Electrical double layer shear plane

Fig. 8. Electrical double layer of a sohd particle and placement of the plane of shear and 2eta potential. = Wall potential, = Stern potential (potential at the plane formed by joining the centers of ions of closest approach to the sohd wall), ] = zeta potential (potential at the shearing surface or plane when the particle and surrounding Hquid move against one another). The particle and surrounding ionic medium satisfy the principle of electroneutrafity.

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

As stated above, the results can be interpreted in terms of potential at the plane of shear, termed the zeta potential ( ). Since the exact location of the shear plane is generally not known, the zeta potential is usually taken to be approximately equal to the potential at the Stern plane. Two simple relations can be used to calculate zeta potentials in limiting cases, one for small particles with thick electric double layers, and one for large particles with thin electric double layers. 

Figure 1 The electrical double layer and the potential distribution at the surface 1, fixed surface charges 2, Stern layer of "fixed" charges 3, Gouy or diffuse charge layer 4, counterions 5, Helmholtz plane 6, plane of shear 7, potential distribution in the electrical double layer.

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

Shear Plane Any species undergoing electrophoretic motion moves with a certain immobile part of the electric double layer that is commonly assumed to be distinguished from the mobile part by a sharp plane, the shear plane. The zeta potential is the potential at the shear plane. 

For the electro-osmotic flow, temperature-induced viscosity change at the plane of shear for the electric double layer is more straightforward. Analysis times will generally shorten with increasing temperature. 

Mpandou, A. and Siffert, B., Sodium carboxylate adsorption onto TiOj Shortest chain length allowing hemimicelle formation and shear plane position in the electric double layer,./. Colloid Intel/. Sci., 102, 138, 1984. 

Siffert. B.. Jada, A., and Letsango, J.E., Location of the shear plane in the electric double layer in an organic medium, J. Colloid Intetf. Sci., 163, 327, 1994. 

FIG. 1 Model of an electrical double layer including an exemplary shear plane and the belonging zeta potential. (From Ref. 1.)... 

Zeta Potential Strictly called the electrokinetic potential, the zeta potential refers to the potential drop across the mobile part of the electric double layer. Any species undergoing electrokinetic motion, such as electrophoresis, moves with a certain immobile part of the electric double layer that is assumed to be distinguished from the mobile part by a distinct plane, the shear plane. The zeta potential is the potential at that plane and is calculated from measured electrokinetic mobilities (e.g., electrophoretic mobility) or potentials (e.g., sedimentation potential) by using one of a number of available theories. 

A theoretical explanation for the increase of the viscosity t) could be found in the so-called electroviscous effect. It is well known that an electrolyte solution streaming between two charged walls shows an increase of the apparent shear viscosity. Assuming that the results obtained for plane parallel channels in a steady state by Levine et al. " may be used for the film situation, it was found that a maximum increase of about 20% can be expected for the viscosity of the solution inside the film compared to the bulk value. This electroviscous effect is expected to be important only in equilibrium films where an overlap of the electrical double layers occurs but nevertheless this phenomenon cannot explain the full discrepancy between theory and experiment. 

When a particle surrounded by an electric double layer is subjected to an electric field, the Stern layer and a part of the diffuse double layer move with the particle. The electrical potential at the plane of shear between the bound and free parts of the double layer is called the zeta potential ( ). It is considered that the shear plane is usually located at a small distance further out from the surface than the Stern plane and that ( is generally marginally smaller in magnitude than the Stern potential (see Figure 21). 

Fig. 5.15 Electric double layer surrounding the particle in the solution 1 rigid Stem s layer, 2 diffusion layer, 3 shear plane...

This layer, which is termed the diffuse electrical double layer, can be described mathematically by the Poisson-Boltzmann equation. Within this layer, the shear plane of the particles is located. The potential at this distance from the surface is particularly important as it is the experimentally accessible zeta-potential. When two different colloidal particles that are electrically charged at their surfaces with ions of the same sign approach each other, they wiU experience a net repulsion force as a result of the interaction between the ions located at their diffuse layers. If the net interaction potential between the particles is repulsive and larger than the kinetic energy of the collision, they wiU not coagulate. 

Zeta potential is defined as the electrical potential at the shear plane of the electric double layer. Measurement techniques are based on indirect readings obtained during electrokinetic experiments. Typically, the magnitude of the zeta potential varies between 0 and 200 mV where both negative and positive values are possible depending on the electrochemistry of the solid-liquid interface. 

The complete mathematical expression for the double layer incorporating the Stern layer is quite complex and will not be given here. However, its existence and related effects are quite significant for practical studies of electro-kinetic phenomena discussed below because it is if/s that is actually being estimated in such procedures. When a charged particle moves relative to an electrolyte solution, or a solution moves relative to a charged surface, viscosity effects dictate that only that portion of the electrical double layer up to (approximately) the Stern layer will move. The ions in the Stern layer will remain with the surface. The dividing line between movement with the solution and that with the surface is referred to as the shear plane (Fig. 5.6). The exact... 

When a (solid) surface moves in a liquid, or vice versa, there is always a layer of liquid adjacent to the surface that moves with the same velocity as the surface. The distance from the surface over which this stagnant liquid layer extends or, in other words, the location of the boundary between the mobile and the stationary phases, the so-called plane of shear or slip plane, is not exactly known. For smooth surfaces, the plane of shear is within a few liquid (water) molecules from the surface (see Figure 9.4), that is, well within the electrical double layer. The stagnant layer is probably somewhat thicker than the Stern layer, so that the plane of shear is located in the diffuse part of the electrical double layer. It follows that the potential at the plane of shear, that is, the electrokinetic potential or the zeta potential is somewhat lower than the Stern potential /j. Because the largest part of the potential drop in the... 

When the surface is coated with a lcx)sely stracTured (polymeric) layer that is permeable for solvent and small ions, the plane of shear is farther outward in the electrical double layer, as is illustrated in Hgure 10.1. In that case, /J. ... 

It may be appreciated that electrokinetic phenomena are determined by electric properties at the plane of shear rather than at the real surface. In the following sections of this chapter, the relation between the measured property and is further analyzed. This is done for electroosmosis, electrophoresis, streaming current, and streaming potential. The sedimentation potential will not be discussed any further, because in practice this phenomenon does not play an important role. The electrokinetic charge density may then be derived from using the theory for the diffuse electrical double layer. 

In the discussion of electrokinetic phenomena, it has hitherto been assumed that the viscosity p of the liquid maintains its bulk value right near the shear plane. The notion shear plane actually implies a discontinuous jump in the value of p from nearly infinitely high within the shear plane to the liquid bulk value beyond it. From a physical point of view, such an abrupt change is not realistic. Rather, the value of p changes gradually from the surface to the bulk over a distance of a few molecular layers. Hence, for a smooth charged surface the distance over which p varies lies well within the electrical double layer. 

Because in an aqueous environment, under most conditions, the potential decays for the largest part across the inner region of the electrical double layer (i.e., in the region enclosed by the plane of shear), usually does not exceed a few tens of millivolts. 

Zeta-potential (or electrokinetic potential) electric potential at the shear (or slip) plane within an electric double layer (EDL) the zeta-potential can be measured in case of a relative motion between the charged surface (and Stem layer) and the bulk liquid (including the difluse layer)—e.g. by application of an electric field or due to sedimentation the concept of a slip plane assumes a sharp transition between a stagnant liquid layer attached to the smface and a hydrodynamically mobile liquid phase which is located very close to the outer Helmholtz plane (OHP) the zeta-potential is, therefore, equal or lower in magnitude than the diffuse layer potential at the OHP (cf Sect. 3.1.5.1). 

Let s now examine the second important mechanistic point. As the surface of the oxidic supports is charged in electrolytic solutions, an electrical double layer is formed between the support surface and the solution. Various models have been developed to describe the oxide/solution interface [43, 56-63]. It has been widely accepted that the triple layer model describes better this interface in the most of cases [33-39, 41]. A simplified picture of this model is illustrated in fig. 9. It should be noted that the SOH2+. SOH and SO groups are considered to be localized on the surface of the support (zero plane). On the other hand the centers of the water molecules surrounding the surface of the support particles constitute the so called Inner Helmholtz Plane (IHP). Moreover, the counter ions (of the indifferent electrolyte) are located on the Outer Helmholtz Plane (OHP). Very near to this plane is the shear plane and then the diffuse part of the double layer and the bulk... 

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