Casagrande 1949, Banerjee and Mitchell 1980, Malama et al 2009ab) and approximately correct, is physically inconsistent. Since thermodynamics requires L 12 = L 21 , setting only one of these coefficients to zero breaks the symmetry identified by Onsager (1931a;b).…”

“…Electroosmosis is utilized widely in microfluidics (Karniadakis et al 2005) and at the pore scale (Coelho et al 1996, Gupta et al 2008 to move fluids through small pores. At the laboratory and field scale it has been used to consolidate soft clays (Banerjee and Mitchell 1980, Banerjee and Vitayasupakorn 1984, Lo et al 1991, Alshawabkeh et al 2004 or mobilize contaminants (Bruell et al 1992, Acar et al 1993, Shapiro and Probstein 1993, Acar and Alshawabkeh 1996, Virkutyte et al 2002, Bertolini et al 2009. Seismoelectric applications consider the electrokinetic response of a porous formation to seismic waves (Pride 1994, Haines and Pride 2006, Revil et al 2015, Peng et al 2019.…”

“…For example, typical streaming potential solutions use the existing solution for flow to a well (ignoring electroosmotic effects) as a source term in the electrical conduction equation (Malama et al 2009a;b, Malama 2014). A typical electroosmosis solution uses the existing solutions for electrical conduction around an electrode (ignoring streaming potential effects) as a source term in the flow equation (Banerjee and Mitchell 1980, Shapiro and Probstein 1993, Reppert and Morgan 2002. Few fully coupled porous-media scale electrokinetic solutions exist; showed under simplified laboratory conditions independent measurement of electroosmotic pressure and streaming potentials can be used to estimate the permeability of porous materials.…”