A review is given on theories of electrokinetic phenomena in a suspension of charged colloidal particles (e.g., electrophoresis of colloidal particles in an applied electric field). A special emphasis is put on the electrophoresis theories of Smoluchowski, Hückel, Henry, and Overbeek. The roles of the particle zeta potential and the electrical double layer formed around a charged particle, the electrophoretic retardation effect, the difference between Smoluchowski’s and Hückel’s theories, and the relaxation effect are extensively discussed. Historical arguments relating to the appearance of a maximum of the electrophoretic mobility plotted as a function of the particle zeta potential are addressed. Finally, the history and present activities of the International Symposium of Electrokinetic Phenomena (ELKIN) starting in 1993 as well as the topics present in the recent symposia are reviewed.

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The electrical double layer is a well-known concept of a charged surface in an electrolyte solution. In the present article, we go back to the original history of electrokinetics to note how the concept has been established. In the first approximation, we pay attention to one dimensional plate model and discuss on the effectiveness of the DLVO theory in relation to the stability of colloidal dispersion. It is already about seventy years from the proposal of the DLVO theory and its effectiveness has been discussed in many respects. Nevertheless, there still exist unanswered important questions on the flocculation of charged colloids moving with diffusive electrical double layer. In terms of history and progress in technology, an approach using fluid mechanics will be essentially important in future.

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The origin and the historical development of the concept of the counterion condensation is described with the emphasis that the concept is inherent to the polyions in rodlike geometry. A couple of experimental results on the microscopic state of the condensed counterions are also discussed. Effects of added salt are discussed in terms of the additivity rule. In the second part, three characteristic aspects of the electrophoretic behavior of polyions are described. (1) The free-draining behavior, (2) Negative stoichiometric transference number of counterions, and (3) The saturation behavior of the mobility with respect to the charge numbers. The last two properties are considered to be due to the counterion condensation. In the final part, arguments are presented regarding the extension of the counterion condensation concept to colloid ions in general, beyond the rod-like geometry. Three operational definitions of the counterion condensation are proposed.

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Electrokinetics in highly concentrated colloid systems were reviewed and introduction of the background of historical and theoretical aspects on electroacoustics was emphasized, because electroacoustics has attracted much interests from academic and industrial fields recently. The theoretical aspects on CVI and ESA, being developed based upon the concept of sedimentation potential in terms of EDL deformation, were explained. In the highly concentrated systems, since particle - particle interactions play an important role for describing the relationship between zeta potential and dynamic electrophoretic mobility, two typical cases with/without interactions were shown.

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Micro-fluidic devices using nonlinear electro-kinetic phenomena (NEKP) are important for promising biomedical applications such as a lab-on-a-chip and micro-total-analysis systems (μTAS). This is because NEKP produce a large flow velocity (~mm/s) with a small voltage (~V) with simple structures and can prevent the occurrence of dc problems such as chemical reactions in an electrolytic solution. In this review, we explain the basis of linear and nonlinear electro-kinetic phenomena, and introduce micro-fluidic devices using NEKP mainly from our studies. We also discuss fundamental problems on an electro-double layer based on our recent discovery on the exact solution of steady PoissonNernst-Planck equations for large applied voltages.

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