Effect of Geometry on Electrokinetic Characterization of Solid Surfaces.

An analytical approach is presented to describe pressure-driven streaming current (Istr) and streaming potential (Ustr) generation in geometrically complex samples, for which the classical Helmholtz–Smoluchowski (H–S) equation is known to be inaccurate. The new approach is valid under the same prerequisite conditions that are used for the development of the H–S equation, that is, the electrical double layers (EDLs) are sufficiently thin and surface conductivity and electroviscous effects are negligible. The analytical methodology is developed using linear velocity profiles to describe liquid flow inside of EDLs and using simplifying approximations to describe macroscopic flow. At first, a general expression is obtained to describe the Istr generated in different cross sections of an arbitrarily shaped sample. Thereafter, assuming that the generated Ustr varies only along the pressure-gradient direction, an expression describing the variation of generated Ustr along the sample length is obtained. These exp...