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The electroosmotic flow plays an important role in electrokinetic phenomena, in particular, in the flow of an electrolyte solution in a microchannel, where the electrokinetic equations need to be solved. In general, theseequations are coupled, nonlinear partial differential equations, and solving them analytically is nontrivial. In this study the electrokinetic equations are solved analytically for the case of a general electrolyte solution flow through a planar slit comprising two planar, parallel surfaces, which can have different charged conditions, and the influences of the key parameters on the flow behavior are discussed. Several interesting phenomena are observed. For example, the absolute value of the mean fluid velocity may exhibit an undulant behavior as the bulk concentration of counterions varies. Also, if both the valence of coions and the bulk concentration of counterions are fixed, then depending upon the level of the latter the absolute value of the mean fluid velocity may have a local maximum or local minimum as the valence of counterions varies.

The critical coagulation concentration of a colloidal dispersion for the case of a general electrolyte solution is estimated under the conditions of constant surface potential. By combination of the Langmuir approximation and the Debye−Huckel approximation, explicit expressions for the electrical potential, the osmotic pressure, and the electrical energy are derived, and the results are used to estimate the critical coagulation concentration of ionic species. The influence of the valence of ionic species on this concentration is discussed. We show that the Schultz−Hardy rule is invalid, in general, and that the effect of co-ions can be too large to be ignored.

The electrical interaction between two planar, parallel dissimilar surfaces, which may have different charged conditions arising from different ion-adsorption mechanisms, in an arbitrary electrolytic solution is investigated theoretically. The electrical interaction force and the interaction energy between these surfaces are evaluated, and analytical expressions for various charged conditions under the Debye-Huckel condition are derived. In general, assuming constant surface potential and assuming constant surface charge density lead respectively to the lower and the upper bounds in the electrical interaction energy between two surfaces. We show that assuming a linear relation between surface potential and surface charge density under the Debye-Huckel condition, as is often done in the literature, is appropriate for two planar parallel surfaces only but becomes inadequate for other orientations or nonplanar surfaces. The present approach does not have this limitation.