Diffusioosmosis of electrolyte solutions in a capillary slit with surface charge layers

The steady diffusioosmotic flow of an electrolyte solution in a fine capillary slit with each of its inside walls covered by a layer of adsorbed polyelectrolytes is analytically studied. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to distribute at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The Debye–Huckel approximation is used to obtain the electrostatic potential distribution on a cross section of the slit. The macroscopic electric field induced by the imposed electrolyte concentration gradient through the slit is determined as a function of the lateral position rather than taken as its constant bulk-phase quantity. Explicit formulas for the fluid velocity profile are derived as the solution of a modified Navier–Stokes/Brinkman equation. The effect of the lateral distribution of the induced axial electric field in the slit on the diffusioosmotic flow is found to be of dominant significance in most practical situations and to drive the fluid towards the end of higher electrolyte concentration. The existence of the surface charge layers can lead to a quite different diffusioosmotic flow from that in a capillary with bare walls.