Streaming Potential near a Rotating Porous Disk

Theory and experimental results for the streaming potential measured in the vicinity of a rotating porous disk-shaped sample are described. Rotation of the sample on its axis draws liquid into its face and casts it from the periphery. Advection within the sample engenders streaming current and streaming potential that are proportional to the zeta potential and the disk’s major dimensions. When Darcy’s law applies, the streaming potential is proportional to the square of the rotation at low rate but becomes invariant with rotation at high rate. The streaming potential is invariant with the sample’s permeability at low rate and is proportional to the inverse square of the permeability at high rate. These predictions were tested by determining the zeta potential and permeability of the loop side of Velcro, a sample otherwise difficult to characterize; reasonable values of −56 mV for zeta and 8.7 × 10–9 m2 for the permeability were obtained. This approach offers the ability to determine both the zeta potential and the permeability of materials having open structures. Compressing them into a porous plug is unnecessary. As part of the development of the theory, a convenient formula for a flow-weighted volume-averaged space-charge density of the porous medium, −εζ/k, was obtained, where ε is the permittivity, ζ is the zeta potential, and k is the Darcy permeability. The formula is correct when Smoluchowski’s equation and Darcy’s law are both valid.