Ind. Eng. Chem. Res. 2004, 43, 2929-2935
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Fluid Properties at Coking Process Conditions Moruf O. Aminu, Janet A. W. Elliott, William C. McCaffrey, and Murray R. Gray* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6 Canada
A new method based on the measurement of the forces on a liquid bridge between two crossed rods was used to determine fluid properties during the cracking of an Athabasca vacuum residue at 300-530 °C. The surface tension was measured at temperatures between 312 and 530 °C. Adhesive forces in the liquid bridge and viscosity were measured with increasing reaction time at 400-530 °C. The results showed that the adhesive force remained constant, until the liquid dried out because of devolatilization and coke formation, where it fell to zero. The surface tension was constant with increasing reaction time, but it decreased with reaction temperature from 21 mN/m at 150 °C to 6 mN/m at 530 °C. The viscosity increased to order 104 mPa‚s before dry-out, for all of the temperatures above 400 °C. Introduction The conversion of the vacuum residue (524 °C+) fraction of petroleum and bitumen involves simultaneous transport of heat, mass, and momentum with rapid changes in composition from reaction and phase exchange. The composition, in turn, determines the fluid properties that control the transport processes. These changes in fluid properties are most profound in the coking processes, wherein high temperatures give vaporization and cracking of the liquid feed to form a residue material that is solid at room temperature and insoluble in solvents, i.e., coke. To understand how the reacting fluids behave in a multiphase reactor, such as a coker, the basic fluid properties of viscosity and surface tension must be measured. Although viscosity can be modeled for simple mixtures of components,1 the viscosity of the heavy fractions of petroleum cannot be predicted as a function of the solvent fraction at room conditions, let alone extent of reaction at high temperatures. Direct measurement of the properties of petroleum fractions during coking requires a combination of kinetics and rheology, where the fluid properties are expected to change with the extent of conversion. At temperatures of 400-530 °C, significant volumes of volatilized material and cracked vapor product are formed, which lead to bubbling if the liquid phase is thicker than a few tens of microns.2 The characteristic times for reaction decrease from minutes at 400 °C to seconds at 530 °C,3 and consequently the time to heat the sample to the reaction temperature must be on the order of several seconds or less and the measurement of the fluid properties must be rapid. The combined requirements of thin liquid films to avoid bubbling and rapid heating rule out the standard methods for measuring the viscosity and surface tension. For example, a cone-andplate viscometer cannot give high heating rates, nor can it tolerate significant formation of a vapor phase. Methods based on liquid droplets, such as the pendant drop method for measuring the surface tension or the contactless viscosity measurement method for measur* To whom correspondence should be addressed. Tel.: 1-780492-7965. Fax: 1-780-492-2881. E-mail: murray.gray@ ualberta.ca.
Figure 1. Liquid bridge between a rod and a plate.
ing viscosity,4 require volumes on the order of 10 µL, giving too large a radius for rapid heating or release of products without forming bubbles. Similarly, measurement of the surface tension by the bubble pressure technique cannot be used when the liquid is reacting.5 Consequently, a new method of measuring liquid properties is required for cases where rapid reactions occur to form large volumes of vapor, as in coking of vacuum residues. This paper describes the development of a device for measuring the viscosity and interfacial tension of reacting liquid films. Following the approach used for measuring surface forces6 and for measuring adhesive forces and drying times during coking,7 the measurement of the forces and dimensions of a liquid bridge between crossed cylinders allows the rapid determination of the viscosity and surface tension. The technique was applied to an Athabasca vacuum residue (AVR) at 312-530 °C. Theory The geometry of a liquid bridge between crossed cylinders is equivalent to a bridge between a sphere and plate, as illustrated in Figure 1.6 The force on the liquid bridge is the sum of the surface force and the viscous force.8-11
FT ) Fs + Fv
(1)
where FT is the total force on the liquid bridge, which is measured experimentally, Fs is the surface force component, and Fv is the viscous force component. The surface force on the liquid bridge is equivalent to the
10.1021/ie030550g CCC: $27.50 © 2004 American Chemical Society Published on Web 12/03/2003
2930 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004
capillary force because the distance of closest approach of the sphere and the plate is very small compared to the radius of the sphere.12 For the case of a cylinder coated with a liquid film, the contact angle is zero. When the bridge is not elongated, then the length (D) is much less than the width of the base of the bridge (b), and
Fs ) 4πRγ
(2)
When the liquid bridge elongates, so that D > b, then the force becomes
(
)
b Fs ) πγb 1 + r1
(4)
This equation is valid only for a constant-volume liquid bridge. When the crossed cylinders are coated with a thin liquid film of thickness, δ, then the volume of the liquid bridge will change because of the drainage of the liquid into and out of the bridge. To use dimensional analysis to develop an empirical solution for the viscous force, the equations for the forces were nondimensionalized by multiplication by D/R2γ. The dimensionless surface force then became
D R
Fs,D )
for D < b
[
πbD b 1+ 2 r R 1
]
(5)
for D g b
(6)
The dimensionless viscous force from eq 4 was proportional to the capillary number, defined as
Ca )
η dD γ dt
(7)
Because of the low velocities, the Reynolds number was less than 2 and was not significant. The viscous force would also be expected to depend on the thickness of the liquid film, δ, and the length of the liquid bridge, D. In nondimensional form, the resulting semiempirical expression was
Fv,D ) k1Ca
(Rδ ) (DR) k2
k3
(8)
where k1, k2, and k3 were empirical constants. The total force on a liquid bridge for D g b was
FT,D )
(
)
()()
πbD b δ 1+ + k1Ca 2 r R R 1
k2
D R
k3
(9)
When the cylinders are close together (D , b) and the bridge is not elongating, Ca ) 0 and the total force would be
(DR)
FT,D ) 4π
(11)
where the values of e1 and e2 were determined at each reaction temperature using data from Gray et al.3 Materials and Methods
3πηR2 dD D dt
Fs,D ) 4π
δt ) [δt)01-e2 + e1t(e2 - 1)]1/(1-e2)
(3)
similar to the relationships given by Fairbrother and Simons13 and Pitois et al.10,11 using the Gorge method for a liquid bridge between two spheres with relative motion. For a cylindrical bridge of fixed dimension, the viscous force is given as10,11
Fv )
During cracking and coking reactions, the original film thickness, δ, was depleted. The kinetics of weight loss from reacting films of the vacuum residue depend on both devolatilization and cracking and do not follow overall first-order kinetics.3 Consequently, the following empirical equation was used to represent the film thickness as a function of time:
(10)
Syncrude Canada Ltd. supplied AVR, the 524 °C+ boiling fraction of Athabasca bitumen, with a density of 1086.8 kg/m3. The AVR contained 5.8% sulfur, 0.7% nitrogen, 24.7 wt % pentane asphaltenes, 27.8% microcarbon residue, 1.8% toluene insolubles, and 1.25% ash. Methylene chloride was supplied by Fisher Scientific (Toronto, Ontario, Canada). Prepurified nitrogen was supplied by PRAXAIR Canada (Mississauga, Ontario, Canada). Viscosity standards for calibration were supplied by Cannon Instrument Co. (State College, PA). Data from the supplier or the Walther equation were used to estimate the viscosity dependence on temperature in the range of 20-26 °C, to correct for the effect of high-intensity lights. Surface tensions of the oils were measured using the pendant drop method as described by Li et al.,14 using a video camera with a microscope objective to capture images, with analysis by software from LIA Technologies Inc. (Woodbridge, Ontario, Canada). Rapid heating of the AVR to a reaction temperature of up to 530 °C was achieved by coating a thin film (2428 µm) on the surface of rods of nickel-iron alloys with Curie points of the desired temperature. For such thin films, the liquid temperature would be the same as that of the underlying metal.2 The rods with Curie point temperatures of 312, 356, and 400 °C, of diameters 0.62, 0.98, and 0.62 mm, respectively, were supplied by DyChrom (San Jose, CA). The Curie point alloy for a temperature of 466 °C, of diameter 1.47 mm, was supplied by National Specialty Alloys (Houston, TX). AMETEK Specialty Metal Products Division (Wallingford, CT) supplied the Curie point alloy for a temperature of 504 °C with a diameter of 1.9558 mm. For a temperature of 530 °C, the flux was removed from the welding rod (UTP Econocast 55NiFeCl, Air Liquide), and then the rod was turned on a lathe to a diameter of 2.04 mm. Experimental Apparatus. A schematic diagram of the equipment used in this study is given in Figure 2. The rods of the Curie point alloy were angled at 45° to the axis of the induction coil to allow them to touch at a 90° angle and still couple with the surrounding induction field. Each rod was mounted in a tube of Pyrex glass (diameter 3.9 mm and length 10 cm) to hold the rods for easy attachment to the hollow aluminum beams. The free beam was connected through a constantforce flexural pivot (model 5010-800, Goodrich Corp., Rome, NY) to a linear variable differential transducer (LVDT1, model D540050HH, Daytronic Corp., Dayton, OH). The controlled aluminum beam and the plunger of LVDT2 were attached to a vertical motion stage, driven by a stepper motor (model 5704M-0202, The Motion Group Inc., Clovis, CA). The two LVDT sensors
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2931
Figure 2. Schematic diagram of the experimental apparatus.
were connected, through a signal conditioner (model 3130, Daytronic Corp., Dayton, OH), to a computer. The computer recorded data from the two LVDTs and controlled the stepper motor with the aid of the LabVIEW program (version 6.0, National Instruments, Austin, TX). The motion of the rods and the changes in the liquid bridge were recorded by a video camera (model TMC7DSP, PULNiX America Inc., Sunnyvale, CA), which was connected to a television monitor (model 20AF14C, Toshiba Inc., Ontario, Canada) via a video timer (model VTG-33, FOR.A Corp. Ltd., Japan) and a time-lapse VCR (model SVT-S480ES, Sony Corp., Japan) to record the bridge dynamics on videotape. The video timer was also controlled through the computer. To collect highquality video images, the equipment was lit by filament lights (models 3852582 and 4187531, Lowel-Light Manufacturing Inc., Brooklyn, NY). The induction furnace (model XP-30, Ameritherm Inc., Scottsville, NY) provided the heating of the films of AVR by heating the Curie point alloys. The heating coil of the induction furnace was connected to an induction furnace controller, which in turn was controlled by a computer. Before being inserted into the induction coil, the Pyrex tubes, bearing the alloy rods, were mounted on the aluminum beams and enclosed in a glass housing attached to the side of a gastight acrylic box. The mounts for the aluminum beams, the LVDT sensors, and the stepper motor were also enclosed in the acrylic box. The equipment was purged with nitrogen at 9-12 dm3/min and controlled by a flowmeter (model DTM-200A, American Meter Co., Burlingame, CA). An electric fan was mounted in the acrylic box to allow for mixing of gas and speedy purging of air from the apparatus. A Faraday shield was mounted around the induction coil to protect surrounding equipment from the field of the coil. Recordings of the changes in the liquid bridge during pull apart of the rods were used in the image analysis of the liquid bridge. The time-lapse VCR was connected to a Marvel digitizing card (model G400-TV, Matrox, Dorval, Quebec, Canada). Digitized frames were analyzed using Sigma Scan Pro (version 4.01, SPSS Science, Chicago, IL) to measure the dimensions of the bridge after scaling with the known diameter of the rods. Experimental Method. The Curie point rods were spray coated using a 2% solution of AVR in methylene
chloride. The rods were masked with tape to expose only the center portion of the rods. After evaporation of the solvent, the thickness of the film was determined by the weight of the film and the density of the AVR. The films were 24-28 µm in thickness. After a pair of rods was mounted on the apparatus, the box was sealed and purged with nitrogen. The power to the furnace was turned on, and after a set interval of heating, the rods were pressed together so that the free rod was displaced upward from its equilibrium position. The controlled rod was then pulled down at a speed of 0.409 mm/s. When there was a liquid film at the point of contact between the rods, the two rods moved together until a point when the liquid bridge formed between the rods was broken. Measurement of the downward displacement of the free rod from its equilibrium position gave the force on the liquid bridge. The experiment was completed the moment the liquid bridge was broken. Results and Discussion Equipment Calibration. The apparatus was first calibrated at room temperature in order to determine the relationship between measured forces and known fluid properties. The data of Figure 3 show a typical time course of the absolute position of the two rods and the forces on the upper rod, given as the sensor reading V, in volts. The difference between the voltage from the sensor at any time t and the equilibrium reading, Vf,e, was converted to a force using a calibration curve. The force on the upper rod at time ts, where the bridge just began to elongate, was used to calculate the surface tension from eq 10. The force measured at the point of breakage of the liquid bridge from films of the viscosity standards at time tv was used in eq 9 to estimate the adjustable parameters k1, k2, and k3. Video images of the bridge were used to calculate the dimensions b and r1, while the absolute positions of the rods gave the length of the bridge, D, and the velocity of elongation, dD/dt. Although the controlled rod was moved by the stepper motor, the rate of elongation of the bridge between the two rods was an independent variable. The data of Figure 4 show the viscosities of the calibration oils from the liquid bridge method versus viscosity by a rheometer. The optimum values of parameters k1, k2, and k3 were obtained by minimizing the
2932 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 Table 1. Measured versus Actual Surface Tension of Standard Oil measured surface tension, mN/m
Figure 3. Time course of rod position and force measurements for the determination of surface and viscous forces.
Figure 4. Plot of measured versus actual viscosity of standard oils. The actual viscosity was corrected for ambient temperature and heating due to lights. Error bars are standard deviations for three repeat experiments.
sum of squared residuals between the measured FT,D and that calculated from eq 9 for five calibration oils with a range of film thicknesses at various times between bridge formation and rupture. The best-fit values were k1 ) 400.0, k2 ) 0.752, and k3 ) 0.677. The data showed that the adhesive force of the bridge was dominated by capillary forces (FT,D ) Fs,D) until the bridge began to elongate. By the time the bridge was visible for video recording, when D g b, the capillary component of the force was negligible and FT,D ) Fv,D. The measured error in the viscosity of the N8000 oil was larger than those of the others. One contributing factor was the sensitivity of the higher viscosity oil to
oil code
actual surface tension, mN/m
sensor method
video method
N600 N1000 N2000 N4000 N8000
32.60 ( 0.07 31.40 ( 0.02 31.70 ( 0.63 30.70 ( 0.06 32.70 ( 0.14
32.30 ( 1.17 30.70 ( 1.22 30.10 ( 1.89 27.70 ( 2.83 31.10 ( 1.80
31.60 ( 1.80 31.20 ( 2.12 33.60 ( 1.50 32.50 ( 1.73 33.50 ( 2.66
the temperature changes under the intense lights used for video recording. Another factor could have been variations in the film thickness on the surface of these rods. The data of Table 1 give the results for the surface tension of the standard oils. The surface tension was determined by two methods. The first method used statistical analysis of the relative position of the two rods to determine when the elongation of the bridge was significant relative to the noise from the sensors (time ts) and calculated the surface tension from eq 10. The second method used video images of the bridge between ts and tv to determine the surface tension from eq 9. The results by both methods were in good agreement with the surface tensions measured by the pendant drop method. In subsequent experiments, the method based on the relative position from the sensors was used to determine the time of bridge elongation, the force at that time (ts in Figure 3) was used to determine the surface tension (FT,D ) Fs,D from eq 10), and the elongation of the bridge at the time of rupture was used to calculate viscosity (with FT,D ) Fv,D from eq 8). Fluid Properties of AVR. The procedure for measuring the properties of AVR during reaction was the same as that illustrated in Figure 3, except that the initial time ta was varied to allow for different extents of reaction. The rods heated rapidly in the induction field, reaching a minimum cracking temperature of 400 °C (for significant reaction in a period of 4 min) in 3.84.9 s. The rods reached 97% of the final temperature in 5.3-7.1 s, and then the temperature of the rods remained steady at the Curie point temperature as expected. The reaction time was defined as the total heating time minus the time to reach 400 °C. The induction coil induced high-frequency noise in the position sensors; therefore, the data were filtered using a low-band-pass filter (Wavelab 8.02, developed by the Stanford University Department of Statistics). The results from AVR at 400, 503, and 530 °C are shown in Figures 5-7. At 400, 466, and 503 °C, the adhesive forces were relatively constant until the film dried out, and no adhesive force was measured. The reaction time for a dry film decreased from 240 s at 400 °C to 14.4 s at 530 °C (Table 2), where dry-out time was defined as the reaction time to produce a film with no measurable adhesive force. The viscosities were calculated from the forces on the liquid bridges, using eq 8. The kinetic constants for estimating the thickness of the liquid film as a function of reaction time, by eq 11, are given in Table 2, from the data of Gray et al.3 As illustrated in Figures 5-7, the viscosity increased significantly with the reaction time to values in the range of 3 × 104-5 × 104 mPa‚s. These maximum values were greater than the range of the calibration oils (Table 1), and the calibration was less accurate at high viscosity (Figure 4); we conclude
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2933
Figure 5. Properties of reacting AVR at 400 °C. Error bars are standard deviations for three repeat experiments.
from these results that the viscosities increased to order 104 mPa‚s. Although the measured forces on the liquid bridges at the time of breakage were relatively constant with time, as illustrated in Figures 5-7, the diminishing thickness of the liquid film (δ), the changes in bridge length (D), and the rate of extension of the bridge (dD/ dt) indicated increasing viscosity. These viscosities should be considered to be apparent viscosities because non-Newtonian behavior of the reacting material during coke formation cannot be ruled out, even though AVR was Newtonian. The viscosity of the unreacted AVR was 150 mPa‚s at 180 °C, decreasing to 30 mPa‚s at 270 °C (RMS 800, TA Instruments, Newcastle, DE). Extrapolation of these viscosity data to 400 °C indicated an initial viscosity of 1-2 mPa‚s. The rapid increase in viscosity from 1-2 to 104 mPa‚s with increasing time of reaction was consistent with evaporation of more volatile components from the liquid film and polymerization of liquid components, driven by thermal cracking reactions, leading to coke formation. The errors in the viscosity values followed the same trend as the calibration in Figure 4, with larger relative error in the reacted films with large viscosities. Radial variations in the film thickness on the rods could contribute to the errors. Some of the liquid on the rods tended to drain into drips, but as long as the drips were not at the point of contact, the drips did not interfere with the measurements. The drips did reduce the volume of liquid in the film, but the impact on the viscosity, from eqs 8 and 11, was within the error of the repeat experiments. The reaction was so rapid at 530 °C that the liquid bridges formed when rods touched after more than 12 s solidified rapidly to form coke, giving tensile forces at
Figure 6. Properties of reacting AVR at 503 °C. Error bars are standard deviations for three repeat experiments.
the time of breakage that were more than 10× larger than those at shorter times. Consequently, the data of Figure 7 show data for the force required for the initial elongation of the liquid bridges. At 530 °C, elongation of liquid bridges was observed at times of 1-2 s longer than the dry-out time of 14.4 s for the liquid films (Figure 7). This result suggests either that films with a viscosity of over 4 × 104 mPa‚s were too viscous to form liquid bridges when touched together under the experimental conditions or that the elongating bridge cooled sufficiently from the temperature of the rods to slow the reaction by several seconds. The data of Figures 5-7 show that the time for viscosity to increase is very sensitive to temperature, consistent with the reaction and vaporization of components as the temperature of the liquid film was increased. Within the uncertainties of the calibration of the instrument, the maximum viscosities were of order 104 mPa‚s at all temperatures. The viscosity data from experiments at 400-530 °C were plotted against the normalized reaction time, defined as the reaction time divided by the time to obtain a dry film, from Table 2 (plotted in Figure 8). This representation emphasizes that the increase in viscosity was similar at several of the temperatures when the time scale was adjusted to account for the reaction processes. The main exception to this observation was the results for viscosity at 466 °C, which increased more rapidly than data at lower and higher temperatures. The surface tension of reacting AVR was insensitive to the extent of reaction at each temperature, as illustrated in Figures 5-7. Both the forces at the time of breakage of the bridges and the forces required to
2934 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004
Figure 9. Surface tension as a function of temperature for the pendant drop method (Li et al.14 equilibrium data; 0) and the liquid bridge method (4).
Figure 7. Properties of reacting AVR at 530 °C. Error bars are standard deviations for three repeat experiments. Table 2. Time to Dry Out Film and Kinetic Parameters for the Film Thickness of Reacting AVR in Equation 11 temperature, °C 400 466 504 530
time to dry out film,a s 240 101 24 14.4
e2
e1 10-7
1.52 × 1.95 × 10-4 2.44 × 10-3 3.77 × 10-3
5.98 3.21 2.66 2.73
a For temperatures above 400 °C, the time is corrected for heating time.
Figure 8. Viscosity of reacting AVR as a function of the normalized reaction time.
begin elongation (proportional to Vf,i - Vf,e in Figure 3) were constant with time within experimental error. Unlike viscosity, surface tensions are much less sensitive to the molecular weight of the liquid; for example, Athabasca bitumen has a surface tension similar to that of toluene.15 The data of Figures 5-7 show that the
changes in the composition of the liquid film during the time of measurement did not have a significant effect on the surface tension. Validation of the Results. As illustrated in Figures 5-7, the viscosity of the liquid increased rapidly with reaction from an initial value of 1-2 mPa‚s before reaction to 104 mPa‚s. Low-viscosity fluids follow eq 9, but Fv,D ≈ Fs,D so that the viscosity of unreacted AVR could not be measured at 312-350 °C for comparison to the data from the rheometer. The surface tensions were measured at short heating times at 312-400 °C to eliminate any effect of the reaction, and these data are presented in Figure 9. Data from Li et al.14 for AVR by the pendant drop technique at lower temperatures are also shown. The measurements by the bridge method at 312-400 °C were lower than the extrapolated values from the data of Li et al.,14 which gave a slope of -0.024 ( 0.010 mN‚m-1‚K-1, but the difference was not statistically significant. The surface tension data at 466-530 °C were significantly lower than the extrapolated estimates from Li et al.14 by a factor of 2. This discrepancy could be due to overextrapolation of limited data or possibly due to changes in surface composition and surface tension, driven by cracking and coking reactions in the first 10 s of the reaction, before data were collected. The trend line in Figure 9 shows the least-squares fit to all of the data available for AVR over the entire range of temperature from 150 to 530 °C, with a slope of -0.043 ( 0.014 mN‚m-1‚K-1. Process Implications. The measured properties of AVR have important implications for the design of reactor systems. The surface tension was insensitive to composition changes driven by reaction, while viscosity changed dramatically with the reaction. At the highest temperature of 530 °C, the data of Figure 8 suggest that the liquid flow would be reduced by orders of magnitude within a few seconds at reaction temperatures. In a fluid-bed or moving-bed reactor, such a rapid increase in viscosity would control the wetting and distribution of the liquid on the solids and limit fouling of reactor internals. Even though feed is added continuously to such reactors, the solids wetted by the liquid feed would be largely segregated, analogous to the batch experiments on liquid behavior presented in this paper. High viscosity would also give a significant reduction in the diffusion rate of cracked products within the liquid phase. The rapid increase in viscosity, and concomitant decrease in the diffusion coefficient, was consistent with
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2935
the important role of mass transfer in liquid films in determining the yield of coke.
T ) total v ) viscous
Conclusions
Literature Cited
1. The liquid bridge method was found to be a useful means of measuring the viscosity and surface tension of reacting liquids with generation of significant vaporphase products. 2. The surface tension of AVR was 14.0-14.7 mN/m at 312-400 °C and 5.8-6.4 mN/m at 466-530 °C. 3. The viscosity of AVR increased by 4 orders of magnitude because of the cracking and coking reactions at 400-530 °C, to order 104 mPa‚s.
(1) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2000. (2) Gray, M. R.; Le, T.; McCaffrey, W. C.; Berruti, F.; Soundararajan, S.; Chan, E.; Huq, I.; Thorne, C. Coupling of mass transfer and reaction in coking of thin films of an Athabasca vacuum residue. Ind. Eng. Chem. Res. 2001, 40, 3317-3324. (3) Gray, M. R.; McCaffrey, W. C.; Huq, I.; Le, T. Kinetics of cracking and devolatilization during coking of Athabasca residues. Ind. Eng. Chem. Res., in press, 2003. (4) Perez, M.; Salvo, L.; Seury, M.; Brechet, Y.; Papoular, M. Contactless viscosity measurement by oscillations of gas-levitated drops. Phys. Rev. E 2000, 61, 2669-2675. (5) Millette, J. P.; Scott, D. S.; Reilly, I. G.; Majerski, P.; Piskorz, J.; Radlein, D.; deBruijn, T. J. W. An apparatus for the measurement of surface tensions at high pressures and temperatures. Can. J. Chem. Eng. 2002, 80, 126-134. (6) Fisher, L. R.; Israelachvili, J. N. Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci. J. Colloid Interface Sci. 1981, 80, 528-541. (7) Gray, M. R.; Zhang, Z.; McCaffrey, W. C.; Huq, I.; Boddez, L.; Xu, Z.; Elliott, J. A. W. Measurement of adhesive forces during coking of Athabasca vacuum residue. Ind. Eng. Chem. Res. 2003, 42, 3549-3554. (8) Mazzone, D. N.; Tardos, G. I.; Pfeffer, R. The behavior of liquid bridges between two relatively moving particles. Powder Technol. 1987, 51, 71-83. (9) Ennis, B. J.; Li, J.; Tardos, G. I.; Pfeffer, R. The influence of viscosity on the strength of an axially strained pendular liquid bridge. Chem. Eng. Sci. 1990, 45, 3071-3088. (10) Pitois, O.; Moucheront, P.; Chateau, X. Liquid bridge between two moving spheres: An experimental study of viscosity effects. J. Colloid Interface Sci. 2000, 231, 26-31. (11) Pitois, O.; Moucheront, P.; Chateau, X. Rupture energy of a pendular liquid bridge. Eur. Phys. J. B 2001, 23, 79-86. (12) Frink, L. J. D.; Van Swol, F. A molecular theory for surface forces adhesion measurements. J. Chem. Phys. 1997, 106, 37823791. (13) Fairbrother, R. J.; Simons, S. J. R. Modeling of binderinduced agglomeration. Part. Part. Syst. Charact. 1998, 15, 1620. (14) Li, X.; Elliott, J. A. W.; McCaffrey, W. C.; Yan, D.; Li, D.; Famulak, D. Dynamic surface tensions of Athabasca bitumen vacuum residue. J. Colloid Interface Sci., submitted for publication, 2003. (15) Isaacs, E. E.; Smolek, K. F. Interfacial tension behavior of Athabasca bitumen/aqueous surfactant systems. Can. J. Chem. Eng. 1983, 61, 233-240.
Acknowledgment The apparatus was constructed and calibrated with invaluable assistance and advice from Walter Boddez, Jack Gibeau, and Bob Scott. Bob Skwarok and Nicole Hamm (Syncrude Canada Ltd.) assisted with photography. M.R.G. holds the Syncrude/NSERC Industrial Research Chair in the Advanced Upgrading of Bitumen, while J.A.W.E. holds a Canada Research Chair in Interfacial Thermodynamics. Nomenclature a ) width of the bridge at the narrowest point, m b ) dimension of the base of the liquid bridge, m Ca ) capillary number D ) length of the liquid bridge based on the separation between rods, m e1, e2 ) empirical constants in eq 11 F ) force on the liquid bridge, mN ht ) height of the liquid bridge to the point of contact, m k1, k2, k3 ) empirical constants in eq 9 R ) radius of the rod, m r1, r2 ) radii of curvature of the liquid bridge, m t ) time, s ta ) approach time, s Greek Letters γ ) surface tension, mN/m δ ) liquid film thickness, m η ) liquid viscosity, mPa‚s Subscripts D ) dimensionless force, multiplied by D/R2γ e ) equilibrium f ) free beam s ) surface
Received for review June 30, 2003 Revised manuscript received September 15, 2003 Accepted October 1, 2003 IE030550G
