Capillaries streaming current

The classical equations relating streaming current or streaming potential to zeta potential are derived for the case of a single circular capillary as follows. 

In this paper we investigate the process of alternate adsorption of cationic polyelectrolyte and anionic surfactant, structure and properties of adsorbed layers depending on different factors (molecular weight of PE, concentration of polyelectrolyte and surfactant, adsorbed layer formation time, the flow rate of the solution) by measuring potential and streaming current using the capillary electrokinetic method. 

Streaming current pressure gradient liquid plug or capillary electric current streaming current per unit of pressure difference C m N S = A m2 N->... 

Streaming currents can in principle be measured by placing two identical reversible electrodes at the ends of the capillaries and connecting them by a low-resistance external lead, see sec. 4.4. 

With plugs and capillaries a number of electrokinetlc (streaming potentials, electro-osmosis, streaming currents) and related phenomena (conductivity, permeability) can be measured, all of these requiring a different mode of operation. 

When the solid phase is fixed (e.g., as a capillary, membrane, or porous plug), a forced flow of liquid induces an electric field. The potential difference is sensed by two identical electrodes. The streaming potential or streaming current can be used to determine the potential. The streaming potential and electro-osmosis can be observed in similar experimental setups, except that the natures of the force and the flux are reversed. Thus, the recommendations and limitations discussed in Section 2.1.2 also apply to measurements based on the streaming potential. For example, the instrument cell induces a streaming potential, which may contribute substantially to the result of the measurement. A linear dependence between the potential obtained by electrophoresis and the streaming current measured by a commercial apparatus was observed in... 

Here, L denotes the length of the capillary. An important advantage of the streaming current measurement is that the surface conductivity does not matter for the calculation (see Equation 5.364), and experimental determination of is not necessary. Similar experiments were performed by Scales et al. to determine the potential of mica surface. 

Equations 5.363 and 5.364 are valid only if the capillary radius is much larger than the thickness of the diffuse layer. A number of modifications were suggested in the literature to extend the theoretical consideration to narrower capillaries and porous plugs (see, for example, the review article by Dukhin and Derjaguin and the book of Hunter ). Measurements of the streaming potential, streaming current, and electrical conductance of plugs made of latex particles were performed and analyzed by van den Hoven and Bijsterbosch. ... 

The streaming potential ( )) must be measured as a function of the applied pressure. The relation between the streaming current and the zeta potential is derived using the Poiseuille equation, which describes the flow velocity of a liquid at a distance (r) from the axis of the capillary ... 

In agreement with the Onsager reciprocity relationship, the streaming current, Ip, generated in the capillary due to external pressure drop, Ap, is given by... 

Here, A is the streaming potential difference developed between the ends of the capillary across which the applied pressure difference is Ap. Using the Helmholtz-Smoluchowski relation to replace by the electroosmotic velocity and Ohm s law to eliminate the conductivity and electric field we obtain the following expression connecting the streaming current, streaming potential, and electroosmotic velocity ... 

The left side of Eq. (7.4.5) is just the power developed by the streaming current, and the right side is the rate of work done by the shear force in causing the electroosmotic flow. This latter statement follows from the fact that, from an overall balance of forces in a steady, fully developed, viscous capillary flow in a circular capillary of radius a. 

The relation between the streaming current and C may be obtained as follows. The velocity v of a fluid at radius r in a capillary of radius a and length / is given by Poiseuille s equation ... 

Assuming that the thickness of the electrical double layer is much smaller than the capillary radius (km 1), and, therefore, the streaming current takes place near the walls of the capillary. Equation 10.20 may be approximated taking x [Pg.164]

It should be realized that is derived from the measured quantity by invoking a model. Then the applicability of the underlying assumptions may be questioned. It is therefore reconunended to compare the values of determined by different electrokinetic methods. The results of electroosmosis and streaming current or potential may be readily compared because they can be obtained using the same capillary... 

Figure 16.4 Electrokinetic phenomena. Two chambers containing electrolytes are separated by a porous wall or capillary, (a) An applied potential V generates a pressure difference Ap, called the electroosmotic pressure, (b) If the fluid is made to flow from one chamber to another by a piston, it generates an electrical current I, called the streaming current...

Boumans, A. A. (1957) Streaming Currents in Turbulent Flows and Metal Capillaries Ph.D. Thesis, Utrecht, 51 pp. 

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