ELECTRO-OSMOTIC PHENOMENA

Electro-osmotic effects are of intrinsic interest also, since they give rise to a number of steady-state phenomena which can be conveniently studied experimentally. These afford examples where the power of non-equilibrium thermodynamics can be easily demonstrated. This is a unique phenomenon where non-linear transport processes have been experimentally observed and studied. 

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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. 

For a thermally fully developed laminar flow, for a fixed dynamic and thermal boundary condition and by neglecting the fluid axial conduction, (Pe oo), viscous dissipation (Br = 0), the flow work fi = 0), and electro-osmotic phenomena (Sl=f = 0), the Nusselt number depends on the cross-sectional geometiy (through the Poiseuille number e) only. 

In this chapter, we will consider simple non-equilibrium phenomena involving two fluxes and two forces. Such a situation arises in membrane transport phenomena (e.g. thermo-osmotic and electro-osmotic phenomena) involving two sub-systems separated by a membrane. In Chapters 5 and 6, transport phenomena in two flux-two force systems in continuous systems without a membrane would be discussed. 

Chapter 4. Electro-osmotic Phenomena Electro-osmotic pressure ... 

In the development of the thermodynamic theory of the electro-osmotic phenomena, it is not necessary to examine how electro-osmosis or streaming potential occurs. The theory is independent of the nature of the membrane or its character. It yields results in terms of phenomenological coefficients. It should be noted that these coefficients do depend on membrane characteristics. The Onsager reciprocal relation would be valid for the same membrane. In order to get the complete picture, including the reason for... 

A theory of electro-osmotic phenomena suited to charged membranes has been developed by Schmid and co-workers [35-37]. It is assumed that an identical composition is maintained on the two sides of the membrane, so that there is no concentration gradient. The distribution of mobile species within the pores is also assumed to be uniform. The ionic fluxes are given by... 

Experimental studies on steady states in the non-linear region, discussed in Chapter 7, demonstrate that fluxes can be represented as power series in fluxes and forces. Onsager reciprocity relation between first-order coefficients is found to be satisfied. Second-order coefficients are found to be functions of forces which influence the membrane characteristics in case of electro-osmotic phenomena. 

All the relevant microscopic equations that govern electro-osmotic phenomena are given in this section, as well as a general description of spatially periodic porous media. 

The simplified equations that govern electro-osmotic phenomena are Eqs. (45)-(49). Apart from some simple situations [31] such as Poiseuille flow, isolated spheres, these equations cannot be solved analytically. Hence, it was found useful to start a systematic numerical analysis, which is summarized below. 

In this first numerical approach to electro-osmotic phenomena, Eqs. (45) and (47a) were linearized by making the classical assumption that the potential is small it is equivalent to assuming that either the surface zeta potential or the surface charge (t° is small. Hence, (45) and (47a) are replaced by... 

Gouy-Chapman theory can also be applied to insulating materials and to colloids. In this case, the potential corresponding to y = 0 is called the zeta potential. The zeta potential plays a crucial role for the stability of colloids and for electro-osmotic phenomena in porous insulating materials. 

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