On the Validity of the “Thin” and “Thick” Double-Layer Assumptions When Calculating Streaming Currents in Porous Media
Figure 2
Excess charge density (Q) as a function of distance from the capillary centre (x) in a circular capillary of radius 4 nm, for a surface charge of (a) 1 mC·m−2 and (b) 50 mC·m−2. Each plot shows results for electrolyte salinities of 0.001 M and 2 M, corresponding to dimensionless capillary radii of 0.41 (i.e., towards the limit for which the thick double layer assumption is valid) and 21.6 (i.e., towards the limit for which the thin double-layer assumption is valid). Solid lines show Q obtained from a numerical solution of the Poisson-Boltzmann equation (1) in conjunction with (16); crosses show Q obtained from an analytic solution to the Poisson-Boltzmann equation assuming a thin double-layer (diagonal crosses show the Gouy-Chapman model given by (24); vertical crosses show the Debye-Hückel model given by (7)); dashed lines show constant Q assuming a thick double layer.
