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Fig. 2. (a, c, e) Schematic view of polarizing cells based on the granular model and (b, d, f) equivalent pore sketches for dense (right) and loose (left) packings of particles at different water content: (a, b) full saturation, (c–f) partial saturation. Gray and white areas indicate water and particles, respectively. In the saturated case (a, b), water-filling intergrain spaces can be considered large pores. Areas of grain contact, where the water is in a closer bond on the grain surface, can be considered throats. In the partially saturated case (c, d), the water film at the surface of moistened grains can be considered a narrow passageway for electric current (throats). Areas of grain contact, where water is more abundant because of surface tension (water "rings"), can be viewed as large passageways (similar to large pores in the saturated case). With further desaturation, cells continuously loose water from the grain contact area and both thickness and diameter of the water rings decrease (e, f).
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, ß, and 
denote solid phase, Helmholtz layer, and diffuse layer, respectively. (b) Schematic distribution of cation (Cc) and anion (Ca) concentrations in the EDL; C0 is the equilibrium ion concentration outside the EDL. (c) Excess and deficiency in ion concentration around a polarized charged spherical particle; dotted arrows indicate the local diffusion flows represented by both cations and anions, dashed arrows show the local diffusion flows near the solid surface mostly represented by cations, solid arrow shows the electric field direction. (d) Excess and deficiency in ion concentration along a polarized throat; diffusion flows and electric field same as in Part c. (e) Schematic distribution of the ion concentration around a polarized spherical particle or along a polarized pore throat; C* denotes the excess concentration produced by the polarizing electric field.
denotes the Debye length. Symbolic graphs of ion concentrations illustrate excess of cations and deficiency of anions in the electrical double layer (EDL) relative to the equilibrium concentration C0. The integrals of cation excess and anion deficiency over the slit aperture represent the effective charges of cations (
1 potential of 0.1 V. The difference in cation transparency strongly increases when a2/a1 is in the region between 3 and 30. Lower graphs, corresponding to a narrow slit with an aperture 1000 and 10000 times larger than the Debye length, can be attributed to saturated cells (Fig. 1a and 1b). Upper graphs, corresponding to a narrow slit with an aperture 10 and 100 times larger than the Debye length, can be attributed to unsaturated cells (Fig. 1c–1f).
