Diffusioosmosis of electrolyte solutions in fine capillaries

An analytical study is presented for the diffusioosmotic flow of an electrolyte solution in a narrow capillary tube or slit caused by a constant concentration gradient imposed along the axial direction at the steady state. The electric double layer adjacent to the charged capillary wall may have an arbitrary thickness relative to the capillary radius. The electrostatic potential distribution on a cross section of the capillary is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low surface potential at the capillary wall. The macroscopic electric field induced by the imposed electrolyte concentration gradient through the capillary is determined as a function of the radial position. Closed-form formulas for the fluid velocity profile due to the combination of electroosmotic and chemiosmotic contributions are derived as the solution of a modified Navier–Stokes equation. The diffusioosmotic velocity can have more than one reversal in direction over a small range of the surface potential. For a given concentration gradient of electrolyte in a capillary, the fluid-flow rate is not necessarily to increase with an increase in the electrokinetic radius of the capillary, which is the capillary radius divided by the Debye screening length. The effect of the radial distribution of the induced axial electric field in the double layer on the diffusioosmotic flow is found to be of dominant significance in most practical situations.