Surface Conductivity

Induced Polarization of Clayey Rocks and Soils: Non‐Linear Complex Conductivity Models

“…$${\sigma }_{\mathrm{c}}^{\ast }$$ is verily what the 2D EDL (in comparison with the pore/grain, cf., Schwarz, 1962) represents itself in 3D since real‐world measurements are all conducted in 3D. Considering the solid phase is insulating except for the surface, surface conduction ( B + iλ ) Q s is equivalent to the bulk conduction of ( B + iλ ) Q v under the relationship of Q v / Q s = 2/Λ, which is absolutely accurate for a spherical grain with the radius of Λ (O'Konski, 1960) or for a cylindrical capillary tube with the internal radius of Λ (Dukhin et al., 2012), but 2/Λ = S por will become effective values for natural rocks and soils. Although $${\sigma }_{\mathrm{c}}^{\ast }$$ is extensively used by many IP practitioners (e.g., Bussian, 1983; de Lima et al., 2005; Niu, Revil, & Saidian, 2016; Revil et al., 2019), it appears that there is not a universal name of $${\sigma }_{\mathrm{c}}^{\ast }$$ in the nomenclature of IP.…”

“…If we hypothesize that (a) There is no E&EM coupling between EDL and pore water, such that they perform as two paralleled circuits; (b) There is a bodiless electrode connecting to the EDL during measurements, the bulk conductivity $${\sigma }^{\ast }$$ shall be a linear circuit model as (Dukhin et al., 2012) $$\begin{align*}{\sigma }^{\ast }=\frac{{\sigma }_{\mathrm{w}}}{F}+{\sigma }_{\mathrm{c}}^{\ast }\\ =\frac{{\sigma }_{\mathrm{w}}}{F}+\frac{2{{\Sigma }}_{\mathrm{s}}^{\ast }}{{\Lambda }}\\ =\frac{{\sigma }_{\mathrm{w}}}{F}+{{\Sigma }}_{\mathrm{s}}^{\ast }{S}_{\text{por}}\\ =\frac{{\sigma }_{\mathrm{w}}}{F}+(B+i\lambda ){Q}_{\mathrm{v}}\end{align*},$$ where the first term is Archie's law with F = ϕ − m the intrinsic formation factor, ϕ porosity and m the cementation exponent (Archie, 1942). $${\sigma }_{\mathrm{c}}^{\ast }=2{{\Sigma }}_{\mathrm{s}}^{\ast }/{\Lambda }$$ denotes the equivalent volume conductivity of the solid phase (i.e., Effective EDL conductivity) since an insulating sphere coated with a non‐thick 2D surface conductivity $${{\Sigma }}_{\mathrm{s}}^{\ast }$$ behaves just as a 3D sphere with uniform conductivity $$2{{\Sigma }}_{\mathrm{s}}^{\ast }/{\Lambda }$$ (O'Konski, 1960; Schurr, 1964), where Λ is the radius of the sphere and, for natural rocks/soils, Λ can be linked to the characteristic pore or grain size (Johnson et al., 1986).…”

“…To make Equation 1 applicable, this can be overcome with equivalent potential approaches such as Donnan equilibrium (Jougnot et al, 2009). If we hypothesize that (a) There is no E&EM coupling between EDL and pore water, such that they perform as two paralleled circuits; (b) There is a bodiless electrode connecting to the EDL during measurements, the bulk conductivity σ * shall be a linear circuit model as (Dukhin et al, 2012)…”

Температурна І Концентраційна Залежність Дзета-Потенціалу Макромолекул Альбуміну У Водно-Сольовому Розчині Згідно З Комірковою Моделлю

“…The zeta potential is the potential of a molecule located at the sliding plane. The zeta potential parameter evaluates the ability of a molecule to adjoin and transport molecules of medicinal substances, hormones, and so forth [6][7][8][9][10][11][12][13][14].…”

“…In dilute solutions, the potential distribution around an isolated macromolecule can be determined using the Debye approximation [15]. According to the result of work [14], the potential created by a molecule decreases exponentially with the distance from it. The effective thickness of the electrical layer around the albumin macromolecule is evaluated in terms of the Debye radius 𝑟 D [16,17].…”