Theories based on models of membranes

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 

Similarly, for a series array having membranes a, (3, 7,. .., we must have 

A typical example of a double membrane system is the epithelial cell bounded on either side with liquid of different permeability properties [20], 

If directional characteristics are considered, the membrane may be either isotropic or anisotropic. Examples of anisotropic membranes are cellular membranes including axonal membranes composed of different layers [21]. It has been pointed out that sandstones [22] and other rocks, sintered metals, sintered glass and unglazed ceramic bodies may be anisotropic with respect to permeability. In the following, we shall consider the case of uncharged membrane or capillary. 

It is believed that in uncharged membranes, electro-osmotic flow occurs on account of the existence of electrical double layer at the solid-liquid interface as shown in Fig. 4.2, where the solid is supposed to be negatively charged. The positive charges move towards the negative electrode when an electric field is applied. The potential near the wall would have a fixed value ( o)- The potential would drop as we move away from the wall in the manner shown in Fig. 4.3, on account of the diffuse nature of the double layer. 

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