Electrosmosis between plane parallel walls produced by high-frequency alternating currents

Abstract

The problem of the motion, under the influence of high-frequency alter­nating currents, of fluid between plane parallel walls whose distance apart is very small, appears to be of interest in certain branches of Physical Chemistry. The following paper contains a mathematical treatment of this type of motion under certain specified conditions. We are greatly indebted to Mr. J. J. Bikerman of the Chemistry Department of the University of Manchester for having brought the problem to our notice, and for having given us a great deal of information concerning the physics of the phenomena involved. In general, when two different substances, or phases, have a common surface, there is an electrokinetic potential difference between them. This is produced by an electric double layer of ions in contact with the common surface. Consider the boundary between a solid and an electrolyte, and let us assume the solid to take a negative charge, as is almost invariably the case when the electrolyte is water or a very dilute aqueous solution. The negative layer consists, probably, of ions adsorbed rigidly to the surface. Near the surface, in the fluid, there will be a preponderance of positively charged ions held more or less firmly in position by electrostatic forces. Very close to the “rigid” layer of negative ions the electrostatic forces will be sufficiently great to keep the positive ions rigidly in place. As we leave the solid surface the forces diminish and ultimately a position is reached where diffusion and thermal forces overcome the electrostatic forces. Beyond this surface in the fluid there will still be a preponderance of positive ions, since the electrostatic forces will still be operative, but these ions will be mobile. At points remote from the solid surface there are approximately equal concentrations of positive and negative ions, and the liquid as a whole is electrically neutral. The equilibrium attained when electrostatic and diffusion forces are operating was first calculated by Gouy; the expression given by Gouy for the charge density is used in this paper. On applying an electric field the mobile ions in the layer near the surface begin to move towards one or other of the two electrodes as illustrated diagramatically in fig. 1, and this motion is transmitted to the liquid as a whole through the operation of viscous forces. As the fluid close to the walls contains more positive ions than negative ions greater forces will be called into play near the walls than in the body of the fluid, and, in a constant field, the liquid will move to the cathode. This phenomenon of the movement of a liquid over a fixed surface under the influence of an applied electric field is called “electrosmosis” or “endosmosis”.