Electro-osmosis and streaming potential

Let us start by considering a liquid on a planar, charged surface. If we apply an electric field parallel to the surface the liquid begins to move (Fig. 5.12). This phenomenon is called electro-osmosis. Why does the liquid start to move The charged surface causes an increase in the concentration of counterions in the liquid close to the surface. This surplus of counterions is moved by the electric field towards the corresponding electrode. The counterions drag the surrounding liquid with them and the liquid starts to flow. 

When treating this simple case of electro-osmosis mathematically we immediately realize that the y component of the Navier-Stokes equation disappears. All y derivatives are zero because no quantity can change with y due to the symmetry. We further assume that the liquid flows only parallel to the x coordinate that is parallel to the applied field. Then vz 0 and vy =0. As a consequence all derivatives of vy and vz are zero. From the equation of 

The electric field in x direction is applied externally. In z direction the field results from the surface charges. We also assume that no pressure in x direction is applied. Then dP/dx disappears and after rearranging the first equation we get 

This equation can be integrated twice in z. The integration starts at a point far away from the surface, where tp = 0 and vx has a stationary value vq, up to the shear plane at a distance 5 from the surface where vx = 0 and tp C Note that, far from the plane, dtp/dz = 0 and dvx/dz = 0. 

The flow velocity is proportional to the zeta potential and to the applied field. 

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Electrophoresis has the greatest practical applicability of these electrokinetic phenomena and has been studied extensively in its various forms, whereas electro-osmosis and streaming potential have been studied to a moderate extent and sedimentation potential rarely, owing to experimental difficulties. 

Combination of equations (7.30) and (7.32) gives a general relationship between electro-osmosis and streaming potential, Saxen s equation, which, by a more general derivation, can be shown to apply independent of plug structure and surface conductance ... 

Aside from chemical osmosis, we have also been studying electro-osmosis and streaming potential, i.e. electrical current due to an hydraulic gradient. Within the research project, experimental results have been obtained for these phenomena that will be compared with modelling data to eventually acquire a combined model for chemico-electro-osmotic phenomena in groundwater. 

Furusawa, K., Sasaki, H., and Nashima, T., Electro-osmosis and streaming potential measurements, in Electrical Phenomena at Interfaces Fundamentals, Measurements, and Applications, 2nd ed., Ohshima, H. and Eurusawa, K., Eds., Marcel Dekker, New York, 1998, chap. 9. 

S. Tamura, T. Yamazaki and M. Tasaka, Electro-osmosis and streaming potential across charged membranes, Koubunshi Ronbunshu, 1977, 34, 719-723. 

Electro-osmosis and streaming potential measurements of aqueous D-glucose solutions across testosterone-plug membranes have been used to determine zeta potentials and to examine the Influence of H-bonding between water molecules and those of D-glucosa. 

We shall first outline the theory of electro-osmosis and streaming potential based on thermodynamics of irreversible processes [9-14], Let us consider two chambers separated by a very thin membrane, so that it merely serves as a dividing surface which we need not consider as a separate phase. 

The efficiency of energy conversion may also be estimated in view of the interest in the engineering applications of electro-kinetic phenomena during recent years [58-61]. One may define the efficiencies of energy conversion and E, which are related to coupling in electro-osmosis and streaming potential, as follows ... 

The above relationship shows that zeta potenticd is a little lower than the Stem potential and this is because it Is located further out from the surface of the macromolecule. The zeta potential of any colloidal solution can be calculated by electrokinetic measurements like electrophoresis, electro-osmosis and streaming potential. Though the methods are different, all lead to the same calculated value of the zeta potential for any particular system. All the methods involve the relative motion of the two surfaces in contact. 

Electrokinetic phenomena, namely electrophoresis, electro-osmosis and streaming potential are discussed in Vol. 1 at a fundamental level. These effects arise because of charge separation at the interface that is induced for example by application of an electric field. The plane at which the liquid starts to move is defined as the shear plane and the potential at this plane is defined as the electrokinetic or zeta potential. A schematic picture is given that describes the shear plane and zeta potential. The latter is mostly assumed to be equal to the Stern potential and in the absence of specific adsorption it can be equated to the surface potential, which is the parameter... 

In later years the equivalence of electro-osmosis and streaming potentials has been tested again In this respect the work of Rutgers and collaborators and that of Wijga deserve special attention In the earlier experiments of Rutgers and his school a systematic difference was found between C and s-p for glass capillaries Later... 

A typical result is shown in Fig 16 from Wijga s work on electro-osmosis and streaming potentials ... 

C-potentials of metals have been investigated mainly by electrophoresis. As a consequence of the conductivity of metals electro-osmosis and streaming potential/ although not altogether excluded/ give rise to very complicated results ... 

Relation between electro-osmosis and streaming potential.. 206... 

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