Corrosion Inhibitors in the Oilfield

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1.1. General background

Corrosion is one of the most common, costly and widespread industrial problems in today’s modern world. Corrosion comes from the Latin word “corrodere” which means “to gnaw away” [1]. It is defined as the degradation or breaking of bonds between the atoms in a metal and the formation of thermodynamically more stable compounds. The processes of corrosion impair the mechanical properties and compromise the structural integrity of a metal. In the field of oil and gas exploration and refining, there is a constant battle against corrosion due to the severe environments encountered in this field. Table 11 shows the estimated annual cost of corrosion per industrial segment in the petroleum industry in 2001 [2]. Improvement in corrosion monitoring, control and prevention can lead to a significant reduction in the production cost.

Table 11. Annual estimated corrosion costs in oil and gas exploration, production and refining sectors in 2001 [2].

Industrial sector

Annual estimated cost / US dollars

OIL AND GAS EXPLORATION AND PRODUCTION

Piping and facilities

589 M

Down-hole tubing

463 M

Capital expenditures

320 M

Total cost

$1.4 Bn

PETROLEUM REFINING

Maintenance

1.8 Bn

Vessel turnaround

1.4 Bn

Fouling cost

0.5 Bn

Total cost

$3.7 Bn

 

Oilfield corrosion manifests itself in several forms amongst which carbon dioxide corrosion (sweet corrosion) and hydrogen sulphide corrosion (sour corrosion) in the produced fluids and oxygen corrosion in water injection systems are by far the most predominant forms of attack encountered in oil and gas production.

Corrosion occurs when a metal in contact with water forms a corrosion cell. The corrosion cell has four components: the aqueous phase which acts as an electrolyte (through which ions migrate), an anode on the metal surface (where the metal is oxidized and goes into the solution as metal ions), a cathode (where excess electrons are consumed) and a metallic path connecting the cathode to the anode. Anodes and cathodes can form on the steel surface of a pipe (due to the slight differences in composition) when it is exposed to brine (Figure 1-2). The electrolyte in this case is the brine. Under these conditions, iron atoms in the steel will dissolve into the solution as Fe.2+ ions. As each Fe.2+ ion is formed, two electrons are left behind, giving that area of the metal a small negative charge. If nothing happens to remove Fe.2+ ions around the anodic site, the tendency of iron metal to dissolve will diminish. In oilfield systems, Fe.2+ ions are commonly removed by reacting with oxygen and/or hydrogen sulphide and/or carbon dioxide. The corrosion products are precipitates or scales of rust (Fe2O3) or iron sulphides (FeSx) or iron carbonate (FeCO3) or as a mixture of all these compounds. Excess electrons flow away from the anodic site to a site where they form a cathode and where reduction occurs. Reduction of oxygenated water forms hydroxyl ions. If oxygen is not present, but CO2 or H2S, then the dominant cathodic reaction is the reduction of hydrogen ions to produce hydrogen gas. If the electrolyte is salty water, chlorine gas is produced [3].

 

Figure 11. Internal corrosion of a crude oil pipeline made of a mild steel. Reproduced from [3].


1.2. Corrosion control by organic corrosion inhibitors

The corrosion of metals cannot be stopped completely, but it can be controlled by decreasing the rate of corrosion. Corrosion control functions by eliminating or reducing the effectiveness of one or more of the corrosion cell components. Corrosion control methods in oilfield systems include cathodic protection, protective coatings, chemical inhibitors, plastic or cement liners, use of special alloys, solids removal and removal of corrosive gases.

In general, cathodic protection is an approach where the metal surface to be protected is made into the cathode of a corrosion cell. Since corrosion and material loss occurs at the anode, this approach protects the metal. Protective coatings can be used to protect tubing, downhole equipment, wellhead components and pressure vessels. Coatings work by reducing the cathodic area available for the corrosion reaction. The use of organic corrosion inhibitors is the most effective way of protecting internal corrosion of carbon steel pipelines for oil product transportation [4].

An inhibitor is a chemical compound which, when added to a system in a small quantity, serves to retard or reduce the corrosion rate of a metal exposed to a corrosive medium. There are many types of corrosion inhibitors with different modes of actions. Inhibition is used internally with carbon steel pipes and vessels as an economic corrosion control alternative to stainless steels, coatings and non-metallic composites. A particular advantage of the corrosion inhibitor is that it can be introduced in-situ without disrupting the transportation process and it adsorbs into the hard-to-reach surfaces inside the pipes. The major industries using corrosion inhibitors are oil and gas exploration and production, petroleum refining, chemical manufacturing, heavy manufacturing, water treatment and the product additive industries. The total consumption of corrosion inhibitors in the United States doubled from approximately 600 million in 1982 to nearly 1.1 billion US dollars in 1998 [2].

1.3. Mechanism of the corrosion inhibition by organic inhibitors

The corrosion inhibitors used in oilfield applications are organic or ioni compounds that are employed in small concentrations (less than 0.1 wt.%). They are often categorised as mixed inhibitors as they adsorb on the steel surface and inhibit both anodic and cathodic reactions. Almost all organic molecules used in oilfield corrosion inhibitor packages are strongly polar, with many being based on nitrogen, such as the amines [5], amides [6], imidazolines [7] or quaternary ammonium salts [8, 9] and compounds containing P, S and O elements [10]. Molecular structures for some of the most commonly used organic corrosion inhibitors in the oilfield system are given in Table 1-2. The organic corrosion inhibitors are typical surface-active agents due to the presence of hydrophilic and hydrophobic moieties within the same molecule.

Typically, the molecules have a hydrocarbon chain attached to the polar group, the length of which varies (e.g. carbon numbers between 12 and 18). The mechanism by which the organic corrosion inhibitor used to reduce the corrosion is not fully understood so far. The polar group of the molecule provides the functionality that displaces the water molecules from the surface (Figure 12). The adsorption of the corrosion inhibitor from aqueous solution onto the metal surface is driven by both of the polar head group and the hydrocarbon tail group. The concentration of inhibitor has a profound effect upon corrosion inhibition.

Table 12. Basic molecular structures of oil field corrosion inhibitors [10].

Chemical Name

Structure

Amide

 

Primary amine

 

Imidazoline

 

 

Quaternary ammonium ion

-R and R1 represent different alkyl groups. 

 

Figure 12. Schematic of action of oilfield corrosion inhibitor [10].

 

At low concentrations, the inhibitor adsorbs parallel or tilted onto the steel surface [11]. As the bulk concentration increases, the hydrophobic tail groups begin to protrude into the aqueous phase to accommodate more surfactant molecules, which increases the surface coverage. At the critical micelle concentration (cmc), a monolayer coverage is achieved and the tailgroups are parallel to each other and perpendicular to the metal surface [11] which becomes hydrophobic. McMahon has shown that the adsorption of oleic imidazoline onto steel surfaces produces a completely hydrophobic surface that has no affinity for water [12]. Therefore, the adsorbed corrosion inhibitor molecules are believed to act as a waterproof barrier between the corrosive aqueous phase and the steel pipe.

An investigation into the inhibition of iron corrosion by a series of imidazoline derivatives by Ramachandran et al. [13, 14] suggests a self-assembled monolayer mechanism for corrosion inhibition. The model suggests the following criteria for an efficient corrosion inhibitor:

I. Adequate solubility and rate of transport of the inhibitor from solution to the surface.

II. Strong binding of the surfactant headgroups to the metal surface.

III. Self-assembly of headgroups to form a dense and ordered layer.

IV. Self-assembly of hydrocarbon tails to form a hydrophobic barrier.

 

Commercially available oilfield corrosion inhibitors usually contain up to six surface active organic compounds dissolved in a carrier solvent. The carrier solvent can be water or an alcohol or a hydrocarbon. A low freezing point solvent (e.g. ethylene glycol) is required for products used in very cold conditions. Demulsifier species may also be included in order to reduce any impact on water-oil separation in the field [10].
 

1.4.1. General structure of corrosion inhibitors

As stated earlier, the organic corrosion inhibitors, by nature of their structure, are surfactants due to the presence of both hydrophilic and hydrophobic moieties within the same molecule. An example of a frequently used corrosion inhibitor molecule is shown in Figure 1-3. The amphiphilic nature of corrosion inhibitors has not been fully used in interpreting their corrosion inhibition performance until very recently [15, 16]. Surfactants are amphiphilic molecules, comprising a hydrophilic part (usually referred to as the head group) and a hydrophobic part (often referred to as the tail group). A surfactant molecule may consist of one, two or three tail groups. Surfactants are classified according to the nature of their headgroup and examples of anionic head groups include sulphonates, sulphates and carboxylates. Cationic headgroups are usually quaternary ammonium or alkyl pyridinium compounds. The zwitterionic surfactants, which are surfactants with both positive and negative groups present in the headgroup, include betaines and sulphobetaines. The fourth class is non-ionic surfactants. The vast majority of non-ionic surfactants contain a polyoxyethylene headgroup.

 

Figure 13. Schematic diagram of an alkylbenzyldimethylammonium chloride corrosion inhibitor (CnBDMAC).

 

 

 
 

 

1.4.2. Adsorption of surfactants at the air-water interface

When a surfactant molecule is added to water, the hydrophilic head group is in a medium of similar polarity to itself but the hydrophobic tail group is not. For this reason, it tends to distribute itself between the bulk solution and the interface between water and air. At the interface, the tail group projects into the air, while the head group remains in the water. The adsorption of surfactant molecules at the air-water interface lowers the polarity difference between air and water, and therefore, lowers the surface tension as well. The surface tension decreases with increasing surfactant concentration as the amount of adsorbed surfactant increases and reaches a saturation value at the cmc (Figure 14).
 
 
Figure 14. The  effect  of  surfactant  adsorption  at  the  air-water  interface  on  the  solution
                     surface tension [19].
 
 

 

For an uncharged solute, the surface tension changes as a function of the solute activity according to the Gibbs’ adsorption equation [17]:

                                                                 Gamma =-frac{1}{RT} frac{d gamma }{d lna}                                                           (11)

where gamma is the surface tension, Gamma is the surface excess concentration at the air-water interface, R is the gas constant, T is absolute temperature and a is the activity of surfactant. The Gibbs’ adsorption equation shows that Γ is positive when the surface tension is lowered by the addition of surfactant. Positive values of Γ indicate that the concentration of surfactant at the surface is higher than that in the bulk solution. The surface tension of pure water (72 mN m-1 at 293 K) can be reduced to about 30-35 mN m-1 by adding a surfactant with a sufficiently long hydrocarbon chain [18]. The above equation is applicable to non-ionic surfactants, neutral molecules or ionic surfactants in the presence of excess inorganic electrolytes (with respect to the surfactant concentration). For monovalent ionic surfactants with monovalent counterions (1:1 ionic surfactants) and zero added electrolyte, both the anions and cations adsorb at the surface to maintain local electrical neutrality, therefore a factor of two is needed for this in the Gibbs’ equation. The modified equation for ionic surfactants is:

                                                                   Gamma =-frac{1}{2RT} frac{d gamma }{d lna}                                                       (12)

If a non-adsorbed electrolyte is present in large excess then the Gibbs adsorption equation for 1:1 ionic surfactants reduces to equation (1-1).

1.4.3. Aggregation of surfactant in aqueous solution

As more and more surfactant molecules are added to the solution, it eventually becomes energetically more favourable for them to form aggregates in the bulk solution rather than adsorb further at the interface. The concentration at which this happens is called the critical micelle concentration (cmc). A surfactant micelle is schematically represented in Figure 15. A micelle is an aggregate of surfactant molecules with hydrophilic headgroups directed into the bulk solution and hydrophobic tails towards the inner space of the micelle. Inside the micelle, practically no water molecules are present, and thus no energetically unfavourable hydrocarbon-water interactions occur.

 

Figure 15. Schematic diagram of a surfactant micelle.

 

 
Generally, micelles can exist in a spherical, rod-like and disc shaped structures depending on  the length of the hydrocarbon chain, the size of the hydrophilic head group and the aggregation number (the number of surfactant molecules comprising the micelle) [20].
Micellisation is a reversible chemical process. There is an equilibrium condition for micellisation between surfactant molecules in micelles and those at the saturated surface. The cmc in aqueous solution is a characteristic property for the surfactant at a given temperature and an inorganic electrolyte concentration. Micelles can only form when the temperature is above the Krafft point. The Krafft point is the temperature (more precisely, narrow temperature range) above which the solubility of a surfactant in the aqueous solution rises sharply [21].
 

1.5.1. Equilibrium microemulsion phase behaviour and its relation to the preferred monolayer

         curvature

As for the air-water interface, surfactants adsorb at the oil-water interface. Water and hydrocarbon oils when placed together will commonly separate into two phases. When surfactant is added to such a system, its state of lowest energy occurs when it is adsorbed at the interface with the head group in the water phase and the tail group in the oil phase. Again, adsorption continues until a critical concentration, known as the critical microemulsion concentration (cμc), is reached [20]. At this concentration, aggregates form either in the water phase, the oil phase or in a third phase depending on a number of factors to be discussed in the following sections.

Microemulsions are thermodynamically stable dispersions of oil and water stabilised by a surfactant. Microemulsions generally appear transparent because the dispersed droplet size is typically 5-50 nm and are similar in structure to the micelles in that they arrange themselves so that the part of the surfactant with a polarity most like the solvent is on the outside of the aggregate and the other is held in the core. Thus for equal volumes of oil and water, if the aggregates form in the water phase, the head groups are on the outside and if the aggregates are formed in the hydrocarbon oil, the tail groups are on the outside.

The microemulsion type formed in a surfactant + water + oil system, where the surfactant concentration is above the cµc, is dependent on the preferred curvature of the surfactant molecule. The preferred curvature of the surfactant monolayer is controlled by geometrical packing considerations of the adsorbed molecules. The packing factor, P, can be defined as [22]: 

                                                P=frac{A_{h} }{A_{t}}                                                                 (1‑3)

where Ah is the effective area of the surfactant tail group and At is the effective area of the surfactant tail group.
 

A Winsor I microemulsion system contains oil-in-water (o/w) aggregates in the water phase plus an excess oil phase (Figure 16). The preferred monolayer curvature for this system is positive (i.e. the effective area of the head group is larger than the effective area of the chain region, P > 1). Alternatively, a Winsor II microemulsion system contains water-in-oil (w/o) aggregates in the oil phase plus an excess water phase and the preferred monolayer curvature is negative. In between these two cases the net curvature is approximately zero and a three phase system is commonly formed. The third phase can either be a bicontinuous microemulsion, which consists of regions of positive and negative curvature (with zero net curvature), or a lamellar phase with planar arrays of surfactant and alternate layers of oil and water. The other two phases are excess oil and water. This is called a Winsor III system [20].

 

Figure 16. Schematic representation of the transition from a two-phase system with an oil-in-water droplet microemulsion (Winsor I) to a three phase system with a bicontinuous microemulsion (Winsor III) to a two-phase system with a water-in-oil droplet microemulsion (Winsor II). The shaded areas represent microemulsions.

 

In Winsor I, II and III systems, the system is free to adopt a spontaneous curvature since the droplets are free to swell or shrink by more or less solubilisation of the excess dispersed phase until the preferred droplet size (and hence preferred monolayer curvature) is attained at equilibrium. It is possible to produce a change in curvature by affecting the relative sizes of the surfactant head group and tail group, hence yielding a Winsor progression (Winsor I Winsor III  Winsor II). If a surfactant + water + oil system is initially a Winsor I microemulsion with aggregates of positive curvature, changing certain parameters of the system can either reduce the effective area of the head group or increase the effective area of the tail group. This in turn reduces P, reduces curvature and causes the system to move through a progression Winsor I  Winsor III  Winsor II that is known as microemulsion phase inversion [23].

Several factors may cause this progression and they are surfactant dependent [24-26]. Changing the surfactant molecular structure changes the effective area of the headgroup and tailgroup and thus affects the preferred curvature. For non-ionic surfactants, temperature effects are large [23]. At low temperatures, the aggregates form in the water phase (Winsor I). As the temperature is increased it has the effect of dehydrating the head group of the surfactant, reducing Ah and P, and thus causing a phase inversion from o/w into w/o microemulsion. Changing the curvature of ionic surfactants can be achieved by adding an electrolyte to the system. This has the effect of screening the repulsions that exist between the charged headgroups, thus reducing the monolayer curvature [25].


1.5.2. Relation between emulsion type and Winsor behaviour

Emulsions are defined as thermodynamically-unstable mixtures of two or more immiscible liquids (usually oil and water) where one phase is dispersed in the other as drops [27]. Simple emulsions can be either oil-in-water (o/w) or water-in-oil (w/o). For o/w emulsions, oil drops are dispersed in an aqueous continuous phase and in w/o emulsions water drops are dispersed in an oil continuous phase. Preparation of an emulsion requires the formation of a large interfacial area between the two liquids. The work required to disperse one liquid within another remains in the system as a potential energy. This means that the system is thermodynamically-unstable and must reduce this energy by decreasing the interfacial area. Therefore, an emulsion will eventually separate into the two bulk phases, if is not stabilised by an appropriate emulsifier. Emulsifiers are surfactants, which facilitate emulsion formation by reducing the interfacial tension between the two immiscible liquids through adsorption at the oil-water interface. The reduction in the interfacial tension reduces the amount of work required to produce the emulsion but the system will only be thermodynamically stable if the interfacial tension can be reduced to near zero. However, emulsions can be considered to be kinetically stable, if the rate of separation of the two phases is sufficiently slow.

It is always observed that in mixtures of equal volumes of water and oil, the type of emulsion formed by the homogenisation of Winsor I or II systems is the same as the equilibrium microemulsion type [27]. For a ternary mixture of oil, water, and surfactant, which phase separates into a surfactant-rich aqueous phase containing an o/w microemulsion and almost pure oil (Winsor I), the surfactant is said to have a positive spontaneous curvature. Under stirring, an o/w emulsion is obtained from a Winsor I system. For a ternary mixture of oil, water, and surfactant, which phase separates into an oil phase containing a w/o microemulsion, and almost pure water (Winsor II), on stirring, a w/o emulsion is obtained. In other words, emulsification of a Winsor I system generally produces an o/w emulsion, the continuous phase of which is an o/w microemulsion. On the other hand, emulsification of a Winsor II system generally produces a w/o emulsion, the continuous phase of which is a w/o microemulsion.

1.5.3. Emulsion stability 

Emulsions are thermodynamically unstable. Hence, their stability is a kinetic rather than a thermodynamic effect. Emulsion stability can be favoured by the formation of a mechanically strong and elastic interfacial film and electrostatic repulsion between the dispersed droplets, depending upon the nature of the emulsifier [27]. In emulsion studies, an emulsion is considered stable, if it is resistant to physical changes over a practical length of time. Several physical processes can indicate instability in an emulsion. The different methods by which an emulsion can become unstable or breakdown are outlined in Figure 17 [28].

During destabilization by the flocculation of an emulsion Figure 17 (a), droplets come together and form aggregates without losing their original size as illustrated in Figure 17 (b). Flocculation depends on the forces between the droplets, which include van der Waals interactions, electrostatic forces and a variety of short-range forces. Creaming and sedimentation processes shown by Figure 17 (c) can take place where the size and size-distribution of emulsion droplets do not change. Creaming and sedimentation are caused by gravity, creating a concentration gradient due to density differences of the two immiscible liquids. For example, oil droplets from an o/w emulsion may be subject to creaming when the oil has a lower density than the aqueous phase. Ostwald ripening shown in Figure 17 (d) occurs in emulsions where the dispersed phase has a limited solubility in the continuous phase so that large drops grow as smaller drops decrease in size due to transport of the soluble liquid from the small droplet to the large droplet through the continuous phase. Coalescence shown in Figure 17 (e) is a phenomenon where many droplets merge to create fewer larger droplets, thereby reducing the total interfacial area of the system. Clearly, the emulsion droplet size-distribution is not conserved and ultimately complete coalescence can occur to yield the two bulk liquids. Another process by which an emulsion is transformed is phase inversion. During this process, the dispersed phase becomes the continuous phase and vice versa. These breaking mechanisms can take place simultaneously or consecutively, depending on several factors.

 
Figure 17. The different processes involved in the breakdown of an unstable emulsion [28].

 

 

 
1.6. SURFACTANT ADSORPTION AT THE SOLID-LIQUID INTERFACE
 
Corrosion inhibitors protect metals against corrosion by adsorbing onto the surface where it acts as a barrier between the metal surface and the corrosive media. Accordingly, the inhibitor efficiency is directly related to the amount of surface-active inhibitor adsorbed as well as the structure of the adsorbed surfactant layer. In this section, we are going to discuss some of the basic concepts about the adsorption of surfactants (mainly ionic surfactants) at the solid-liquid interface (polar surfaces). These include the electrical properties of surfactant ions near the metal surface, the mechanism of ionic surfactant adsorption, the adsorption isotherms and finally recent models for ionic surfactant adsorption at the solid-liquid interface.
 
 

Most solid surfaces become charged when placed into aqueous solution. Different processes can lead to charging such as ions adsorbing to a surface or dissociating from it. Most metal oxides are often negatively charged when in contact with aqueous neutral solution due to the dissociation of protons from the surface hydroxyl groups (MOH → MO- + H+). These surface charges cause an electric field, which attracts counterions to maintain electrical neutrality. The layer of surface charges and counter ions is called “The Electric Double Layer” [29].

The concept of the existence of the double layer at a flat surface of a metal in contact with an aqueous solution appeared in 1879 by Helmholtz [30]. This first theoretical model assumed the presence of a compact layer of ions in contact with the charged metal surface. The next model of Gouy [31] and Chapman [32], involves a diffuse double layer in which the accumulated ions, due to the Boltzmann distribution, extend to some distance from the solid surface. In further developments, Stern [33] suggested that the solid-liquid interface includes both the rigid Helmholtz layer and the diffuse one of Gouy and Chapman. Specific adsorption of ions at the metal surface was pointed out by Graham in 1947 [34]. In 1963, Bockris et. al. [35] pointed out the role of the solvent at the interface. They suggested that orientation of solvent molecules would occur depending on the excess charges at the electrode and the presence or absence of specifically adsorbed ions at the surface.

In the Gouy-Chapman-Stern model (Figure 18), the double layer is divided into two parts: an inner part, the Stern layer, and an outer part, the Gouy or diffuse layer. Essentially, the Stern layer is a layer of ions that is directly adsorbed to the surface and that is immobile. In contrast, the Gouy-Chapman layer consists of mobile ions. The Stern layer is then subdivided into an inner Helmholtz layer (IHL) and an outer Helmholtz layer (OHL). The IHL contains ions that are specifically adsorbed and bind tightly at a short distance. Due to the size of the counter ions, which in water might include their hydration shell, the adsorbed solvated cations cannot get infinitely close to the surface, but always remain at a certain distance and will be located in the OHL. Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centre of specifically adsorbed ions. The second plane is called the outer Helmholtz plane (OHP) and passes through the centres of the hydrated ions that are in contact with the metal surface [37].

 

Figure 18. Schematic model of the electrical double layer (EDL) at the metal oxide-aqueous solution interface, showing elements of the Gouy-Chapman-Stern model, including specifically adsorbed anions (Graham model). Reproduced with modifications from [36].

 

 
 

A good model for the structure of many metallic surfaces in an aqueous medium is shown in Figure 18 [36]. The metal oxide itself is negatively charged. This can be due to an applied potential or due to the dissolution of metal cations. Certain anions can bind specifically to metal. Water molecules show a distinct preferential orientation and they determine the inner Helmholtz plane. Next, comes a layer of non-specifically adsorbed counter ions with their hydration shell. This layer specifies the outer Helmholtz plane. Finally, there is the diffuse layer.

The change in the electric potential within the double layer is illustrated in Figure 19. It is assumed that the solid surface is negatively charged. The figure shows the variation of electrical potential from the metal surface, where its value is ψo, to a distance far into the solution, where the potential is taken as zero. The potential at the OHP, at distance d from the surface, is called the diffuse-layer potential, ψd (also known as the Stern potential, ψs): it is the potential at the beginning of the diffuse part of the double layer. The potential at the IHP, located at distance β (0 ≤ β ≤ d) from the surface, the IHP potential, is given the symbol ψi. All potentials are defined with respect to the potential in bulk solution. Generally there will be various dissolved salts in the aqueous phase and hence a range of cations and anions. In fact, because of electrostatic repulsion, there will also be a deficit of co-ions (anions in this case) close to the charged surface.

 

 

Figure 19. Schematic representation of the charges and potentials at a negatively charged interface. The IHP (electric potential ψi; charge density σi) is the locus of specifically adsorbed ions. The diffuse layer starts at x = d (OHP), with potential ψd and charge density σd. The slip plane or shear plane is located at x = dek. The potential at the slip plane is the electrokinetic or zeta-potential, ζ. The electrokinetic charge density is σek. Adapted from [37].

 
 

All of the surface charge is compensated by excess counterions in the double layer region. The system as a whole (charged surface and solution) is electrically neutral. The surface-charge density is denoted σo, the charge density at the IHP denoted σi, and that in the diffuse layer σd. As the system is electroneutral [37]:

                        σo + σi + σd = 0                                                                             (14)

The potential varies in an approximately exponential manner from the Stern plane into the solution, through the diffuse layer. Tangential liquid flow along a charged solid surface can be caused by an external electric field (electrophoresis, electro-osmosis) or by an applied mechanical force (streaming potential). In such tangential motion, a very thin layer of fluid adheres to the surface. This thin layer is called the hydrodynamically stagnant layer, which extends from the surface to some specified distance, d.ek, where a so-called hydrodynamic slip plane is assumed to exist. The potential at the plane where slip with respect to bulk solution is postulated to occur is identified as the zeta-potential (ζ) [37]. The OHP has been interpreted earlier as a sharp boundary between the diffuse and the non-diffuse parts of the EDL, but it is very difficult to locate it exactly. The same applies for the slip plane.

 

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