The Combined Effects of Deterministic DLVO Forces and Random

Article pubs.acs.org/Langmuir

Stability of Emulsified Heavy Oil: The Combined Effects of Deterministic DLVO Forces and Random Surface Charges Payman Esmaeili, Feng Lin, and Anthony Yeung* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2 V4 ABSTRACT: When dispersed in aqueous solution, droplets of bitumen (extra heavy oil) are known to acquire negative surface charges. The resulting electrostatic repulsion, according to traditional DLVO theory, is far too strong for any droplet coalescence to occur. However, from experience it is known that bitumen droplets do coalesce in aqueous suspensions. Furthermore, the process appears to be random, with the probability of coalescence increasing sharply with the drop size. To explain these facts, we modeled the bitumen−water interface as a heterogeneous surface comprising charged “patches”; the zeta potentials of the patches constitute a random variable that is assumed to be Gaussian. The traditional DLVO theory, according to this model, remains sound on the local scale (i.e., for patches interacting across an intervening water layer). Such a theory can predict the probabilities of coalescence in remarkable detail. A parameter central to this theory is the lateral extent of the charged patches, which was estimated to be in the neighborhood of 0.6 μm.

1. INTRODUCTION The Canadian oil sands in northern Alberta represent the second largest proven reserves in the world.1 The predominant method of recovering this heavy oil  also called bitumen  involves not the drilling of wells, but is a mining + flotation process (much like in mineral processing).2 For such an operation to be successful, it is imperative that the bitumen droplets be able to coalesce readily with one another in an aqueous environment (i.e., in the flotation vessel); this allows the oil droplets to combine as a “froth” and be collected at the top of the flotation vessel. In practice, bitumen is recovered by flotation often with remarkable success, suggesting that the bitumen droplets do coalesce in aqueous suspensions. There is, however, a caveat to this: under certain (unfavorable) conditions, when the bitumen exists as finely dispersed droplets (typically 100 μm or less), the amount of oil recovered is known to decrease sharply  sometimes to practically zero. This implies that smaller oil droplets are much less likely to coalesce than larger ones. As visual confirmation, the coalescence of bitumen drops can be observed directly through special viewing cells. As expected, coalescence is much more prominent among large bitumen drops (i.e., those that are millimeters in size). Although the coalescence of bitumen in water is undeniable, the science behind such a process remains poorly (if at all) understood. The following are apparent discrepancies between empirical observations and the basic principles of colloid science: • The surfaces of bitumen droplets are negatively charged, with zeta potentials having magnitudes of order 10 mV. The resulting repulsive stress between the liquid drops, according to traditional DLVO theory (assuming typical © 2012 American Chemical Society

values for the various physical parameters), is far too strong for any coalescence to occur. (In making this argument, we use the fact that the maximum compressive stress between two liquid drops is of the same order as the Laplace pressure, whose order of magnitude can be estimated based on an interfacial tension of ∼10 mN/m; see ref 15) • Traditional DLVO theory cannot explain the fact that larger droplets are more prone to coalescence than smaller ones. Indeed, larger liquids drops are more “floppy” (due to lower Laplace pressures) and thus are less capable of overcoming disjoining pressures when they collide. • The DLVO theory is deterministic; that is, for a given set of experimental conditions, the theory predicts either coalescence or otherwise, with 100% certainty in either case. This, as will be demonstrated in this study, is in stark contrast to what is observed: even under carefully controlled conditions, coalescence appears to be a random occurrence. (We would like to point out here a possible source of confusion: The aggregation of Brownian particles via DLVO forces, for example, may appear random. However, the stochastic nature of Brownian aggregation is due entirely to its transport mechanism; the DLVO interactions are fundamentally deterministic.) It is perhaps tempting to invoke “non-DLVO” forces, such as the hydrophobic interaction,3 to explain the first anomaly. Received: October 30, 2011 Revised: February 18, 2012 Published: February 27, 2012 4948

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The first point to note is that, with controlled contact experiments, the role of hydrodynamics in droplet−droplet coalescence is completely removed. Two points are noted here regarding the circumvention of hydrodynamics: (a) As the droplets are not transported by orthokinetics, the collision frequency between droplets is no longer a function of particle size; small droplets can now be manipulated into contact just as frequently as the larger ones. (b) For each test, the two oil droplets are maintained in contact for 60 s (assuming, of course, coalescence does not occur during this time). This is to allow sufficient time for any film drainage dynamics to fade out. (It is estimated that the intervening water film between two droplets would drain out over a characteristic time of ∼0.1 s.4) This careful avoidance of hydrodynamics allows what remains, the true interparticle interaction, to be studied in a systematic manner. In what follows, details regarding the setup of such an experiment are discussed. 2.1. Bitumen Suspension: Preparation and Control of Droplet Surface Charge. In this study, bitumen supplied by Syncrude Canada Ltd. (the so-called “DRU bottoms”) was used as the dispersed oil phase. This is extra heavy crude oil extracted from the Athabasca oil sands that is ready for downstream upgrading. Prior to its usage in our contact tests, submicrometer clay particles must be removed from the bitumen by first diluting it in toluene (90% toluene by weight) and centrifuging the solution at 50 000 g for 30 min. Based on simple Stokes drag analysis, all solid particles larger than 50 nm are expected to have been eliminated by this procedure. To remove the toluene from the “solids-free” supernatant, a combination of rotary evaporator (BÜ CHI, model no. R200) and vacuum oven (Fisher Scientific, model no. 285 A) was used. Much of the toluene was first recovered by the rotoevaporator at 60 °C for 1 h; the remaining toluene residue was then evaporated by leaving the rotoevaporator concentrate in an oven at 70 °C until the original bitumen mass was recovered. For the suspending (aqueous) phase, “simulated process water” (SPW) was used. This was an electrolyte designed to mimic the chemistry of actual commercial process water used in bitumen extraction. (Chemical analysis of the process water was provided by Syncrude Canada Ltd.) SPW was made by dissolving 25 mM of NaCl, 15 mM of NaHCO3, and 2 mM of Na2SO4 into deionized water. The concentration of calcium ions in SPW was left as an adjustable parameter (by adding varying amounts of CaCl2). This was done because Ca2+ is known to be a strong potential-determining ion for bitumen in water. As such, calcium ions (in trace amounts) was used in this study as a control of the surface zeta potential. The pH of the SPW at all calcium ion concentrations was 8.5 ± 0.1. Bitumen suspensions were created by adding 20 mL of SPW to 1 g of solids-free bitumen. The mixture was agitated in an ultrasonic bath (Fisher Scientific, model FS6) at 80 °C. An elevated temperature was chosen to reduce the viscosity of the oil phase. Depending on the duration of sonication, the average size of the bitumen drops could range from millimeters to micrometres (with sonication times of 30 and 60 s, respectively). After sonication, the heated suspension was left to cool to room temperature before experimentation. As mentioned above, the surface charge of bitumen droplets depends very strongly on the concentration of Ca2+ ions. To characterize such an effect, trace amounts of CaCl2 was added to the bitumen suspensions, and the resulting zeta potential of the dispersed oil droplets was determined from electrophoresis (using Brookhaven ZetaPALS) assuming the Smoluchowski limit. 2.2. Contact Experiment and the Probability of Coalescence. Micropipets, as shown in Figure 1, were used to study the interactions between suspended oil drops. This technique was originally developed in the field of biophysics for studying blood cells and surfactant membranes;5,6 it was recently adapted for engineering research studies.7,8 As shown in Figure 2, a suspension of bitumen droplets was placed in a “sample chamber.” Two small glass suction pipettes were extended into the chamber to capture and manipulate individual oil droplets (whose sizes ranged from 10 to 1000 μm). The micropipets were mounted on hydraulic manipulators, which enabled motions of the

However, such forces are invariably deterministic (at least in the forms that they are proposed) and thus are incongruent with the third observation  that coalescence is a random process. The non-DLVO forces also cannot account for the size-dependent effect (second point above). Regarding size dependence, it is true that hydrodynamics can be an underlying cause, as larger particles collide more frequently than smaller ones in a flow situation, and thus have higher chances for coalescence (e.g., in simple shear, the collision frequency increases as the third power of the particle size). Nevertheless, we will demonstrate in this study that the effect of particle size remains very prominent even under quiescent conditions. As such, hydrodynamics, although important, cannot be the only reason for the strong dependence of coalescence on drop size, and one is compelled to seek an alternative  and more fundamental  explanation. The present study concerns the colloidal stability of emulsified bitumen droplets in aqueous suspensions, with particular emphasis on the above-mentioned anomalies. We will first introduce, in the next section, a special procedure which utilizes micropipets to perform contact experiments between emulsified oil drops in aqueous environments. These experiments are tailored to reveal  and more importantly, quantify  the various effects associated with the three anomalies. We then put forward a model which combines the classical DLVO theory with randomly distributed surface charges, and demonstrate that such a theoretical construct can predict quantitatively all of the apparently inexplicable features associated with droplet−droplet coalescence.

2. MATERIALS AND METHODS In this study, we take the most direct approach to studying the colloidal stability of bitumen droplets in aqueous suspension: two dispersed oil drops of roughly equal size, with diameters ranging from 10 to 1000 μm, are captured by suction micropipets and pressed together. The controlled variables include: the chemistry of the surrounding aqueous phase, the zeta potential of oil drop surfaces (through adjustment of calcium ion concentration in the aqueous phase), the drop size, and the degree of deformation of the droplets. The quantifiable result is whether coalescence would occur or not (i.e., a binary outcome). A photograph of such a “contact test” is shown in Figure 1 below:

Figure 1. The contact experiment: two bitumen droplets, with diameter of order 10 μm, are being pressed together using micropipets; the surrounding liquid is an electrolyte referred to as “simulated process water.” Even under carefully controlled conditions, this experiment may or may not result in coalescence of the droplets. The coalescence process appears stochastic. 4949

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3. THEORY OF SURFACE HETEROGENEITY The main shortcoming of traditional DLVO theory is that it assumes the interacting surfaces to be homogeneous, i.e. the surfaces are considered molecularly smooth and uniformly charged. For liquid−liquid interfaces, such as the case here, the assumption of smooth surfaces is likely valid.9,10 On the other hand, it is entirely possible that bitumen-water interfaces can be randomly charged. This, for example, can be due to random distributions of different ionized groups at the oil drop surface. (If one could map the variations of the zeta potential ζ along the bitumen surface with sufficient resolution, the result may appear as a random signal.) As such, the obtained values of zeta potential from electrophoretic measurements may in fact be averaged zeta potentials. It is worth mentioning that previous efforts to measure the bitumen surface potential using atomic force microscopy confirmed that the surface potential indeed fluctuated locally along the surface.11 Although that study was the first of its kind, it did demonstrate two important points: (a) that the zeta potential along the oil−water interface was indeed nonuniform, and (b) the fluctuations in zeta potential did show characteristic length scales that were much larger than molecular dimensions The notion of unevenly charged surfaces had been suggested by Velegol and co-workers,12 who considered the effects of surface charge heterogeneities on the electrophoretic translation and rotation of colloidal particles. Subsequent studies by Adamczyk and co-workers,13 and also Santore and coworkers,14 have clearly demonstrated the significant impact of surface heterogeneities on colloidal stability. For bitumen-water interfaces, a similar idea of charge heterogeneity was independently proposed by Yeung et al.15 Here, to capture this complexity, we will assume the bitumen drop surface to comprise many local “patches”; the patches are characterized by a size L, and each patch possesses its unique zeta potential ζi (see Figure 3).

Figure 2. A schematic of the micropipet setup. An oil dispersion is placed in a small glass cell as shown in the blow-up view. Individual oil droplets can be captured by micropipets and controlled using micromanipulators. pipet tips to be controlled on the micrometer scale. These experiments were monitored in real time under an inverted microscope (Zeiss Axiovert 200), and the images were recorded for subsequent analyses. In our experiments, droplet pairs of diameter 10 μm, 100 μm, and 1000 μm were chosen; the error in drop size was ±5% or better. It is noted that the process of choosing droplets of the appropriate size was not as painstaking as one might expect, as we had the “luxury” of picking single drops from a very large selection. Droplets of the desired diameter were quickly identified with the aid of “electronic calipers” that was equipped with the Axiovert microscope. The glass micropipets were prepared from capillary tubes (Kimble Glass Inc.) with outer and inner diameters of 1 mm and 0.7 mm, respectively. Using a hot wire pipet puller (Kopf, model 730), the glass tubings were stretched in the axial direction under high temperature to create tapered capillary tips. With a homemade forging apparatus, the ends of the pipettes were truncated to produce very smooth tips with desired internal diameters which could range between 5 to 500 μm. To capture individual oil droplets, suction pressure was applied at the pipet tips. This was achieved by connecting the large (back) end of the pipet to a syringe through flexible tubing; as such, suction pressures at the pipet tips could be adjusted easily. With these capabilities, it was possible to conduct contact experiments by holding two individual droplets at the tips of suction pipettes and pressing them together (see monitor image in Figure 1). As standard procedure, every droplet pair was forced to remain in contact for 60 s. The deformation ratio DR, which was the ratio of the major to minor axes of a deformed drop (i.e., the ratio of the longest to shortest lengths), was kept at predetermined values. It is important to note that, under identical experimental conditions, two oil droplets may or may not coalesce. The underlying mechanism of bitumen coalescence appears therefore not to be deterministic; it may, however, be quantified through a probabilistic approach as follows: After repeating the contact experiments a number of times (typically 100 trials), the probability of coalescence was obtained. Such a probability was defined as the fraction of events which resulted in positive outcomes. To be clear, the probability of coalescence Φexp is

Φexp ≡

number of contacts that resulted in coalescence total number of contacts

Figure 3. Model of a heterogeneously charged bitumen drop surface. The patches have characteristic size L, and each patch possesses its unique zeta potential ζi. The average zeta potential, ζave, is determined from electrophoresis.

As the simplest model, we will assume the ζi’s to be statistically independent and follow a Gaussian distribution with average ζave and standard deviation σζ. The value ζave is assumed to coincide with what is measured from electrophoresis (results in next section) and is thus considered to be a known quantity. This leaves the present model with two undetermined parameters: σζ and L. These parameters will be curve fitted to the experimental data from eq 1. Before proceeding with this, we will first discuss how the theoretical coalescence probability Φ is determined within this theoretical construct. Consider two bitumen droplets that are pressed together using micropipets (as shown in Figure 1). What is controlled in

(1)

where the subscript “exp” denotes “experimental.” (Note that Φexp is just the reciprocal of the stability ratio.) As we noted earlier, the probabilistic nature of the coalescence process cannot be explained by the DLVO theory. However, if we envisioned the surface charges to be distributed randomly on the bitumen-water interface, it is possible to model the observed randomness. Such a model of surface heterogeneity is described in the following section. 4950

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destabilization can now be calculated from relations 4 and 5 as follows:

such an experiment is the degree of deformation DR, defined as the ratio of the major to minor axes of the deformed drop. The value DR can be related to the actual radius of contact rc (through a detailed calculation of drop shapes based on the Young−Laplace equation16). The area of contact, given by πrc2, is thus considered to be known once DR is specified. Assuming the bitumen drop surface to be composed of local charged patches of size L, the situation in Figure 1 would lead to “DLVO interactions” of N pairs of opposing patches, where N is given roughly by N≈

φ=

∫ζ ζ < 64 mV2 f (ζ1, ζ2) dζ1 dζ2 1 2

(6)

Graphically, φ is the volume under the probability density function that is within the region defined by eq 4; this is depicted in Figure 4.

πrc 2 L2

(2)

It is clear that, out of these N pairs of opposing patches, if only one pair is destabilized (i.e., they come together to form an oil bridge across the water film) then coalescence will follow irreversibly. To reflect this fact, we first define the local and global probabilities of destabilization as follows: φ ≡ the probability that a local pair of opposing patches will destabilize; Φ ≡ the probability that out of the N pairs of opposing patches, any one or more of the local pairs will destabilize (Φ is thus the global probability). Assuming the N patch pairs to be statistically independent, it is straightforward to show that the local and global probabilities are related by Φ = 1 − (1 − φ)N

Figure 4. The probability of local destabilization, φ, is the volume under the joint probability distribution functions that is within the hyperbolic region as shown. The hyperbola represents the destabilization criterion given by eq 4.

(3)

Given L and σζ, it is now possible to calculate the coalescence probability Φ for different values of [Ca2+] (with a one-to-one relation with ζave), bitumen drop size, and deformation ratio (DR). The optimal values for L and σζ were considered to be those that minimized the following least-squares functional:

We now equate the theoretical probability of coalescence Φ (given by eq 3) to its experimental counterpart Φexp (eq 1). With N given by eq 2, the global probability Φ can be determined if the local probability φ is known; the latter is obtained from the analysis outlined below. For local destabilization, we apply the DLVO theory to bitumen systems. By weighing the competing effects of electrostatic repulsion and van der Waals attraction against one another, Yeung and co-workers15 suggested that destabilization (i.e., the coming together of two charged surfaces) will occur when the condition (ζ1ζ2)1/2 < 8 mV

n

ψ≡

∑ [Φi(theoretical) − Φi(experimental)]2 i=1

(7)

The summation in eq 7 is from 1 to n, where n represents the total number of data points in the coalescence experiments. By minimizing ψ with respect to L and σζ, we arrive at the optimal values for the two free parameters. Having obtained L and σζ from least-squares minimization, one can finally predict the probability of coalescence between two oil droplets in water. Before concluding this theoretical section, we should comment on the parameter L, which represents the typical size (i.e., lateral extent) of a charged patch. It is of course unreasonable to assume that the charged patches, as illustrated in Figure 3, are separated by sharp boundaries and have uniform zeta potentials within each domain. In reality, we envision the zeta potential variations along the bitumen−water interface to resemble a random noise signal. If the autocorrelation of such a signal were evaluated, then the parameter L would correspond to the decay length of the autocorrelation function (to within a factor on the order of unity). This would be consistent with our earlier stipulation that the ζi’s of the patches are statistically independent and thus constitute a random variable.

(4)

is met. Here, ζ1 and ζ2 are the zeta potentials of the two opposing surfaces. (Relation 4 was derived on the basis of a typical value of the Hamaker constant for oil|water|oil systems and by using the linear superposition approximation of DLVO theory.17 The inequality is meant to be only an estimate; the value of 8 mV must not be taken as a precise cutoff.) Recall that the zeta potentials of the opposing patches are treated as statistically independent random variables, with both having a common Gaussian distribution with mean ζave and standard deviation σζ. Because ζ1 and ζ2 are statistically independent, their joint probability density (denoted f) is simply the product of two Gaussians: ⎡ (ζ − ζ )2 + (ζ − ζ )2 ⎤ ave 2 ave ⎥ f (ζ1, ζ2) = exp⎢ − 1 2 ⎢ ⎥ 2πσζ2 σ 2 ⎣ ⎦ ζ 1

4. RESULTS AND DISCUSSION Despite all apparent issues associated with the application of DLVO theory to bitumen systems (e.g., strong dependence of coalescence probability on drop size, random nature of the

(5)

The function f, when plotted against ζ1 and ζ2 in three dimensions, will exhibit a downward-facing bell shape (with the ζ1 − ζ2 plane oriented horizontally). The probability φ of local 4951

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corresponded to enormous repulsive stress barriers). Hence, it may be concluded that, according to DLVO theory, coalescence between bitumen droplets should never occur. Nevertheless, in contact experiments such as that shown in Figure 1, it was observed that coalescence did occur, albeit in a stochastic manner. To be clear, under identical experimental conditions, the encounter of two bitumen droplets may or may not result in coalescence; such a random event can at best be characterized by a probability. This probability of coalescence, Φexp, was determined using the method mentioned earlier (eq 1). For every probability value, the number of attempted contacts was 100. Every pair of bitumen droplets was pressed into contact for 60 s (to ensure complete drainage of the intervening water film) or until coalescence occurred. Invariably, it was observed that coalescence would take place either immediately upon contact or not at all. All experiments were carried out at room temperature (23 °C). Figure 6 presents a summary of coalescence probability measurements (the discrete symbols; we will ignore the solid lines for the moment) under a large number of experimental

coalescence, etc.), it is undeniable that the two main components of the theoryelectric double layer repulsion and van der Waals attractionare founded on sound physical principles. Instead of discarding these rigorous notions of physics, we will begin by examining the consequences and predictions of the traditional DLVO formalism. Where the theory fails, we will invoke the above-mentioned surface heterogeneity model, which is a simple extension of the wellfounded DLVO theory. To determine the electrostatic repulsion between bitumen droplets, we must first know their zeta potentials. The zeta potentials of bitumen suspensions were measured through electrophoretic experiments. Because the zeta potential (ζ) is known to depend strongly on the calcium ion concentration ([Ca2+]) in bitumen systems,18 we have chosen to present ζ as a function of [Ca2+]. Figure 5 shows the variation of ζ as [Ca2+]

Figure 5. Zeta potentials of suspended bitumen droplets in simulated process water (SPW). The potentials were measured through electrophoretic experiments. Here, the horizontal axis indicates the concentration of calcium ions in SPW, and the vertical axis shows the absolute values of the measured zeta potentials. The sizes of the bitumen droplets were approximately 1 μm, and the data were obtained at room temperature. The dashed line is a spline fit through the data points.

is increased; the aqueous phase in all cases was simulated process water (SPW) with different calcium ion concentrations. For the remainder of this section, experimental data will be shown with [Ca2+] as the independent variable. It is understood that, through adjustment of [Ca2+], we are controlling the surface zeta potentials of the bitumen drops and hence the electrostatic repulsive forces. (The ionic strength of the aqueous solution increased only very slightly, from 46 mM in the absence of Ca2+ ions to 50 mM at the maximum [Ca2+].) We should also note that the zeta potentials in Figure 5 were independent of the drop size (to within our experimental resolution). At this point, it is important to remember the main difficulty in applying DLVO theory to bitumen systems. As noted earlier, it was predicted that destabilization (i.e., the coming together of two charged surfaces into molecular contact) occurs when (ζ1ζ2)1/2 < 8mV

Figure 6. Probability of coalescence plots. The discrete symbols are experimental probabilities (determined using eq 1 on the basis of 100 contact tests). The solid lines are theoretical predictions based on two fitting parameters: σζ= 27 mV and L = 0.6 μm. To avoid overcrowding of information, the data is plotted separately for the two deformation ratios (DRs): (a) 1.1 and (b) 1.2. Note that the six theoretical curves in the above figures are calculated from the same two parameters (i.e., 27 mV and 0.6 μm), giving a remarkable fit to all 30 data points.

(4)

where ζ1 and ζ2 are the zeta potentials of the two opposing surfaces. However, as shown in Figure 5, the lowest ζ within our experimental range was 50 mV in magnitude (which 4952

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conditions. The parameters that were varied include [Ca2+] (and hence the zeta potential), the bitumen drop diameter (10, 100, and 1000 μm), and the deformation ratio DR (1.1 and 1.2). For clarity, experimental data corresponding to DR = 1.1 and 1.2 are shown on separate plots. The first obvious feature in these figures is the agreement with actual experience, that larger bitumen drops tended to coalesce much more easily (indeed, all millimeter-sized drops coalesced on contact, giving rise to 100% coalescence probabilities). Also, and not surprisingly, the coalescence probabilities are seen to increase with (a) the deformation ratio DR (i.e., the extent of contact) and (b) the increase in [Ca2+] (i.e., the lowering of electrostatic repulsion). What is most remarkable about this data is the complete failure of the DLVO theory to predict the trends. In particular, the DLVO theory cannot account for the following: • that there is coalescence at all (traditional DLVO theory predicts an overwhelming electrostatic repulsion that prohibits any form of close contact); • that there is a size dependence (i.e., larger drops are easier to coalesce than smaller ones; • that the coalescence process is random rather than deterministic. (As discussed in the Introduction, the coalescence process in the present context does not include perikinetics or any other form of transport phenomenon. As such, the observed randomness reflected the true nature of the colloidal interactions.) Here, we submit that the apparent failure of the DLVO theory is due to surface charge heterogeneities at the oil−water interface. As noted earlier, the traditional theory assumes the interacting surfaces to be perfectly smooth and uniformly charged; these assumptions can be questionable in many real situations. In the present case, because the interacting surfaces are fluid interfaces, the assumption of surface smoothness is likely justified. However, charge heterogeneities may still exist at the bitumen drop surfaces. (Because of the large viscosity of the hydrocarbon phase, charged domains at the surfaces may effectively be “frozen” on the timescales of the experiments.) In what follows, we will apply the theory that was developed in section 3 (DLVO + surface heterogeneity) to account for the observed variations in probabilities. Recall that the proposed theory of surface heterogeneity has only two free parameters: the standard deviation σζ of the local zeta potentials and the lateral extent of a local patch L. These two parameters are determined by minimizing the least-squares functional as defined in eq 7; the number of probability measurements in this case is n = 30 (15 data points in each of the two plots in Figure 6). The resulting optimal values are

to reconcile the experimental results, in terms of both the qualitative trends and the actual numerical values, is remarkable. Note that although this is, in the end, an exercise in fitting data to a two-parameter model, the process is far more complex than linear regression (which also involves two parameters). The empirical observations, we should note here, present a far greater challenge than a set of data points that lie more or less along a straight line. As such, the quality of the fits lends support to the validity of the theory that was proposed in section 3.

5. CONCLUSIONS The coalescence of bitumen droplets in water was studied experimentally as well as theoretically. Experimentally, it was demonstrated that the coalescence between two oil droplets was a random process, with larger drops showing a much higher tendency toward coalescence. In this study, it was postulated that the random nature of the coalescence process was due to the presence of surface charge heterogeneities (nonuniformities) at the bitumen−water interface. On the basis of this postulate, a theory was developed that could quantitatively predict the probabilities of droplet−droplet coalescence. The study suggests that traditional DLVO theory remains sound on the local scale. With surface heterogeneities properly accounted for, there is no need to introduce any “exotic”, and not as wellfounded, non-DLVO forces. It is also very likely that the proposed theory of surface heterogeneity is not limited only to bitumen/crude oil systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been conducted with the support of the NSERC (Natural Sciences and Engineering Research Council of Canada) and Syncrude Canada Ltd.

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REFERENCES

(1) Anonymous. Worldwide Look at Reserves and Production. Oil Gas J. 2004, 102, 22−23. (2) Masliyah, J.; Zhou, Z.; Xu, Z.; Czarnecki, J.; Hamza, H. Understanding Water-Based Bitumen Extraction from Athabasca Oil Sands. Can. J. Chem. Eng. 2004, 82, 628−654. (3) Hammer, M. U.; Anderson, T. H.; Chaimovich, A.; Shell, M. S.; Israelachvili, J. The Search for the Hydrophobic Force Law. Faraday Discuss. 2010, 146, 299−308. (4) Yeung, A.; Dabros, T.; Czarnecki, J.; Masliyah, J. On the Interfacial Properties of Micrometre-Sized Water Droplets in Crude Oil. Proc. R. Soc. London, Sect. A 1999, 455, 3709−3723. (5) Evans, E.; Needham, D. Physical Properties of Surfactant Bilayer Membranes: Thermal Transitions, Elasticity, Rigidity, Cohesion, and Colloidal Interactions. J. Phys. Chem. 1987, 91, 4219−4228. (6) Evans, E. A.; Skalak, R. Mechanics and Thermodynamics of Biomembranes; CRC Press: Boca Raton, FL, 1980. (7) Yeung, A.; Pelton, R. Micromechanics: A New Approach to Studying the Strength and Breakup of Flocs. J. Colloid Interface Sci. 1996, 184, 579−585. (8) Yeung, A.; Dabros, T.; Masliyah, J.; Czarnecki, J. Micropipette: A New Technique in Emulsion Research. Colloids Surf., A 2000, 174, 169−181.

σζ = 27 mV and L = 0.6 μm

It is noted that the above parameters are unique in that if the values were varied by as little as 10% then the remarkable fits shown in Figure 6 would be lost. One interesting point about the minimization results is the value of the standard deviation σζ for the charged patches. It suggests that, although the average potentials are negative over the entire range of [Ca2+] (Figure 5), there exist some local patches that can acquire very low potentials. These areas can allow for local destabilization, which leads to the coalescence of bitumen drops upon close contact. The solid lines in Figure 6 are theoretical curves based on the above two parameters. (The same two numbers are used in Figure 6a,b.) As can be seen, the ability of the proposed theory 4953

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dx.doi.org/10.1021/la204254m | Langmuir 2012, 28, 4948−4954