Electrohydrodynamics of thin double layers: a model for the streaming potential profile

• Published in: Journal of colloid and interface science Vol. 154; no. 1; pp. 87 - 96
• Main Authors: Bike, S.G, Prieve, D.C
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.11.1992; Elsevier
• Subjects: Chemistry; Exact sciences and technology; General and physical chemistry; Solution properties; Solutions; Surface charge; Ion mobility; Electrolyte solution; Flow(fluid); Reynolds number; Theoretical study; Hydrodynamics; Convection
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/0021-9797(92)90080-6

The motion of an electrolyte solution past a charged surface gives rise to convection of the ions within the double layer surrounding the surface. To conserve charge a streaming potential arises, generating an electrokinetic force on the surface. We have previously calculated this force in the lubrication limit for two bodies bearing thin, equilibrium double layers and moving slowly relative to each other; for this case, the streaming potential satisfies an equation analogous to Reynolds equation for the pressure. In this paper, we relax the lubrication approximation and address the electrohydrodynamics of thin double layers with regard to the streaming potential profile. Outside the double layer, the streaming potential satisfies Laplace's equation. We have developed a boundary condition for the streaming potential from the requirement of charge conservation at the outer edge of the double layer despite nonuniform convection inside the double layer. In particular, at the outer edge of the double layer the normal derivative of the streaming potential is directly proportional to the normal derivative of pressure profile generated by motion. We illustrate the solution of Laplace's equation using this boundary condition by calculating the dipole moment generated by a charged sphere sedimenting in an unbounded electrolyte solution (the Dorn effect) and the electrokinetic lift force on a charged sphere translating parallel to a distant wall.