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Electrochemical monitoring of water–surfactant interactions in industrial lubricants
Journal of Electroanalytical Chemistry 534 (2002) 171 /180 www.elsevier.com/locate/jelechem
Electrochemical monitoring of water surfactant interactions in industrial lubricants /
Matthew F. Smiechowski a, Vadim F. Lvovich b,* a
Department of Chemical Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106, USA b The Lubrizol Corporation, 29400 Lakeland Blvd., Wickliffe, OH 44092, USA Received 10 June 2002; received in revised form 23 July 2002; accepted 10 August 2002
Abstract A few hundred ppm of water can cause detrimental changes in the lubricating properties of engine oil. Electrochemical sensors based on electrochemical impedance spectroscopy and cyclic voltammetry were utilized to detect water leaks and continuously monitor the time dependent dynamics of water /oil interactions following the injection of water into industrial lubricant. Immediately following the injection, water molecules interacted with the oil additives (surfactants) forming a water-in-oil emulsion based on inverse micelles. Emulsification was followed by gradual loss of water from the solution through evaporation and electrolysis. On-line data were used to characterize the dynamics of water micellization, evaporation, and electrolysis. The values of kinetic rate constants and diffusion coefficients for the components of the water/oil system were determined. In order to support the experimental data and establish the kinetics of water /oil interactions, literature equations describing these interactions were adopted to develop a computational analysis model. The model illustrated the processes occurring in the water/oil system and resulted in an increased understanding of the recorded experimental data. # 2002 Published by Elsevier Science B.V. Keywords: Cyclic voltammetry; Ac impedance spectroscopy; Sensors; Emulsions; Inverse micelles; Mathematical modeling
1. Introduction The useful life of engine oil depends on several factors such as: base oil formulation, type and amount of oil additives, engine size and vehicle operating conditions [1]. Base oil alone cannot satisfy the lubrication needs of modern equipment. It requires the help of oil additives, which improve chemical and physical properties, performance and long-term stability of engine oil. During its life, oil undergoes substantial chemical changes due to oxidative degradation and contamination by water, ethylene glycol, fuel, soot, and wear metals. Degradation of industrial lubricant is a result of its exposure to high temperature and the presence of nitrogen oxides, moisture and air [2]. Chemically active oil additives interact with engine oil contaminants and oxidative byproducts of oil degradation (high aldehydes, ketones, and carboxylic acids) to make them innocuous. Such additives include dispersants, detergents (surfactants), * Corresponding author E-mail address: [email protected] (V.F. Lvovich).
oxidation inhibitors, and antiwear agents. The mechanism by which these additives perform in an engine is quite complex. Simply stated, detergents protect metal surfaces by forming protective films and by neutralizing the acidic products of combustion and thermo-oxidation. Detergents also actively interact with water, glycol, and other polar components. Dispersants suspend products of combustion and thermo-oxidation in the bulk lubricant through association. Oxidation inhibitors reduce a lubricant’s rate of oxidation, while antiwear agents provide protection against wear by forming protective films on metal surfaces. An additive system can contain any number of additives depending upon the application [3]. Currently, determination of quality for both fresh oil and oil deteriorated as a result of its performance in an engine, calls for several time consuming physical and chemical tests. These tests routinely performed by major engine and lubricants manufacturers include determination of oil viscosity, total acid number (TAN), total base number (TBN), insolubles (such as soot) content, fuel
0022-0728/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 7 2 8 ( 0 2 ) 0 1 1 0 6 - 3
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and water dilution, glycol contamination, and metals content. Generally, as oil degrades its TAN increases and its TBN decreases. Polar species such as water, alcohols, glycol and combustion products may enter the oil and the oil itself may oxidize. All of these changes affect the electrochemical reactivity of the oil [2]. In every-day practice, used lubricants are changed after a given service time or mileage without prior testing. Several major manufacturers are currently seeking an on-line sensor capable of determining oil condition. The major advantage of an oil-condition sensor is that it could signal the need for an oil change when the oil’s condition warrants it, reducing the likelihood for costly repairs due to overdue maintenance and equally eliminating unnecessary maintenance. A significant obstacle in the development of an online sensor is the large variety of oil formulations. It is necessary to look for common traits among oils to use in the development of an electrochemical sensor. An important factor that affects all oils is contamination by water. Water contamination may be caused by leaks from weak seals, moisture entering the lubricant stream from ambient sources, or by combustion. Water interferes with the lubricating properties of the oil by covering the working surfaces and increasing viscosity. It can also promote wear by increasing the rate of corrosion. Major engine manufacturers require a close monitoring of ppm amounts of water, with 2000 ppm (0.2% weight) commonly being used as a threshold for an engine shut down and lubricant change. If an engine is run for short periods, especially in cold weather, water and other combustion products can be condensed from the blow-by gases and result in high levels of absorbed and emulsified water in the oil. Development of an on-line sensor capable of accurate monitoring of ppm amounts of water contamination is an important step in making engines more efficient and safe. However, the development and application of any sensor to direct measurements in lubricating oils is complicated due to the complex nature of lubricant chemistry, the large variety of oil formulations, and different mechanisms of lubricant failure. For example, water may interact with oil through various mechanisms, leading to the formation of inverse micelles, microemulsions, and free non-bound water. Out of all available oil additives, detergents, considering their strong surfactant nature, will have the highest potential of interacting with water, leading to a formation of inverse micelles in a continuous hydrocarbon oil phase with detergent surrounding the water in microdroplets [4]. A continuous exchange between free non-bound water and water contained inside the inverse micelles occurs over a significant time period. At the same time water /oil balance can be affected by external factors, such as water evaporation at elevated temperatures, oxidative decomposition of oil additives, etc. These
processes add an additional degree of complexity to the problem of water quantification in industrial lubricants. Therefore, it becomes essential to study water /oil kinetics, including water equilibration between its predominant free non-bound and micellated phases, and the long-term chemical effects of water contamination on the properties of oil in order to develop an intelligent on-line water monitoring device. Versatile, sensitive, inexpensive electrochemical methods provide an ideal solution to the issue of monitoring of chemistry in highly resistive media, including oil degradation. Among these methods, cyclic voltammetry (CV) on microelectrodes and ac electrochemical impedance spectroscopy (EIS) demonstrated a remarkable potential for direct analysis of complex non-aqueous systems, including industrial lubricants [5 /11]. This work presents an application of a combination of microelectrode CV and EIS to continuous monitoring of the electrochemical properties of a typical diesel lubricant following an injection of a ppm amount of water. The monitoring was conducted over several days, allowing for careful studies of changes in the water/ lubricant system. CV was employed for an instantaneous detection of water-induced changes, while the ac impedance technique was utilized for monitoring water distribution among various spatially separated regions within the solution analyzed. At high frequencies the resistance of the bulk oil layer (Rbulk) can be determined, while at lower frequencies the interfacial or chargetransfer resistance (Rct) can be measured. Rct is inversely proportional to the electrochemical reactivity of the electrode j lubricant interfacial region, while Rbulk reflects the resistance of the engine oil [8]. In order to increase an understanding of the complex kinetics of water /oil interactions an empirical model of the phenomena was developed. The model consists of rate equations describing mass transport and charge transfer processes taking place over time, such as water emulsification resulting in formation of inverse micelles, evaporation of free and emulsified water, and water electrolysis. This type of application of mathematical analysis to verification of experimental data has been demonstrated before [12]. The kinetic rate constants for the water /oil interactions, often mentioned in the literature in a general sense, were verified both experimentally and through a numerical integration.
2. Experimental Three sets of experiments were run on a continuous flow system with a volume of approximately 40 l. Commercial SAE 15W-40 fresh and drain (end of test) oils were studied at both 50 and 60 8C (fresh) and only at 60 8C (drain). The fluid viscosity was approximately 15 cSt (100 8C). All oil samples were run continuously
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at a flow rate of /2.5 l min 1 and a pressure of /20 psi. Some fluctuations in flow and pressure (within 20%) were observed over the course of the experiment, although no visible effects on both EIS and CV signals were detected. The CV sensor comprised a three-electrode arrangement having a silver oxide wire acting as a reference electrode (RE), a Pt wire acting as a counter electrode (CE), and a Pt microwire serving as a working electrode (WE). The Pt WE (d /25 mm) and Pt CE were flamesealed in a glass capillary. The RE was prepared by oxidizing the Ag wire in aqueous acetate buffer solution at a potential of /1000 mV (vs. an Ag/AgCl/KClsat RE) for 10 min. The prepared electrode maintained a constant potential of approximately /350 mV (vs. Ag/ AgCl) for all experiments conducted, in both aqueous and non-aqueous systems. WE, CE, and RE were enclosed in a Teflon body with an outside stainless steel shell. CV scans were applied at 5 mV s1 between /10 and /10 V (vs. Ag/Ag2O) using a 660A Electrochemical Workstation (CH Instruments, Austin, TX). The EIS sensor consisted of two 1 cm2 Pt parallel plates spaced 0.5 mm apart. The ac impedance signal was measured between 100 kHz and 3 mHz at a sinusoidal input amplitude of 500 mV with a single run taking approximately 2 h. Electrochemical reactions were monitored with a Voltalab 40 potentiostat (Radiometer Inc., Westlake, OH). The distance between the oil tank and EIS and CV sensors was 3.175 m. Before the water injection a single measurement at both CV and EIS sensors was made to establish a baseline and to ensure that the oil was water-free. The water was injected between 0.05 and 1% by volume, with 0.2% (80 g) of water being the most typical amount injected. The first measurement was started immediately after the water injection, followed by a total of 25 /30 consecutive EIS and several CV sweeps to allow adequate time to show water loss (50 /60 h). At the end of the experimental session, some residual water still remained in the oil.
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rent on the electrode surface of a microelectrode can be expressed as [4]: Il 4nFDc rme
(1)
a function of the number of electrons in the electrochemical reaction (n ), Faraday’s constant (F ), the diffusion coefficient of the component in question (D ), the concentration of free water (water not incorporated into a micelle) in the bulk solution (c), and the radius of the microelectrode used in CV measurements (rme). The EIS analysis was based on continuous monitoring of the high-frequency bulk feature and the low-frequency charge transfer region on the impedance diagram relating real (Zreal) and imaginary (Zim) parts of the electrochemical impedance. Analysis of the EIS data revealed a complicated, time-dependent pattern of changes for both bulk and charge transfer semicircles for the fresh and drain oil samples. The results of all three EIS experiments are shown in Fig. 1. Before the injection of water the oil is mixed well with an excessive concentration of surface-active and generally negatively charged detergent molecules on the electrode interface. The EIS displays two clearly seen semi-circles: Rbulk, which is the electrical resistance of the bulk solution,
3. Results and discussion The first CV scan in the oil system following water injection revealed the appearance of an additional diffusion-controlled semi-reversible oxidation peak at //4.5 V with the corresponding reduction occurring at //3 V. The heights of both peaks were proportional to the amount of injected water between 100 and 10,000 ppm. The peaks rapidly decreased over time, finally disappearing after /2 h for the drain oil solution, and between 3 and 4 h for the fresh oil. An irreversible diffusion-limited peak at //5 V, corresponding to detergent oxidation, remained visible throughout the experiment. The diffusion-limited cur-
Fig. 1. Experimental time-dependent data following the water injection for: (a) Rbulk; and (b) Rct for: (A, a) Drain oil at 60 8C; (B, b) Fresh oil at 60 8C; (C, c) Fresh oil at 50 8C.
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and Rct, which is the electrical resistance near the electrode interface. It may be observed (Fig. 1) that immediately following the water injection the bulk resistance Rbulk increases dramatically, while Rct virtually disappears. This rapid change is followed over the duration of several hours by a gradual increase in Rbulk until it reaches its largest value, while the Rct semicircle remains insignificant. Later the Rct semicircle on the EIS diagram becomes visible again, while Rbulk gradually decreases with intermittent periods of stabilization. Several hours later the Rct reaches a maximum value while Rbulk continues its slow decrease. Then both Rbulk and Rct decrease gradually, with the decline of Rct being more pronounced. Several days after the injection, the EIS graph returns to its general original shape and Rbulk and Rct to values close to their original values, when all of the water is finally removed from the system. In Fig. 1, the complete time extensive process is clearly illustrated only by curve A. For processes illustrated by curves B and C more time would be required to remove water completely from the system. The complex kinetics of water /oil interactions, which combine several mutually dependent mass transport and charge transfer processes, are responsible for these time dependent changes of Rbulk and Rct values. We attempted to explain the above experimental data by proposing a simplified model describing mass- and charge-transfer processes in a water/oil system. The processes taken into account included emulsification of free non-bound water resulting in formation of inverse micelles, evaporation and electrolysis of both free and micellated water. Following the injection into the lubricant, the water gradually forms inverse micelles with surface-active oil additives (predominantly detergents). Bulk solution resistance increases due to immobilization of charge carrying detergents as a result of water entrapment inside inverse micelles. The immediate disappearance of a semicircle associated with charge transfer processes on the EIS plot (Rct 0/0) following the water injection allows for a very straightforward qualitative detection of water in the oil media. We suggest that a short-term electrophoretictype separation of water and hydrocarbon oil phase occur in the external electric field in the vicinity of the electrode surface. Under even a moderate electric field the mass transport of small water dipoles, with a dielectric constant of /80, is much more facile than that of large bulky polymers, with a dielectric constant of /2 [13]. A high local concentration of water dipoles is likely to be created in the vicinity of the electrode interface as a result of water redistribution in an external electric field. Relatively high water conductivity and the facile nature of charge-transfer reactions carried out through the water dipoles located in the interfacial region can explain the dramatic decrease in charge-
transfer resistance immediately following the water injection. Deposition of conductive layers of water on the electrode j solution interface and the significant presence of water dipoles in the diffusion layer cause displacement of polymer-based ionic and dipole oil species, normally responsible for charge-transfer processes. The contribution of these polymer-based species to charge-transfer processes becomes virtually nonexistent until the water is depleted from the surface. The similar effects of a water leak into an industrial lubricant, such as impairment of the lubricant film, oil additive precipitation, and formation of water pockets on the surfaces, have been observed before [3]. In the bulk solution, free non-emulsified water remains in equilibrium with the water entrapped inside the inverse micelles. After several hours, a point is reached where the maximum amount of detergent and water in the bulk is incorporated in the formation of the inverse micelles. This leads to a situation of lowest bulk solution conductivity as the two most prevalently conductive types of species, water and detergents, render each other electrically inactive through their mutual binding in inverse micelles. At this point the Rbulk value is at its largest, while the Rct is still insignificant. Over this period of time free water loss and water loss from the inverse micelles through temperature-induced evaporation also occur. It is quite plausible that evaporation of free water will be more facile than that of water entrapped inside inverse micelles, where the evaporation is hindered by electrostatic and steric effects of surrounding surfactant molecules. Eventually, the number of water layers concentrated at the electrode surface begins to decrease as the water is consumed through micelle formation, evaporation, and direct electrolysis on the electrode surface. The interfacial water consumption occurs faster than its replenishment by the remaining non-bound water in the bulk due to the dwindling supply of free water. As the space on the electrode surface becomes more readily available, due to water loss, the active detergent molecules begin to move to the interface to replace the water. Detergents, as we mentioned above, are generally not as electrochemically active as free water molecules. Rct starts to increase as the charge transfer processes on the interface become less facile, while Rbulk decreases slightly due to the decreasing effective concentration of the non-conductive water-containing inverse micelles as a result of their breakdown caused by evaporation of entrapped water. Several hours later, the remaining free water in the bulk is completely consumed, either by evaporation or formation of inverse micelles The bulk resistance continues to decrease at a very slow rate due to the decrease in the apparent concentration of water-containing inverse micelles. The breakdown of inverse micelles caused by the evaporation and electrolysis of micellized
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water increases the effective amount of available detergents. The Rct value reaches a maximum value representing the point of absence of free water at the interface. Any water remaining there is incorporated in inverse micelles, which discharge about 100 times more slowly than free water and even detergents (see discussion below). At the end of the experiment the remaining water in the system is slowly being removed from the inverse micelles through evaporation and discharge. The EIS graph will eventually return to the general shape that it was in before the injection, after all water is removed from the system.
4. Mathematical modeling In order to increase our understanding of the complex kinetics of water /oil interactions we have developed an empirical model describing the dynamics of water /oil interactions following the injection. The model consists of rate equations describing mass transport and charge transfer processes such as evaporation, absorption into inverse micelles, and electrolysis of water taking place over time in the water/oil system. These rate equations were initially solved by an Euler integration using both a 30 and a 3000 s time step. The results from these calculations were confirmed by using a Runge-Kutta Fehlberg algorithm included in the Polymath Software package.1 The definition of the equations for the water /oil interaction kinetics required several assumptions based on chemical engineering, thermodynamic, and electrochemical principles: . The water can be consumed in fresh or drain oil in three basic ways */by evaporation, electrolysis at the electrode surface, and absorption into inverse micelles. These processes are illustrated in Fig. 2. . The homogeneous mixing of water is assumed to occur instantaneously upon addition to the oil. . Inverse micelles are formed between free non-bound water and detergents (surfactants) of the oil additive package. Detergents are the only component of the oil solution that is interacting with water. . The chemical activity of detergents before and after emulsification of water is similar. . Water incorporated into an inverse micelle is lost through evaporation, and dissociation of the inverse micelles at the electrode followed by electrolysis. . Fundamental equations describing temperature-induced water loss in an open system are applicable 1 M. Sachham and M.B. Cutlip http://www.polymathsoftware.com/order/.
Fig. 2. Proposed mechanism of water interactions in the oil system after injection.
.
.
.
. . . .
. . . . .
to evaporation of water contained inside an oil-filled continuous flow system. Differences in charge transfer and bulk resistances between samples with and without water correspond to the charge transfer resistance incurred by free or micellized water. Experimentally determined rate constants for inverse micelle formation and average diffusion coefficients for inverse micelles are accurate. Immediately following injection, free water displaces all oil additives on and in the immediate vicinity of the electrode surface. Agglomerates of free (not incorporated into a micelle) water and micelles both have a spherical shape. There is no next neighbor interaction between water molecules on the electrode surface. Water molecules have 100% packing efficiency on the electrode surface. Electrolysis at the electrode surface occurs by direct electron transfer between the reacting species and the electrode. Inverse micelle formation is a first order process. The inverse micelle radii are approximately 10 nm for fresh, and 8 nm for drain samples [14]. The micellated water evaporation equation [15] holds for our modeling. Evaporation rates of free water on the electrode surface and in the bulk are identical. Steady state conditions exist for all equations.
4.1. Free water loss The first step necessary for the calculation of the kinetics of oil /water interactions is to determine the diffusion coefficient of free water in oil. For the initial calculations, we assumed that the water was broken down to the molecular level, r /300 pm [16], and would diffuse through the oil in this fashion. The diffusion
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Table 1 Results from free water calculations
105 DE S (cm2 s 1) 1010 DCV (cm2 s 1) 106 h (m s 1) 109 k (cm s 1) R (mm) 10 15 V (nm3) 10 16 n
Fresh 50 8C
Fresh 60 8C
Drain 60 8C
7.58 1.87 4.28 8.88 96 3.63 3.21
7.82 2.42 4.37 15.9 122 7.53 6.67
7.82 7.46 4.37 47.6 31 1.30 0.12
I nF pr2me c k3
DE S, diffusion coefficient from the Einstein /Stokes equation for one water molecule; DCV, diffusion coefficient by CV for a water agglomerate; h , mass transfer coefficient; k , rate of charge transfer; R , radius of water agglomerate; V , volume of water agglomerate; n , number of molecules in water agglomerate.
coefficient for a single molecule of water is derived from the Einstein/Stokes equation (D /kbT /(6pmr)) (Table 1). This diffusion coefficient is used in an equation that describes the mass transport of water through the system [17]. Sh hl=D 0:664Re1=2 Sc1=3 Re vl=m Sc m=D
(2) (3) (4)
where ‘v’ is velocity, ‘l’ is the characteristic length, ‘D ’ is the diffusion coefficient, and ‘m ’ is viscosity. Eq. (2) is generally used for fluids diffusing into gases (with ‘Sh ’ as the Sherwood number, ‘Re ’ as the Reynolds number, and ‘Sc ’ as the Schmidt number), but was modified to fit the current situation based on assumptions made about the oil/water system. The characteristic length (l ) used in this equation was the width of the tank (30.5 cm). By solving the equations for (h), the mass transfer coefficient, the result was used in the following equation (evaporation of one component from a two component system) [17] to determine the rate (k1, in g s 1) at which free water evaporates from the oil of surface area (A ): k1 hArf (1f)
by the applied potential and electrolyzed at the surface [18]. The diffusion coefficients can be calculated from the CV data and Eq. (1). The rate of charge transfer for water is calculated from the CV data and Eq. (6) [19]:
(5)
Eq. (5) considers that the rate of evaporation will be limited by the amount of water vapor that can be held in the oil, through the application of saturation density (rf /0.129 kg m 3 [17]) and relative humidity (f). The vapor phase water in the oil will eventually leave the system either by passing into the air above the oil tank or condensing on the flow pipes of the system. The model does not take the variability induced by these effects into account. The specific densities of water in the oil in the fluid and vapor will remain constant since the water is going from a liquid in oil to a vapor in the oil phase at constant temperature. Table 1 shows the values obtained from these equations. The next loss of free water from the system occurs at the electrode. Here the water is drawn to the electrode
(6)
where ‘I’ is the current, ‘n’ is the number of electrons, ‘F ’ is Faraday’s constant, ‘rme’ is the radius of the microelectrode, and ‘c’ is the concentration of water in the bulk. This predicts a rate of charge transfer (k3) on the order of 1/108 cm s 1 and a diffusion coefficient for water on the order of 1 /1010 cm2 s 1 (Table 1). Note that experimental diffusion coefficients (Eq. (1)) are / 105 times smaller than the theoretical diffusion coefficients calculated by the Einstein /Stokes equation for a single water molecule (Table 1). In reality, when water is injected into oil it remains in large agglomerates of water molecules for an extended time. By comparing the experimental diffusion coefficients to those obtained for free water from the Einstein/Stokes equation the average size of a water agglomerate in the oil can be determined. The ratio of the diffusion coefficients is inversely proportional to the ratio of particle radii. When the radius corresponding to a water agglomerate is obtained its volume can be divided by the volume of a single water molecule, with a radius of /0.3 nm [16] (4/ 3p /0.33 nm3 /0.11 nm3). By assuming 100% packing efficiency, the number of water molecules in a single water agglomerate can be calculated (Table 1). The average size and number of molecules contained in a water agglomerate represents what happens to the water immediately after it is added to the oil before the mixing and chemical interactions with oil additives (detergents) break it apart. Over time the average agglomerate size decreases as water is evaporated, taken into inverse micelles, and electrolyzed. The agglomerates are larger in the 50 8C sample than the 60 8C sample due to increased temperature facilitating finer water dispersion. The average volume of water agglomerates in the drain is smaller probably due to stronger chemical interactions with the more polar drain components (Table 1). The third process considered for removing free water from the system was the formation of inverse micelles [4]. The rate constant of inverse micelle formation for each oil system depends on the chemical composition of the oil. Due to the lack of definitive literature data describing this phenomenon, rate constants were chosen so that the model would fit the time dependent changes in Rbulk values. An initial step was to determine the process of inverse micelle formation. This was done by setting up models for both first and second order formation rates; the first order process provided a better fit to the time dependent changes in the experimental data. For the fresh oil at 60 8C the rate constant was estimated as 104 s 1, for the fresh oil at 50 8C the rate
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constant was 7.5 /105 s 1. For the drain oil the estimated rate constant was approximately 1.5 times greater (1.5 /10 4 s 1) than the fresh oil for the same conditions. In the work by Clint et al. [15], it was assumed that the water added to a sample would be emulsified over a period of several minutes. This corresponds to a rate constant of about 10 3 s 1. Our assumed values for the rate of water evaporation from an inverse micelle differ from this value by an order of magnitude; considering the differences between our samples and the prepared samples used in their experiments the estimation seems reasonable. It should be noted that the drain rate constant is not applicable for any drain oil at all times. The chemical conditions of the drain oil are never the same, so this approximation holds only for the drain oil used in this experiment. The final step in modeling the amount of free water is to put the three rates; evaporation from the bulk and the electrode surface (k1), inverse micelle formation (k2), and electrolysis at the electrode (k3) together. This is shown below: rate dc=dt$ Dc=Dt (cf ci )=Dt k1 k2 cf k3 cf
(7) (8)
The resulting equation for the Euler integration relating initial (ci) and final (cf) concentrations of water over time is as follows: cf (ci k1 Dt)=(Dt(k2 k3 )1)
(9)
Fig. 3 shows a plot of the data for all three oil cases. The arrows on the chart display approximately where the free water is completely consumed for each case. For the smaller step size, the theoretical results predict faster water consumption than the experimental ones. This can be explained by either the lower time accuracy of our method of experimentation, where 2 h elapsed between consecutive measurements, or from an over-approximation in our model caused by our assumptions. The values for the above calculations are illustrated in Table 2. The table illustrates that the calculated values for the disappearance of free water correspond well to the
experimental values obtained with EIS. As the temperature decreased by 10 8C, the amount of time required till all of the free water was consumed increased by approximately 33%. For the drain, it took 70% less time for complete free water consumption than for the fresh oil at 60 8C. 4.2. Loss of water from inverse micelles The process by which water enters the inverse micelle has already been described; the water is lost from an inverse micelle by evaporation or it is dissociated from the inverse micelle [4]. Describing the evaporative losses from the inverse micelles is a complex task. By adopting an equation describing a dodecane/detergent solution [15] to a water/oil system, we were able to predict the evaporative losses from inverse micelles in the solution. The equation, derived by Clint et al. [15], presents a relative mass loss as: m=mo 8p2
X
(2z1)1 exp[(2z1)2 h2 t Dt]
z0
km
(10)
Where ‘D ’ is the diffusion coefficient for the inverse micelles in the solution calculated by the Einstein/ Stokes equation, ‘z ’ is the summation index and ‘ht’ is the height of the oil in the tank. The theory behind the evaporation equation and how the end value of the sum is chosen is described in detail in the literature [15]. The result is expressed in the fraction of mass remaining after a period of time, and is independent of the original starting mass (80 g), much like the evaporation of the free water. The summation in the evaporation equation for water in inverse micelles is carried out until the required degree of accuracy (the value of the next iteration of the summation) is obtained. Table 3 shows the results from these calculations. It was assumed that the inverse micelles would be attracted to the electrode and once there, spontaneously split apart, releasing the water to the electrode. The equation for the dissociation process is [20]: k4 RT=((nF )2 Ac c Rct )
Fig. 3. Illustration of calculated free water in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
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(11)
where ‘k4’ is the rate of micelle electrolysis, ‘R ’ is the ideal gas constant, ‘n ’ is the number of electrons, ‘F ’ is Faraday’s constant, ‘Ac’ is the area of the electrode, ‘c’ is the bulk concentration, and ‘Rct’ is the charge transfer resistance. The largest Rct values from the experimental data (Fig. 1) were selected for this calculation. This corresponds to the highest accumulation of the electrochemically inactive inverse micelles in the interfacial region. The results from this calculation are listed in Table 3. The charge transfer coefficients calculated in this method are less than those for water (Table 1) because
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Table 2 Experimental vs. calculated results Fresh 50 8C
Fresh 60 8C
Drain 60 8C
Theoretical time till free water consumption, 3000 s step size (h) Theoretical time till free water consumption, 30 s step size (h) Experimental time range till free water consumption (h)
24 21 20 /26
18 16 16 /20
14 11 12 /16
Theoretical time of peak inverse micelle formation, 3000 s step size (h) Theoretical time of peak inverse micelle formation, 30 s step size (h) Experimental time of bulk peak inverse micelle formation (h)
15.0 7.3 6 /8
12.5 6.0 6 /8
9.2 4.5 4 /6
Calculated maximum mass of water on surface (ng) Calculated maximum thickness of water layer (mm) Calculated time when evaporation stops (h) Experimental time when evaporation stops (h)
448 1.27 21.3 20 /26
583 1.65 15.7 16 /20
1480 4.20 11.2 12 /16
Table 3 Inverse micelle calculations Fresh 50 8C 106 DE S (cm2 s 1) Fraction of mass remaining after 30 s 10 6 Charge transfer resistance (V) 1010 k (cm s 1)
2.28 0.99953 18.0 1.44
Fresh 60 8C
Drain 60 8C
2.35 0.99952
2.93 0.99947
6.8
3.5
3.94
7.65
DE S, diffusion coefficient from the Einstein /Stokes equation for one inverse micelle; k , rate of charge transfer.
of sluggish electron transfer through the inverse micelle hindered by the spatial impediments and the nonconducting nature of water /oil structures. The electrons tunnel through the associated structures of inverse micelles in the vicinity of the electrode surface (diffusion layer) at a rate much slower than a reduction/oxidation reaction of free water (k3 water / /1/108 cm s1) or a single detergent molecule at the surface (k3 detergent / /1 /108 cm s 1). This last value was calculated from CV data and Eq. (6). Electrons, even from inverse micelles positioned directly on the surface of the electrode, have to travel across a distance of approximately 5 nm to reach the electrode [4]. The equation for modeling the concentration of water in inverse micelles is derived when rate constants of evaporation from inverse micelles (km), inverse micelle dissociation and discharge (k4), and the rate of formation of inverse micelles (k2) are considered. The resulting equation is solved for the final concentration of water in inverse micelles (cmf), rate dc=dt$ Dc=Dt (cmf cmi )=Dt
experimental time factors for inverse micelle formation were taken to be equal to the time when Rbulk in the EIS diagram reaches its largest value. Fig. 4 shows that the drain oil has the earliest inverse micelle peak, this corresponds with the fact that the drain oil will have oxidation products, such as carboxylic acids, that will also form inverse micelles with water and consume it faster. The other two curves representing the fresh oil correspond to the mechanism, but are slightly slower in peak time and encapsulate less total water due to a lower temperature and less chemically active starting material to form inverse micelles. The mathematical model predicts that the mass of water in the inverse micelles drops quickly over time (Fig. 4), while the experimental EIS data demonstrate a more gradual reduction. This discrepancy can be explained by what the model estimates and the EIS measures. The model approximates the amount of water in inverse micelles at a given period of time, and the Rbulk from the EIS data is proportional to the amount of inverse micelles in the bulk. An inverse micelle can hold one to several molecules of water. So the water loss shown by the model can be correlated to the EIS data through the loss of water in inverse micelles, not the loss of inverse micelles themselves. Another possible explanation of this discrepancy is an overestimation in the
(12)
cmi km k2 cf k4 cmi
(13)
cmf cmi km k2 cf Dtcmi k4 Dt
(14)
Table 2 shows that the calculated results from Eq. (13) are comparable with the experimental EIS data. The
Fig. 4. Illustration of calculated mass of water in micelles in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
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rate of water evaporation from the inverse micelles. We assumed that this equation describing evaporation of water from dodecane/surfactant would be applicable to oil/water systems in general.
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In the case of the preceding equations, k1 is the evaporation rate constant for free water in the entire system, which is dependent only on temperature. The value of k1 is multiplied by the ratio of the concentration of free water at the electrode surface to the amount of free water in the bulk to account for the portion of water on the electrode surface compared to the total amount of free water in the system. When the value of ci reaches zero the evaporation term is applied without the ratio of cei to ci. Fig. 5 illustrates the time dependent results of Eqs. (15) /(17) used to calculate the amount of water on the surface of the electrode for all three cases studied.
The results of this model correlated well to the EIS data. The arrow at the end of each curve corresponds to the point in time when evaporation stops affecting the water on the surface of the electrode. This point is also aligned with the time when there is no more free water in the bulk, and water is no longer replenished at the interface. Although the graph appears to show the absence of water on the interface, this is not entirely correct. A closer look at the data shows that once the water is reduced to approximately 3 layers (3 layers/(pr2)) / (electrode surface area/6.022 /1023) /3/(p /3002 2 2 pm ) /(1 cm /6.022 /1023) /3 /107 g), the attractive force of the electrode’s potential field holds the water in place. This phenomenon has been observed before [21]. The only way water can be removed from the surface in this case is by electrolysis since the amount of energy required to overcome the potential field for the water to evaporate or be absorbed into an inverse micelle is too large. Therefore, these last layers of water will remain on the surface of the electrode for several hours due to the slow rate of electrolysis. Eq. (17) can also be used to calculate the total number of layers of water molecules on the surface of the electrode (Fig. 6). The number of molecules of water on the electrode surface is calculated from the mass of water on the surface. This number is then multiplied by the area of a water molecule (pr2 /p /3002 pm2 / 2.8 /1015 cm2) and divided by the area of the electrode surface (1 cm2). By assuming a 100% packing ability the thickness of the water layer can also be determined by multiplying the number of layers by the diameter of a water molecule (d/600 pm). In all three cases the thickness of the water layer never grew to a size that could be considered out of proportion to the electrode spacing (0.05 cm) (Table 2). If we were to assume only a 50% packing efficiency for the water on the electrode surface, the results of water thickness would still be reasonable when compared to the electrode spacing. This is important when considering that not only water will be on the electrode surface but
Fig. 5. Illustration of calculated water mass on the electrode surface in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
Fig. 6. Calculated number of water layers on the electrode surface assuming perfect packing in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
4.3. Water on the electrode surface Modeling of the interaction of water at the surface of the electrode also corresponds to data points collected through EIS and provides another test of the model’s accuracy. By assuming that the evaporation of free water on the surface of the electrode occurs at the same rate as the evaporation of the free water left in the bulk, the evaporation of free water from the electrode surface would stop at the same time as the free water in the bulk had been consumed. An equilibrium state was assumed between the free water on the electrode surface and the water in inverse micelles in the bulk, resulting in zero net loss of water to inverse micelle formation from the electrode. The following equation was developed to describe the initial (cei) and final (cef) concentration of water on the electrode surface as functions of the diffusion to the electrode (k5), the rate of evaporation (k1), and the rate of dissociation (k3): rate dc=dt$ Dc=Dt (cef cei )=Dt k5 (ci cei )k1 cei =ci k3 cei cef cei (1k5 tk1 Dt=ci k3 Dt)k5 Dtci
(15) (16) (17)
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also inverse micelles and polymeric oil additives will be attracted to the surface and in the process take up available space.
5. Conclusions When water is injected into oil it forms large agglomerates with the size depending on mixing and interaction with the oil additives, mostly detergents. These water agglomerates decrease in size over time as water is evaporated, electrolyzed, and emulsified. The predicted size of the water agglomerates was smaller with higher temperature and increased oil aging, due to higher temperatures facilitating finer water distribution and aged oil containing a larger amount of polar components. At the same time a short-term separation of the water and hydrocarbon oil phases occurs in the external electric field near the electrode surface. Deposition of conductive layers of water on the electrode j solution interface and a significant presence of water dipoles in the diffusion layer causes displacement of polymer-based ionic and dipole species, normally responsible for charge-transfer processes. Relatively high water conductivity and the facile nature of charge-transfer reactions carried out through water dipoles located in the interfacial region explain the dramatic decrease in Rct immediately following the water injection. Several processes can describe the history of water /oil interactions: incorporation into inverse micelles, evaporation of free and emulsified water, and electrolysis. The experimental and computed data demonstrated that electrolysis is negligible and that evaporation of emulsified water is a slow process (Figs. 3 /5). Through the comparison of the diffusion coefficients and relative electrochemical activities of water, detergent, and inverse micelles in the vicinity of the electrode, the mechanism of corrosion inhibition can be envisioned. The electrochemical activities for detergent and especially water are higher than the electrochemical activity of an inverse water/detergent micelle by several orders of magnitude. The interaction between water and detergent resulting in the formation of an inverse micelle is much faster than redox reactions of either water or detergents. This results in electrochemically passive inverse micelles forming on the surface of the electrode, and suppression of individual redox reactions involving water or detergents. The experimental data and mathematical model presented demonstrate the applicability of the electrochemical approach to development of a water monitoring on-line device capable of providing information on time-dependent water /oil interactions in industrial lubricants. Empirical kinetic parameters from the model were in reasonable agreement with the general literature data, which serves as another indirect indicator of
viability of the presented method of combining electrochemical experiments and mathematical modeling. The experimental approach combining voltammetry and ac impedance techniques can be used in practice for development of water-in-oil sensors, while the mathematical model can be utilized for broader evaluations of time-dependent water /oil interactions. The model developed provides a good evaluation for the history of water after it enters the oil-based system and illustrates the complex nature of water/oil interactions many hours after water injection. It is recommended that more work be done to confirm the accuracy of the assumptions, and to perform further studies to model the effects of aging on oil. Acknowledgements The authors would like to thank the Lubrizol Corporation for their financial support and for allowing this paper to be published. References [1] D. Cipris, A. Walsh, T. Palanisamy, in: D.R. Turner (Ed.), Sensors for Motor Oil Quality, The Electrochemical Society Proceedings Series, Pennington, NJ, PV 87-9, 1990, p. 401. [2] S.S. Wang, H.S. Lee, D.J. Smolenski, Sens. Actuators B 17 (1994) 179. [3] S.Q.A. Rizvi, Lubricants and Lubricant Additives, Lubrizol Corp., 1995. [4] J.F. Rusling, in: A.J. Bard (Ed.), Electroanalytical Chemistry, A Series of Advances, vol. 18, Marcel Dekker Inc., New York, 1994, pp. 1 /88. [5] A.M. Farrington, J.M. Slater, Analyst 122 (1997) 593. [6] S.R. Jacob, R.G. Compton, J. Electrochem. Soc. 146 (1999) 2598. [7] R.J. Price, L.J. Clarke, Analyst 116 (1991) 1121. [8] S.S. Wang, H.S. Lee, Sens. Actuators B 40 (1997) 193. [9] S. Wang, Sens. Actuators B 73 (2001) 106. [10] S. Wang, Tribology Trans. 44 (2001) 411. [11] S. Wang, Sens. Actuators B 4305 (2002) 1. [12] V.F. Lvovich, A. Scheeline, Anal. Chem. 69 (1997) 454. [13] S. Grimnes, O.G. Martinsen, Bioimpedance and Bioelectricity Basics, Academic Press, London, 2000, p. 60. [14] R.E. Kornbrekke, P. Patrzyk-Semanik, T. Kirchner-Jean, M.G. Raguz, E.A. Bardasz, Advances in Powertrain Tribology, SP1390, 1998. [15] J.H. Clint, P.D.I. Fletcher, I.T. Todorov, Phys. Chem. Chem. Phys. 21 (1999) 5005. [16] J.A. Dean, Lange’s Handbook of Chemistry, 15th ed., McGrawHill, New York, 1999, p. 439. [17] F.D. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley and Sons, New York, 1996, pp. 284 /332. [18] I.G. Harpur, N.J. Wayth, A.G. Bailey, M.T. Thew, T.J. Williams, O. Urdahl, J. Electrostat. 40 /41 (1997) 135. [19] A.J. Bard, L.R. Faulkner, Electrochemical Methods, John Wiley and Sons, New York, 1981, p. 91. [20] J.R. Macdonald, Impedance Spectroscopy: Emphasizing Solid Materials and Systems, John Wiley and Sons, New York, 1987, p. 21. [21] T. Doll, I. Eisele, 8th International Meeting on Chemical Sensors, Abstract Book, Basel, Switzerland, 2000, p. 110.
Electrochemical monitoring of water surfactant interactions in industrial lubricants /
Matthew F. Smiechowski a, Vadim F. Lvovich b,* a
Department of Chemical Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106, USA b The Lubrizol Corporation, 29400 Lakeland Blvd., Wickliffe, OH 44092, USA Received 10 June 2002; received in revised form 23 July 2002; accepted 10 August 2002
Abstract A few hundred ppm of water can cause detrimental changes in the lubricating properties of engine oil. Electrochemical sensors based on electrochemical impedance spectroscopy and cyclic voltammetry were utilized to detect water leaks and continuously monitor the time dependent dynamics of water /oil interactions following the injection of water into industrial lubricant. Immediately following the injection, water molecules interacted with the oil additives (surfactants) forming a water-in-oil emulsion based on inverse micelles. Emulsification was followed by gradual loss of water from the solution through evaporation and electrolysis. On-line data were used to characterize the dynamics of water micellization, evaporation, and electrolysis. The values of kinetic rate constants and diffusion coefficients for the components of the water/oil system were determined. In order to support the experimental data and establish the kinetics of water /oil interactions, literature equations describing these interactions were adopted to develop a computational analysis model. The model illustrated the processes occurring in the water/oil system and resulted in an increased understanding of the recorded experimental data. # 2002 Published by Elsevier Science B.V. Keywords: Cyclic voltammetry; Ac impedance spectroscopy; Sensors; Emulsions; Inverse micelles; Mathematical modeling
1. Introduction The useful life of engine oil depends on several factors such as: base oil formulation, type and amount of oil additives, engine size and vehicle operating conditions [1]. Base oil alone cannot satisfy the lubrication needs of modern equipment. It requires the help of oil additives, which improve chemical and physical properties, performance and long-term stability of engine oil. During its life, oil undergoes substantial chemical changes due to oxidative degradation and contamination by water, ethylene glycol, fuel, soot, and wear metals. Degradation of industrial lubricant is a result of its exposure to high temperature and the presence of nitrogen oxides, moisture and air [2]. Chemically active oil additives interact with engine oil contaminants and oxidative byproducts of oil degradation (high aldehydes, ketones, and carboxylic acids) to make them innocuous. Such additives include dispersants, detergents (surfactants), * Corresponding author E-mail address: [email protected] (V.F. Lvovich).
oxidation inhibitors, and antiwear agents. The mechanism by which these additives perform in an engine is quite complex. Simply stated, detergents protect metal surfaces by forming protective films and by neutralizing the acidic products of combustion and thermo-oxidation. Detergents also actively interact with water, glycol, and other polar components. Dispersants suspend products of combustion and thermo-oxidation in the bulk lubricant through association. Oxidation inhibitors reduce a lubricant’s rate of oxidation, while antiwear agents provide protection against wear by forming protective films on metal surfaces. An additive system can contain any number of additives depending upon the application [3]. Currently, determination of quality for both fresh oil and oil deteriorated as a result of its performance in an engine, calls for several time consuming physical and chemical tests. These tests routinely performed by major engine and lubricants manufacturers include determination of oil viscosity, total acid number (TAN), total base number (TBN), insolubles (such as soot) content, fuel
0022-0728/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 7 2 8 ( 0 2 ) 0 1 1 0 6 - 3
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and water dilution, glycol contamination, and metals content. Generally, as oil degrades its TAN increases and its TBN decreases. Polar species such as water, alcohols, glycol and combustion products may enter the oil and the oil itself may oxidize. All of these changes affect the electrochemical reactivity of the oil [2]. In every-day practice, used lubricants are changed after a given service time or mileage without prior testing. Several major manufacturers are currently seeking an on-line sensor capable of determining oil condition. The major advantage of an oil-condition sensor is that it could signal the need for an oil change when the oil’s condition warrants it, reducing the likelihood for costly repairs due to overdue maintenance and equally eliminating unnecessary maintenance. A significant obstacle in the development of an online sensor is the large variety of oil formulations. It is necessary to look for common traits among oils to use in the development of an electrochemical sensor. An important factor that affects all oils is contamination by water. Water contamination may be caused by leaks from weak seals, moisture entering the lubricant stream from ambient sources, or by combustion. Water interferes with the lubricating properties of the oil by covering the working surfaces and increasing viscosity. It can also promote wear by increasing the rate of corrosion. Major engine manufacturers require a close monitoring of ppm amounts of water, with 2000 ppm (0.2% weight) commonly being used as a threshold for an engine shut down and lubricant change. If an engine is run for short periods, especially in cold weather, water and other combustion products can be condensed from the blow-by gases and result in high levels of absorbed and emulsified water in the oil. Development of an on-line sensor capable of accurate monitoring of ppm amounts of water contamination is an important step in making engines more efficient and safe. However, the development and application of any sensor to direct measurements in lubricating oils is complicated due to the complex nature of lubricant chemistry, the large variety of oil formulations, and different mechanisms of lubricant failure. For example, water may interact with oil through various mechanisms, leading to the formation of inverse micelles, microemulsions, and free non-bound water. Out of all available oil additives, detergents, considering their strong surfactant nature, will have the highest potential of interacting with water, leading to a formation of inverse micelles in a continuous hydrocarbon oil phase with detergent surrounding the water in microdroplets [4]. A continuous exchange between free non-bound water and water contained inside the inverse micelles occurs over a significant time period. At the same time water /oil balance can be affected by external factors, such as water evaporation at elevated temperatures, oxidative decomposition of oil additives, etc. These
processes add an additional degree of complexity to the problem of water quantification in industrial lubricants. Therefore, it becomes essential to study water /oil kinetics, including water equilibration between its predominant free non-bound and micellated phases, and the long-term chemical effects of water contamination on the properties of oil in order to develop an intelligent on-line water monitoring device. Versatile, sensitive, inexpensive electrochemical methods provide an ideal solution to the issue of monitoring of chemistry in highly resistive media, including oil degradation. Among these methods, cyclic voltammetry (CV) on microelectrodes and ac electrochemical impedance spectroscopy (EIS) demonstrated a remarkable potential for direct analysis of complex non-aqueous systems, including industrial lubricants [5 /11]. This work presents an application of a combination of microelectrode CV and EIS to continuous monitoring of the electrochemical properties of a typical diesel lubricant following an injection of a ppm amount of water. The monitoring was conducted over several days, allowing for careful studies of changes in the water/ lubricant system. CV was employed for an instantaneous detection of water-induced changes, while the ac impedance technique was utilized for monitoring water distribution among various spatially separated regions within the solution analyzed. At high frequencies the resistance of the bulk oil layer (Rbulk) can be determined, while at lower frequencies the interfacial or chargetransfer resistance (Rct) can be measured. Rct is inversely proportional to the electrochemical reactivity of the electrode j lubricant interfacial region, while Rbulk reflects the resistance of the engine oil [8]. In order to increase an understanding of the complex kinetics of water /oil interactions an empirical model of the phenomena was developed. The model consists of rate equations describing mass transport and charge transfer processes taking place over time, such as water emulsification resulting in formation of inverse micelles, evaporation of free and emulsified water, and water electrolysis. This type of application of mathematical analysis to verification of experimental data has been demonstrated before [12]. The kinetic rate constants for the water /oil interactions, often mentioned in the literature in a general sense, were verified both experimentally and through a numerical integration.
2. Experimental Three sets of experiments were run on a continuous flow system with a volume of approximately 40 l. Commercial SAE 15W-40 fresh and drain (end of test) oils were studied at both 50 and 60 8C (fresh) and only at 60 8C (drain). The fluid viscosity was approximately 15 cSt (100 8C). All oil samples were run continuously
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at a flow rate of /2.5 l min 1 and a pressure of /20 psi. Some fluctuations in flow and pressure (within 20%) were observed over the course of the experiment, although no visible effects on both EIS and CV signals were detected. The CV sensor comprised a three-electrode arrangement having a silver oxide wire acting as a reference electrode (RE), a Pt wire acting as a counter electrode (CE), and a Pt microwire serving as a working electrode (WE). The Pt WE (d /25 mm) and Pt CE were flamesealed in a glass capillary. The RE was prepared by oxidizing the Ag wire in aqueous acetate buffer solution at a potential of /1000 mV (vs. an Ag/AgCl/KClsat RE) for 10 min. The prepared electrode maintained a constant potential of approximately /350 mV (vs. Ag/ AgCl) for all experiments conducted, in both aqueous and non-aqueous systems. WE, CE, and RE were enclosed in a Teflon body with an outside stainless steel shell. CV scans were applied at 5 mV s1 between /10 and /10 V (vs. Ag/Ag2O) using a 660A Electrochemical Workstation (CH Instruments, Austin, TX). The EIS sensor consisted of two 1 cm2 Pt parallel plates spaced 0.5 mm apart. The ac impedance signal was measured between 100 kHz and 3 mHz at a sinusoidal input amplitude of 500 mV with a single run taking approximately 2 h. Electrochemical reactions were monitored with a Voltalab 40 potentiostat (Radiometer Inc., Westlake, OH). The distance between the oil tank and EIS and CV sensors was 3.175 m. Before the water injection a single measurement at both CV and EIS sensors was made to establish a baseline and to ensure that the oil was water-free. The water was injected between 0.05 and 1% by volume, with 0.2% (80 g) of water being the most typical amount injected. The first measurement was started immediately after the water injection, followed by a total of 25 /30 consecutive EIS and several CV sweeps to allow adequate time to show water loss (50 /60 h). At the end of the experimental session, some residual water still remained in the oil.
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rent on the electrode surface of a microelectrode can be expressed as [4]: Il 4nFDc rme
(1)
a function of the number of electrons in the electrochemical reaction (n ), Faraday’s constant (F ), the diffusion coefficient of the component in question (D ), the concentration of free water (water not incorporated into a micelle) in the bulk solution (c), and the radius of the microelectrode used in CV measurements (rme). The EIS analysis was based on continuous monitoring of the high-frequency bulk feature and the low-frequency charge transfer region on the impedance diagram relating real (Zreal) and imaginary (Zim) parts of the electrochemical impedance. Analysis of the EIS data revealed a complicated, time-dependent pattern of changes for both bulk and charge transfer semicircles for the fresh and drain oil samples. The results of all three EIS experiments are shown in Fig. 1. Before the injection of water the oil is mixed well with an excessive concentration of surface-active and generally negatively charged detergent molecules on the electrode interface. The EIS displays two clearly seen semi-circles: Rbulk, which is the electrical resistance of the bulk solution,
3. Results and discussion The first CV scan in the oil system following water injection revealed the appearance of an additional diffusion-controlled semi-reversible oxidation peak at //4.5 V with the corresponding reduction occurring at //3 V. The heights of both peaks were proportional to the amount of injected water between 100 and 10,000 ppm. The peaks rapidly decreased over time, finally disappearing after /2 h for the drain oil solution, and between 3 and 4 h for the fresh oil. An irreversible diffusion-limited peak at //5 V, corresponding to detergent oxidation, remained visible throughout the experiment. The diffusion-limited cur-
Fig. 1. Experimental time-dependent data following the water injection for: (a) Rbulk; and (b) Rct for: (A, a) Drain oil at 60 8C; (B, b) Fresh oil at 60 8C; (C, c) Fresh oil at 50 8C.
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and Rct, which is the electrical resistance near the electrode interface. It may be observed (Fig. 1) that immediately following the water injection the bulk resistance Rbulk increases dramatically, while Rct virtually disappears. This rapid change is followed over the duration of several hours by a gradual increase in Rbulk until it reaches its largest value, while the Rct semicircle remains insignificant. Later the Rct semicircle on the EIS diagram becomes visible again, while Rbulk gradually decreases with intermittent periods of stabilization. Several hours later the Rct reaches a maximum value while Rbulk continues its slow decrease. Then both Rbulk and Rct decrease gradually, with the decline of Rct being more pronounced. Several days after the injection, the EIS graph returns to its general original shape and Rbulk and Rct to values close to their original values, when all of the water is finally removed from the system. In Fig. 1, the complete time extensive process is clearly illustrated only by curve A. For processes illustrated by curves B and C more time would be required to remove water completely from the system. The complex kinetics of water /oil interactions, which combine several mutually dependent mass transport and charge transfer processes, are responsible for these time dependent changes of Rbulk and Rct values. We attempted to explain the above experimental data by proposing a simplified model describing mass- and charge-transfer processes in a water/oil system. The processes taken into account included emulsification of free non-bound water resulting in formation of inverse micelles, evaporation and electrolysis of both free and micellated water. Following the injection into the lubricant, the water gradually forms inverse micelles with surface-active oil additives (predominantly detergents). Bulk solution resistance increases due to immobilization of charge carrying detergents as a result of water entrapment inside inverse micelles. The immediate disappearance of a semicircle associated with charge transfer processes on the EIS plot (Rct 0/0) following the water injection allows for a very straightforward qualitative detection of water in the oil media. We suggest that a short-term electrophoretictype separation of water and hydrocarbon oil phase occur in the external electric field in the vicinity of the electrode surface. Under even a moderate electric field the mass transport of small water dipoles, with a dielectric constant of /80, is much more facile than that of large bulky polymers, with a dielectric constant of /2 [13]. A high local concentration of water dipoles is likely to be created in the vicinity of the electrode interface as a result of water redistribution in an external electric field. Relatively high water conductivity and the facile nature of charge-transfer reactions carried out through the water dipoles located in the interfacial region can explain the dramatic decrease in charge-
transfer resistance immediately following the water injection. Deposition of conductive layers of water on the electrode j solution interface and the significant presence of water dipoles in the diffusion layer cause displacement of polymer-based ionic and dipole oil species, normally responsible for charge-transfer processes. The contribution of these polymer-based species to charge-transfer processes becomes virtually nonexistent until the water is depleted from the surface. The similar effects of a water leak into an industrial lubricant, such as impairment of the lubricant film, oil additive precipitation, and formation of water pockets on the surfaces, have been observed before [3]. In the bulk solution, free non-emulsified water remains in equilibrium with the water entrapped inside the inverse micelles. After several hours, a point is reached where the maximum amount of detergent and water in the bulk is incorporated in the formation of the inverse micelles. This leads to a situation of lowest bulk solution conductivity as the two most prevalently conductive types of species, water and detergents, render each other electrically inactive through their mutual binding in inverse micelles. At this point the Rbulk value is at its largest, while the Rct is still insignificant. Over this period of time free water loss and water loss from the inverse micelles through temperature-induced evaporation also occur. It is quite plausible that evaporation of free water will be more facile than that of water entrapped inside inverse micelles, where the evaporation is hindered by electrostatic and steric effects of surrounding surfactant molecules. Eventually, the number of water layers concentrated at the electrode surface begins to decrease as the water is consumed through micelle formation, evaporation, and direct electrolysis on the electrode surface. The interfacial water consumption occurs faster than its replenishment by the remaining non-bound water in the bulk due to the dwindling supply of free water. As the space on the electrode surface becomes more readily available, due to water loss, the active detergent molecules begin to move to the interface to replace the water. Detergents, as we mentioned above, are generally not as electrochemically active as free water molecules. Rct starts to increase as the charge transfer processes on the interface become less facile, while Rbulk decreases slightly due to the decreasing effective concentration of the non-conductive water-containing inverse micelles as a result of their breakdown caused by evaporation of entrapped water. Several hours later, the remaining free water in the bulk is completely consumed, either by evaporation or formation of inverse micelles The bulk resistance continues to decrease at a very slow rate due to the decrease in the apparent concentration of water-containing inverse micelles. The breakdown of inverse micelles caused by the evaporation and electrolysis of micellized
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water increases the effective amount of available detergents. The Rct value reaches a maximum value representing the point of absence of free water at the interface. Any water remaining there is incorporated in inverse micelles, which discharge about 100 times more slowly than free water and even detergents (see discussion below). At the end of the experiment the remaining water in the system is slowly being removed from the inverse micelles through evaporation and discharge. The EIS graph will eventually return to the general shape that it was in before the injection, after all water is removed from the system.
4. Mathematical modeling In order to increase our understanding of the complex kinetics of water /oil interactions we have developed an empirical model describing the dynamics of water /oil interactions following the injection. The model consists of rate equations describing mass transport and charge transfer processes such as evaporation, absorption into inverse micelles, and electrolysis of water taking place over time in the water/oil system. These rate equations were initially solved by an Euler integration using both a 30 and a 3000 s time step. The results from these calculations were confirmed by using a Runge-Kutta Fehlberg algorithm included in the Polymath Software package.1 The definition of the equations for the water /oil interaction kinetics required several assumptions based on chemical engineering, thermodynamic, and electrochemical principles: . The water can be consumed in fresh or drain oil in three basic ways */by evaporation, electrolysis at the electrode surface, and absorption into inverse micelles. These processes are illustrated in Fig. 2. . The homogeneous mixing of water is assumed to occur instantaneously upon addition to the oil. . Inverse micelles are formed between free non-bound water and detergents (surfactants) of the oil additive package. Detergents are the only component of the oil solution that is interacting with water. . The chemical activity of detergents before and after emulsification of water is similar. . Water incorporated into an inverse micelle is lost through evaporation, and dissociation of the inverse micelles at the electrode followed by electrolysis. . Fundamental equations describing temperature-induced water loss in an open system are applicable 1 M. Sachham and M.B. Cutlip http://www.polymathsoftware.com/order/.
Fig. 2. Proposed mechanism of water interactions in the oil system after injection.
.
.
.
. . . .
. . . . .
to evaporation of water contained inside an oil-filled continuous flow system. Differences in charge transfer and bulk resistances between samples with and without water correspond to the charge transfer resistance incurred by free or micellized water. Experimentally determined rate constants for inverse micelle formation and average diffusion coefficients for inverse micelles are accurate. Immediately following injection, free water displaces all oil additives on and in the immediate vicinity of the electrode surface. Agglomerates of free (not incorporated into a micelle) water and micelles both have a spherical shape. There is no next neighbor interaction between water molecules on the electrode surface. Water molecules have 100% packing efficiency on the electrode surface. Electrolysis at the electrode surface occurs by direct electron transfer between the reacting species and the electrode. Inverse micelle formation is a first order process. The inverse micelle radii are approximately 10 nm for fresh, and 8 nm for drain samples [14]. The micellated water evaporation equation [15] holds for our modeling. Evaporation rates of free water on the electrode surface and in the bulk are identical. Steady state conditions exist for all equations.
4.1. Free water loss The first step necessary for the calculation of the kinetics of oil /water interactions is to determine the diffusion coefficient of free water in oil. For the initial calculations, we assumed that the water was broken down to the molecular level, r /300 pm [16], and would diffuse through the oil in this fashion. The diffusion
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Table 1 Results from free water calculations
105 DE S (cm2 s 1) 1010 DCV (cm2 s 1) 106 h (m s 1) 109 k (cm s 1) R (mm) 10 15 V (nm3) 10 16 n
Fresh 50 8C
Fresh 60 8C
Drain 60 8C
7.58 1.87 4.28 8.88 96 3.63 3.21
7.82 2.42 4.37 15.9 122 7.53 6.67
7.82 7.46 4.37 47.6 31 1.30 0.12
I nF pr2me c k3
DE S, diffusion coefficient from the Einstein /Stokes equation for one water molecule; DCV, diffusion coefficient by CV for a water agglomerate; h , mass transfer coefficient; k , rate of charge transfer; R , radius of water agglomerate; V , volume of water agglomerate; n , number of molecules in water agglomerate.
coefficient for a single molecule of water is derived from the Einstein/Stokes equation (D /kbT /(6pmr)) (Table 1). This diffusion coefficient is used in an equation that describes the mass transport of water through the system [17]. Sh hl=D 0:664Re1=2 Sc1=3 Re vl=m Sc m=D
(2) (3) (4)
where ‘v’ is velocity, ‘l’ is the characteristic length, ‘D ’ is the diffusion coefficient, and ‘m ’ is viscosity. Eq. (2) is generally used for fluids diffusing into gases (with ‘Sh ’ as the Sherwood number, ‘Re ’ as the Reynolds number, and ‘Sc ’ as the Schmidt number), but was modified to fit the current situation based on assumptions made about the oil/water system. The characteristic length (l ) used in this equation was the width of the tank (30.5 cm). By solving the equations for (h), the mass transfer coefficient, the result was used in the following equation (evaporation of one component from a two component system) [17] to determine the rate (k1, in g s 1) at which free water evaporates from the oil of surface area (A ): k1 hArf (1f)
by the applied potential and electrolyzed at the surface [18]. The diffusion coefficients can be calculated from the CV data and Eq. (1). The rate of charge transfer for water is calculated from the CV data and Eq. (6) [19]:
(5)
Eq. (5) considers that the rate of evaporation will be limited by the amount of water vapor that can be held in the oil, through the application of saturation density (rf /0.129 kg m 3 [17]) and relative humidity (f). The vapor phase water in the oil will eventually leave the system either by passing into the air above the oil tank or condensing on the flow pipes of the system. The model does not take the variability induced by these effects into account. The specific densities of water in the oil in the fluid and vapor will remain constant since the water is going from a liquid in oil to a vapor in the oil phase at constant temperature. Table 1 shows the values obtained from these equations. The next loss of free water from the system occurs at the electrode. Here the water is drawn to the electrode
(6)
where ‘I’ is the current, ‘n’ is the number of electrons, ‘F ’ is Faraday’s constant, ‘rme’ is the radius of the microelectrode, and ‘c’ is the concentration of water in the bulk. This predicts a rate of charge transfer (k3) on the order of 1/108 cm s 1 and a diffusion coefficient for water on the order of 1 /1010 cm2 s 1 (Table 1). Note that experimental diffusion coefficients (Eq. (1)) are / 105 times smaller than the theoretical diffusion coefficients calculated by the Einstein /Stokes equation for a single water molecule (Table 1). In reality, when water is injected into oil it remains in large agglomerates of water molecules for an extended time. By comparing the experimental diffusion coefficients to those obtained for free water from the Einstein/Stokes equation the average size of a water agglomerate in the oil can be determined. The ratio of the diffusion coefficients is inversely proportional to the ratio of particle radii. When the radius corresponding to a water agglomerate is obtained its volume can be divided by the volume of a single water molecule, with a radius of /0.3 nm [16] (4/ 3p /0.33 nm3 /0.11 nm3). By assuming 100% packing efficiency, the number of water molecules in a single water agglomerate can be calculated (Table 1). The average size and number of molecules contained in a water agglomerate represents what happens to the water immediately after it is added to the oil before the mixing and chemical interactions with oil additives (detergents) break it apart. Over time the average agglomerate size decreases as water is evaporated, taken into inverse micelles, and electrolyzed. The agglomerates are larger in the 50 8C sample than the 60 8C sample due to increased temperature facilitating finer water dispersion. The average volume of water agglomerates in the drain is smaller probably due to stronger chemical interactions with the more polar drain components (Table 1). The third process considered for removing free water from the system was the formation of inverse micelles [4]. The rate constant of inverse micelle formation for each oil system depends on the chemical composition of the oil. Due to the lack of definitive literature data describing this phenomenon, rate constants were chosen so that the model would fit the time dependent changes in Rbulk values. An initial step was to determine the process of inverse micelle formation. This was done by setting up models for both first and second order formation rates; the first order process provided a better fit to the time dependent changes in the experimental data. For the fresh oil at 60 8C the rate constant was estimated as 104 s 1, for the fresh oil at 50 8C the rate
M.F. Smiechowski, V.F. Lvovich / Journal of Electroanalytical Chemistry 534 (2002) 171 /180
constant was 7.5 /105 s 1. For the drain oil the estimated rate constant was approximately 1.5 times greater (1.5 /10 4 s 1) than the fresh oil for the same conditions. In the work by Clint et al. [15], it was assumed that the water added to a sample would be emulsified over a period of several minutes. This corresponds to a rate constant of about 10 3 s 1. Our assumed values for the rate of water evaporation from an inverse micelle differ from this value by an order of magnitude; considering the differences between our samples and the prepared samples used in their experiments the estimation seems reasonable. It should be noted that the drain rate constant is not applicable for any drain oil at all times. The chemical conditions of the drain oil are never the same, so this approximation holds only for the drain oil used in this experiment. The final step in modeling the amount of free water is to put the three rates; evaporation from the bulk and the electrode surface (k1), inverse micelle formation (k2), and electrolysis at the electrode (k3) together. This is shown below: rate dc=dt$ Dc=Dt (cf ci )=Dt k1 k2 cf k3 cf
(7) (8)
The resulting equation for the Euler integration relating initial (ci) and final (cf) concentrations of water over time is as follows: cf (ci k1 Dt)=(Dt(k2 k3 )1)
(9)
Fig. 3 shows a plot of the data for all three oil cases. The arrows on the chart display approximately where the free water is completely consumed for each case. For the smaller step size, the theoretical results predict faster water consumption than the experimental ones. This can be explained by either the lower time accuracy of our method of experimentation, where 2 h elapsed between consecutive measurements, or from an over-approximation in our model caused by our assumptions. The values for the above calculations are illustrated in Table 2. The table illustrates that the calculated values for the disappearance of free water correspond well to the
experimental values obtained with EIS. As the temperature decreased by 10 8C, the amount of time required till all of the free water was consumed increased by approximately 33%. For the drain, it took 70% less time for complete free water consumption than for the fresh oil at 60 8C. 4.2. Loss of water from inverse micelles The process by which water enters the inverse micelle has already been described; the water is lost from an inverse micelle by evaporation or it is dissociated from the inverse micelle [4]. Describing the evaporative losses from the inverse micelles is a complex task. By adopting an equation describing a dodecane/detergent solution [15] to a water/oil system, we were able to predict the evaporative losses from inverse micelles in the solution. The equation, derived by Clint et al. [15], presents a relative mass loss as: m=mo 8p2
X
(2z1)1 exp[(2z1)2 h2 t Dt]
z0
km
(10)
Where ‘D ’ is the diffusion coefficient for the inverse micelles in the solution calculated by the Einstein/ Stokes equation, ‘z ’ is the summation index and ‘ht’ is the height of the oil in the tank. The theory behind the evaporation equation and how the end value of the sum is chosen is described in detail in the literature [15]. The result is expressed in the fraction of mass remaining after a period of time, and is independent of the original starting mass (80 g), much like the evaporation of the free water. The summation in the evaporation equation for water in inverse micelles is carried out until the required degree of accuracy (the value of the next iteration of the summation) is obtained. Table 3 shows the results from these calculations. It was assumed that the inverse micelles would be attracted to the electrode and once there, spontaneously split apart, releasing the water to the electrode. The equation for the dissociation process is [20]: k4 RT=((nF )2 Ac c Rct )
Fig. 3. Illustration of calculated free water in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
177
(11)
where ‘k4’ is the rate of micelle electrolysis, ‘R ’ is the ideal gas constant, ‘n ’ is the number of electrons, ‘F ’ is Faraday’s constant, ‘Ac’ is the area of the electrode, ‘c’ is the bulk concentration, and ‘Rct’ is the charge transfer resistance. The largest Rct values from the experimental data (Fig. 1) were selected for this calculation. This corresponds to the highest accumulation of the electrochemically inactive inverse micelles in the interfacial region. The results from this calculation are listed in Table 3. The charge transfer coefficients calculated in this method are less than those for water (Table 1) because
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Table 2 Experimental vs. calculated results Fresh 50 8C
Fresh 60 8C
Drain 60 8C
Theoretical time till free water consumption, 3000 s step size (h) Theoretical time till free water consumption, 30 s step size (h) Experimental time range till free water consumption (h)
24 21 20 /26
18 16 16 /20
14 11 12 /16
Theoretical time of peak inverse micelle formation, 3000 s step size (h) Theoretical time of peak inverse micelle formation, 30 s step size (h) Experimental time of bulk peak inverse micelle formation (h)
15.0 7.3 6 /8
12.5 6.0 6 /8
9.2 4.5 4 /6
Calculated maximum mass of water on surface (ng) Calculated maximum thickness of water layer (mm) Calculated time when evaporation stops (h) Experimental time when evaporation stops (h)
448 1.27 21.3 20 /26
583 1.65 15.7 16 /20
1480 4.20 11.2 12 /16
Table 3 Inverse micelle calculations Fresh 50 8C 106 DE S (cm2 s 1) Fraction of mass remaining after 30 s 10 6 Charge transfer resistance (V) 1010 k (cm s 1)
2.28 0.99953 18.0 1.44
Fresh 60 8C
Drain 60 8C
2.35 0.99952
2.93 0.99947
6.8
3.5
3.94
7.65
DE S, diffusion coefficient from the Einstein /Stokes equation for one inverse micelle; k , rate of charge transfer.
of sluggish electron transfer through the inverse micelle hindered by the spatial impediments and the nonconducting nature of water /oil structures. The electrons tunnel through the associated structures of inverse micelles in the vicinity of the electrode surface (diffusion layer) at a rate much slower than a reduction/oxidation reaction of free water (k3 water / /1/108 cm s1) or a single detergent molecule at the surface (k3 detergent / /1 /108 cm s 1). This last value was calculated from CV data and Eq. (6). Electrons, even from inverse micelles positioned directly on the surface of the electrode, have to travel across a distance of approximately 5 nm to reach the electrode [4]. The equation for modeling the concentration of water in inverse micelles is derived when rate constants of evaporation from inverse micelles (km), inverse micelle dissociation and discharge (k4), and the rate of formation of inverse micelles (k2) are considered. The resulting equation is solved for the final concentration of water in inverse micelles (cmf), rate dc=dt$ Dc=Dt (cmf cmi )=Dt
experimental time factors for inverse micelle formation were taken to be equal to the time when Rbulk in the EIS diagram reaches its largest value. Fig. 4 shows that the drain oil has the earliest inverse micelle peak, this corresponds with the fact that the drain oil will have oxidation products, such as carboxylic acids, that will also form inverse micelles with water and consume it faster. The other two curves representing the fresh oil correspond to the mechanism, but are slightly slower in peak time and encapsulate less total water due to a lower temperature and less chemically active starting material to form inverse micelles. The mathematical model predicts that the mass of water in the inverse micelles drops quickly over time (Fig. 4), while the experimental EIS data demonstrate a more gradual reduction. This discrepancy can be explained by what the model estimates and the EIS measures. The model approximates the amount of water in inverse micelles at a given period of time, and the Rbulk from the EIS data is proportional to the amount of inverse micelles in the bulk. An inverse micelle can hold one to several molecules of water. So the water loss shown by the model can be correlated to the EIS data through the loss of water in inverse micelles, not the loss of inverse micelles themselves. Another possible explanation of this discrepancy is an overestimation in the
(12)
cmi km k2 cf k4 cmi
(13)
cmf cmi km k2 cf Dtcmi k4 Dt
(14)
Table 2 shows that the calculated results from Eq. (13) are comparable with the experimental EIS data. The
Fig. 4. Illustration of calculated mass of water in micelles in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
M.F. Smiechowski, V.F. Lvovich / Journal of Electroanalytical Chemistry 534 (2002) 171 /180
rate of water evaporation from the inverse micelles. We assumed that this equation describing evaporation of water from dodecane/surfactant would be applicable to oil/water systems in general.
179
In the case of the preceding equations, k1 is the evaporation rate constant for free water in the entire system, which is dependent only on temperature. The value of k1 is multiplied by the ratio of the concentration of free water at the electrode surface to the amount of free water in the bulk to account for the portion of water on the electrode surface compared to the total amount of free water in the system. When the value of ci reaches zero the evaporation term is applied without the ratio of cei to ci. Fig. 5 illustrates the time dependent results of Eqs. (15) /(17) used to calculate the amount of water on the surface of the electrode for all three cases studied.
The results of this model correlated well to the EIS data. The arrow at the end of each curve corresponds to the point in time when evaporation stops affecting the water on the surface of the electrode. This point is also aligned with the time when there is no more free water in the bulk, and water is no longer replenished at the interface. Although the graph appears to show the absence of water on the interface, this is not entirely correct. A closer look at the data shows that once the water is reduced to approximately 3 layers (3 layers/(pr2)) / (electrode surface area/6.022 /1023) /3/(p /3002 2 2 pm ) /(1 cm /6.022 /1023) /3 /107 g), the attractive force of the electrode’s potential field holds the water in place. This phenomenon has been observed before [21]. The only way water can be removed from the surface in this case is by electrolysis since the amount of energy required to overcome the potential field for the water to evaporate or be absorbed into an inverse micelle is too large. Therefore, these last layers of water will remain on the surface of the electrode for several hours due to the slow rate of electrolysis. Eq. (17) can also be used to calculate the total number of layers of water molecules on the surface of the electrode (Fig. 6). The number of molecules of water on the electrode surface is calculated from the mass of water on the surface. This number is then multiplied by the area of a water molecule (pr2 /p /3002 pm2 / 2.8 /1015 cm2) and divided by the area of the electrode surface (1 cm2). By assuming a 100% packing ability the thickness of the water layer can also be determined by multiplying the number of layers by the diameter of a water molecule (d/600 pm). In all three cases the thickness of the water layer never grew to a size that could be considered out of proportion to the electrode spacing (0.05 cm) (Table 2). If we were to assume only a 50% packing efficiency for the water on the electrode surface, the results of water thickness would still be reasonable when compared to the electrode spacing. This is important when considering that not only water will be on the electrode surface but
Fig. 5. Illustration of calculated water mass on the electrode surface in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
Fig. 6. Calculated number of water layers on the electrode surface assuming perfect packing in: (a) Drain oil at 60 8C; (b) Fresh oil at 60 8C; (c) Fresh oil at 50 8C.
4.3. Water on the electrode surface Modeling of the interaction of water at the surface of the electrode also corresponds to data points collected through EIS and provides another test of the model’s accuracy. By assuming that the evaporation of free water on the surface of the electrode occurs at the same rate as the evaporation of the free water left in the bulk, the evaporation of free water from the electrode surface would stop at the same time as the free water in the bulk had been consumed. An equilibrium state was assumed between the free water on the electrode surface and the water in inverse micelles in the bulk, resulting in zero net loss of water to inverse micelle formation from the electrode. The following equation was developed to describe the initial (cei) and final (cef) concentration of water on the electrode surface as functions of the diffusion to the electrode (k5), the rate of evaporation (k1), and the rate of dissociation (k3): rate dc=dt$ Dc=Dt (cef cei )=Dt k5 (ci cei )k1 cei =ci k3 cei cef cei (1k5 tk1 Dt=ci k3 Dt)k5 Dtci
(15) (16) (17)
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also inverse micelles and polymeric oil additives will be attracted to the surface and in the process take up available space.
5. Conclusions When water is injected into oil it forms large agglomerates with the size depending on mixing and interaction with the oil additives, mostly detergents. These water agglomerates decrease in size over time as water is evaporated, electrolyzed, and emulsified. The predicted size of the water agglomerates was smaller with higher temperature and increased oil aging, due to higher temperatures facilitating finer water distribution and aged oil containing a larger amount of polar components. At the same time a short-term separation of the water and hydrocarbon oil phases occurs in the external electric field near the electrode surface. Deposition of conductive layers of water on the electrode j solution interface and a significant presence of water dipoles in the diffusion layer causes displacement of polymer-based ionic and dipole species, normally responsible for charge-transfer processes. Relatively high water conductivity and the facile nature of charge-transfer reactions carried out through water dipoles located in the interfacial region explain the dramatic decrease in Rct immediately following the water injection. Several processes can describe the history of water /oil interactions: incorporation into inverse micelles, evaporation of free and emulsified water, and electrolysis. The experimental and computed data demonstrated that electrolysis is negligible and that evaporation of emulsified water is a slow process (Figs. 3 /5). Through the comparison of the diffusion coefficients and relative electrochemical activities of water, detergent, and inverse micelles in the vicinity of the electrode, the mechanism of corrosion inhibition can be envisioned. The electrochemical activities for detergent and especially water are higher than the electrochemical activity of an inverse water/detergent micelle by several orders of magnitude. The interaction between water and detergent resulting in the formation of an inverse micelle is much faster than redox reactions of either water or detergents. This results in electrochemically passive inverse micelles forming on the surface of the electrode, and suppression of individual redox reactions involving water or detergents. The experimental data and mathematical model presented demonstrate the applicability of the electrochemical approach to development of a water monitoring on-line device capable of providing information on time-dependent water /oil interactions in industrial lubricants. Empirical kinetic parameters from the model were in reasonable agreement with the general literature data, which serves as another indirect indicator of
viability of the presented method of combining electrochemical experiments and mathematical modeling. The experimental approach combining voltammetry and ac impedance techniques can be used in practice for development of water-in-oil sensors, while the mathematical model can be utilized for broader evaluations of time-dependent water /oil interactions. The model developed provides a good evaluation for the history of water after it enters the oil-based system and illustrates the complex nature of water/oil interactions many hours after water injection. It is recommended that more work be done to confirm the accuracy of the assumptions, and to perform further studies to model the effects of aging on oil. Acknowledgements The authors would like to thank the Lubrizol Corporation for their financial support and for allowing this paper to be published. References [1] D. Cipris, A. Walsh, T. Palanisamy, in: D.R. Turner (Ed.), Sensors for Motor Oil Quality, The Electrochemical Society Proceedings Series, Pennington, NJ, PV 87-9, 1990, p. 401. [2] S.S. Wang, H.S. Lee, D.J. Smolenski, Sens. Actuators B 17 (1994) 179. [3] S.Q.A. Rizvi, Lubricants and Lubricant Additives, Lubrizol Corp., 1995. [4] J.F. Rusling, in: A.J. Bard (Ed.), Electroanalytical Chemistry, A Series of Advances, vol. 18, Marcel Dekker Inc., New York, 1994, pp. 1 /88. [5] A.M. Farrington, J.M. Slater, Analyst 122 (1997) 593. [6] S.R. Jacob, R.G. Compton, J. Electrochem. Soc. 146 (1999) 2598. [7] R.J. Price, L.J. Clarke, Analyst 116 (1991) 1121. [8] S.S. Wang, H.S. Lee, Sens. Actuators B 40 (1997) 193. [9] S. Wang, Sens. Actuators B 73 (2001) 106. [10] S. Wang, Tribology Trans. 44 (2001) 411. [11] S. Wang, Sens. Actuators B 4305 (2002) 1. [12] V.F. Lvovich, A. Scheeline, Anal. Chem. 69 (1997) 454. [13] S. Grimnes, O.G. Martinsen, Bioimpedance and Bioelectricity Basics, Academic Press, London, 2000, p. 60. [14] R.E. Kornbrekke, P. Patrzyk-Semanik, T. Kirchner-Jean, M.G. Raguz, E.A. Bardasz, Advances in Powertrain Tribology, SP1390, 1998. [15] J.H. Clint, P.D.I. Fletcher, I.T. Todorov, Phys. Chem. Chem. Phys. 21 (1999) 5005. [16] J.A. Dean, Lange’s Handbook of Chemistry, 15th ed., McGrawHill, New York, 1999, p. 439. [17] F.D. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley and Sons, New York, 1996, pp. 284 /332. [18] I.G. Harpur, N.J. Wayth, A.G. Bailey, M.T. Thew, T.J. Williams, O. Urdahl, J. Electrostat. 40 /41 (1997) 135. [19] A.J. Bard, L.R. Faulkner, Electrochemical Methods, John Wiley and Sons, New York, 1981, p. 91. [20] J.R. Macdonald, Impedance Spectroscopy: Emphasizing Solid Materials and Systems, John Wiley and Sons, New York, 1987, p. 21. [21] T. Doll, I. Eisele, 8th International Meeting on Chemical Sensors, Abstract Book, Basel, Switzerland, 2000, p. 110.