A note on the streaming potential method for measuring surface potentials

Due to the fact that the classical analysis of the streaming potential method for measuring surface potential is somewhat crude, the problem was analyzed by applying the fundamental principles of electrochemistry. It was found that the classical Helmholz-Smoluchowski equation is valid provided that the duct is long and narrow, in which case the potential in the bulk is uniform over the duct's cross-sectional area and varies linearly over its length.In order to follow how the surface potential of a filter varies with time, investigators have measured the streaming potential across the filter's length as well as across segments of the filter. The problem is what do such measurements mean and do the classical equations apply. It was found that the classical result is expressible in differential form from which it followed that the streaming potential over any section of the filter gives a measure of the average surface potential of that section. This is an important result because it shows that the surface potential profile of a filter can be determined from measurements of the streaming potential profile across the filter.