Streaming potentials

Membrane potential (MP) gives information on the effective fixed charge associated with the bulk membrane phase, Dorman equilibrium between the membrane, and the adjacent solution, and the relative flow of ion through the membrane (ion transport number). 

Impedance spectroscopy (IS) allows both electrical and geometrical characterization by analyzing the impedance plots and using equivalent circuits as models. If membrane (or active layer) thickness is known, conductivity can be determined from electrical resistance values. Moreover, from capacitance results the thickness of dense membranes (or active layers) can be estimated if the material dielectric constant is known. 

When a solid charged surface is in contact with an electrolyte, a distribution of charge in the liquid phase, named electrical double layer (e.d.l.), can be 

A simple relation between the streaming potential and the zeta potential ( ) or electrical potential at the shear plane can be obtained by the Helmholtz-Smoluchowski equation [33]  

Surface charge density at the shear plane or electrokinetic surface charge density (Oe) can be determined from zeta potential values by [33]  

Equipment for measurements of potentials based on electro-osmosis is not commercially available. A few descriptions of home-made electro-osmosis devices can be found in the literature [278-283]. 

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 

The tables in Chapter 3 report results obtained using the following commercial instruments based on streaming potential  

EKA and SurPASS from Paar (Anton Paar, an illustration of the measurement cell can be found in [287]) 

A few illustrations and descriptions of home-made streaming potential devices can be found in the literature [235,288-297], An illustration and a description of a radial flow apparatus designed to measure streaming potential can be found in [298], 

This phenomenon is the reverse effect from electroosmosis a velocity field is applied along an interface and one observes the appearance of an electric field (or a an electric potential difference)associated to the flow. 

The mathematical formulation of this effect will depend on the boundary conditions of the problem, as for electroosmosis [4]. 

In this paragraph only one example of such phenomena will be considered, in relation with the previous parts on electroosmosis. 

Consider a cylindrical capillary with charged walls, through which a liquid is pushed under the action of an applied pressure Ap. A parabolic Poiseuille flow is then produced  

This flow drags counterions by respect to the fixed charged sites and then a streaming eleetrie current is produced. 

The situation in electroosmosis may be reversed when the solution is caused to flow down the tube, and an induced potential, the streaming potential, is measured. The derivation, again due to Smoluchowski [69], begins with the assumption of Poiseuille flow such that the velocity at a radius x from the center of the tube is 

The double-layer is centered at x = r - t, and substitution into Eq. V-43 gives the double-layer velocity 

If k is the specific conductance of the solution, then the actual conductance of the liquid in the capillary tube is C = irr k/Z, and by Ohm s law, the streaming potential, , is given by = i/C. Combining these equations (including Eq. V-44) 

Streaming potentials, like other electrokinetic effects, are difficult to measure reproducibly. One means involves forcing a liquid under pressure through a porous plug or capillary and measuring E by means of electrodes in the solution on either side [6, 23, 71-73]. 

The measurement of the streaming potential developed when a solution flows through two parallel plates [74-76] allows the characterization of macroscopic surfaces such as mica. 

When hydraulic pressure is applied to, for example, a negatively charged membrane, an electrical potential is generated across the membrane, which is lower at the upper-stream (high pressure) side. This is a streaming potential, as explained in Chapter 2.12. The streaming potential, AE, is correlated to the zeta-potential, , according to the Smoluchowski-Helmholz equation,49 

On the other hand, according to non-equilibrium thermodynamic theory,51 the dissipation function, t , is expressed as follows when there are no concentration or temperature differences across the charged membrane, 

Therefore, the volume flux (Jw, cm3 s-1) and current density (/, mA cm 2) are expressed by the differences in electrical potential (A p) and hydraulic pressure (AP) as follows, 

When there is no hydraulic pressure difference across the membrane, the electroosmosis ( Jv/I)ap=o is 

If L21 = L22 (Onsager s theory of reciprocity), the equation predicted by the Saxen relation is obtained 52 

The velocity of a liquid flowing in a capillary varies with the distance from the centre of the tube as shown in Fig. 7.9. The liquid at the surface of the tube is stationary so that the double layer at the interface consists of a stationary and a moving part. It is the relative movement of these two planes of the double layer which gives rise to the streaming potential. The velocity of the liquid at any point on the parabolic front distant x from the wall is given by 

Variation of liquid velocity through a capillary with distance from the centre. 

the moving part of the double layer, at a distance (r — 8) from the centre of the tube, moves with a velocity given by 

As the movement of the front of liquid forces one layer of charges past the other, a current is produced which must be given by the product of the total charge around a unit length of tube and the velocity of the moving part of the layer, i.e. 

---

The flow can be radial, that is, in or out through a hole in the center of one of the plates [75] the relationship between E and f (Eq. V-46) is independent of geometry. As an example, a streaming potential of 8 mV was measured for 2-cm-radius mica disks (one with a 3-mm exit hole) under an applied pressure of 20 cm H2 on QT M KCl at 21°C [75]. The i potentials of mica measured from the streaming potential correspond well to those obtained from force balance measurements (see Section V-6 and Chapter VI) for some univalent electrolytes however, important discrepancies arise for some monovalent and all multivalent ions. The streaming potential results generally support a single-site dissociation model for mica with Oo, Uff, and at defined by the surface site equilibrium [76]. 

Streaming potential measurements are to be made using a glass capillary tube and a particular electrolyte solution, for example, O.OIM sodium acetate in water. Discuss whether the streaming potential should or should not vary appreciably with temperature. 

Related phenomena are electro-osmosis, where a liquid flows past a surface under the influence of an electric field and the reverse effect, the streaming potential due to the flow of a liquid past a charged surface. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

In the past decade adjustments in many of the more subtle variables that affect the feed to a filter ha e begun to be used to control dewatering presses and improve their pertorrnance. These variables allect the perrneabilitv, compressibility, and rheological properties ot the feed and the resulting cake. For example, pll, streaming potential. 

There are four related electrokinetic phenomena which are generally defined as follows electrophoresis—the movement of a charged surface (i.e., suspended particle) relative to astationaiy hquid induced by an applied ectrical field, sedimentation potential— the electric field which is crested when charged particles move relative to a stationary hquid, electroosmosis—the movement of a liquid relative to a stationaiy charged surface (i.e., capiUaty wall), and streaming potential—the electric field which is created when liquid is made to flow relative to a stationary charged surface. The effects summarized by Eq. (22-26) form the basis of these electrokinetic phenomena. 

In 1861, Georg Hermann Quincke described a phenomenon that is the converse of electroosmosis When an electrolyte solution is forced through a porous diaphragm by means of an external hydrostatic pressure P (Fig. 31.1ft), a potential difference called the streaming potential arises between indicator electrodes placed on different sides of the diaphragm. Exactly in the same sense, in 1880, Friedrich Ernst Dorn described a phenomenon that is the converse of electrophoresis During... 

FIGURE 31.1 Schematic design of cells for studying electroosmosis (a) and streaming potentials (b), the velocity of electroosmotic transport can be measured in terms of the rate of displacement of the meniscus in the capillary tube (in the right-hand part of the cell). 

The electrokinetic processes can actually be observed only when one of the phases is highly disperse (i.e., with electrolyte in the fine capillaries of a porous solid in the cases of electroosmosis and streaming potentials), with finely divided particles in the cases of electrophoresis and sedimentation potentials (we are concerned here with degrees of dispersion where the particles retain the properties of an individual phase, not of particles molecularly dispersed, such as individual molecules or ions). These processes are of great importance in particular for colloidal systems. 

Streaming Potential When the solution is forced through the porous solid under the effect of an external pressure P, the character of liquid motion in the cylindrical pores will be different from that in electroosmotic transport. Since the external pressure acts uniformly on the full pore cross section, the velocity of the liquid will be highest in the center of the pore, and it will gradually decrease with decreasing distance from the pore walls (Fig. 31.5). The velocity distribution across the pore is quantitatively described by the Poiseuille equation. 

Current flow in a pore of length I and total cross section S produces an ohmic potential drop in the solution, which is the streaming potential ... 

Like the velocity of electroosmosis, the value of the streaming potential is independent of geometric parameters of the porous sohd through which the liquid is forced. 

Interrelations Between the Electrokinetic Processes Equation (31.4) for electroosmosis and Eq. (31.10) for the streaming potential, as well as the analogous equations for the other two electrokinetic processes, yield the relation... 

Tranter of Ions Mass transfer of ions in ED is described by many electrochemical equations. The equations used in practice are empirical. If temperature, the flux of individual components, elec-troosmotic effects, streaming potential and other indirect effects are... 

---