On the Validity of the “Thin” and “Thick” Double-Layer Assumptions When Calculating Streaming Currents in Porous Media
Figure 1
(a) Flow velocity (solid line) and excess countecharge within a capillary, invoking the “thin” (short dashes) and “thick” (long dashes) double-layer assumption and assuming a constant excess surface charge density. The width of the “thin” double-layer has been greatly exaggerated. The excess charge on the capillary surface, and hence the total excess countercharge within the capillary, are the same for both the “thin” and “thick” double layer assumptions; the only difference between the models is the distribution of the countercharge within the capillary. (b) Calculation of the streaming current. Assuming Poiseuille flow, each cylinder of fluid of thickness travels at velocity and transports an excess charge density . The distribution of excess charge within the capillary impacts on the streaming current because excess charge at the centre of the capillary is transported more rapidly by the flow than excess charge at the margin of the capillary. Modified from Jackson [6].
