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Determining the Colloidal Forces between Bitumen Droplets in Water Using the Hydrodynamic Force Balance Technique X. Wu,*,† T. Dabros,‡ and J. Czarnecki† Syncrude Canada Ltd., Edmonton Research Center, Edmonton, Alberta, Canada T6N 1H4, and CANMET, One Oil Patch Drive, P.O. Bag 1280, Devon, Alberta, Canada T0C 1E0 Received April 15, 1999. In Final Form: August 16, 1999 A novel technique using a “hydrodynamic force balance” was introduced to determine the maximum value of attractive forces between two micrometer-sized bitumen droplets in a doublet suspended in water. The technique is based on breaking up a doublet in a gradually increasing wall shear flow and calculating the colloidal force between the two droplets from the breakup shear rate. The measurable force ranges from 10-13 to 10-11 N. The upper limit can be further raised after some modifications to the instrument. The validity of the method has been verified by comparing the determined Hamaker constant of bitumenwater-bitumen with both the experimental data obtained from another force-measurement technique and the literature value. The methed is applicable to both emulsion and suspension systems although only a bitumen-in-water emulsion was investigated in this study. A bitumen droplet surface contains isolated “bumps” of 50-100 nm in horizontal diameter according to previous study. A disk-sphere model assuming a single disk-shaped protrusion attached to the bitumen droplet was used to interpret the force data. The calculation yielded the thickness values of the protrusions mostly in the range of 0-20 nm, which are consistent with the previous findings.
Introduction Colloidal forces are generally regarded as a crucial element that ultimately determines the stability and other physicochemical properties of colloidal dispersions.1 Determination of these forces between two solid particles or between a particle and a wall has been receiving considerable attention in the past decade.1-6 By contrast, the forces between emulsion droplets were seldom measured, probably due to various technical difficulties in handling deformable and spreadable liquid drops. A few successful experiments in this area include the determination of the adhesive forces between red blood cells using a micropipet technique7 and the measurement of the colloidal forces between bitumen (a heavy crude oil) droplets in water8 and between water droplets in diluted bitumen9 using the colloidal particle scattering (CPS) technique. The micropipet technique showed many promising features in the force measurement of biological systems.10 The range of detectable forces lies between 10-14 and 10-9 N. However, the requirement of gluing the target particle to a membrane capsule, which serves as a force transducer, may hinder its application to some emulsion systems. * Corresponding author. † Syncrude Canada Ltd. ‡ CANMET. (1) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, CA, 1992. (2) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (3) Li, Y. Q.; Tao, N. J.; Garcia, A. A.; Lindsay, S. M. Langmuir 1993, 9, 637. (4) Prieve, D. C.; Frej, N. A. Langmuir 1990, 6, 396. (5) Schumacher, G. A.; van de Ven, T. G. M. Langmuir 1991, 7, 2028. (6) van de Ven, T. G. M.; Warszynski, P.; Wu, X.; Dabros, T. Langmuir 1994, 10, 3046. (7) Evans, E.; Berk, D.; Leung, A. Biophys. J. 1991, 59, 838. (8) Wu, X.; Hamza, N.; Czarnecki, J.; Masliyah, J. Langmuir 1999, 15, 5244-5250. (9) Wu, X.; van de Ven, T. G. M.; Czarnecki, J. Colloids Surf., A 1999, 149, 577. (10) Evans, E.; Ritchie, K.; Merkel, R. Biophys. J. 1995, 68, 2580.
In this paper, a novel technique employing a “hydrodynamic force balance” (HFB) is introduced to determine the interaction forces between emulsion droplets. The HFB, in essence, is a shear-generating instrument that breaks up a doublet in a precisely controlled wall shear. The doublet is composed of a micrometer-sized droplet fixed on a glass wall and an equal-sized “free” droplet susceptible to the hydrodynamic drag (cf. Figure 1). At the onset of doublet breakup, the maximum attractive force between these two droplets approximately equals the drag force, which can be calculated based on hydrodynamic theory.11 Breaking up swollen red blood cell doublets by a simple shear flow was attempted using a traveling microtube apparatus12,13 and a plate rheoscope.13 Although statistical properties, such as number of doublet breakups in a certain range of the normal hydrodynamic forces, were obtained, no direct measurement of the attractive force in an individual doublet was performed. This might be due to the difficulty in determining the exact orientation of the doublet in a breakup process. The problem becomes easier to solve in HFB experiments because the doublet is artificially created shortly before the breakup and the “free” droplet can be placed anywhere around the fixed droplet at will. We usually place the “free” droplet directly behind the fixed droplet to simplify the force calculation. An additional benefit of breaking up a newly formed doublet is the capability of studying the kinetics of the development of an adhesive force in a doublet, which will be the topic of future publications. A similar principle to breaking up a colloidal doublet with a known force was employed in another force (11) Dabros, T.; van de Ven, T. G. M. J. Colloid Interface Sci. 1992, 149, 493. (12) Tha, S. P.; Shuster, J.; Goldsmith, H. L. Biophys. J. 1986, 50, 1117. (13) Tees, D. F. J.; Coenen, O.; Goldsmith, H. L. Biophys. J. 1993, 65, 1318.
10.1021/la990452t CCC: $18.00 © 1999 American Chemical Society Published on Web 10/05/1999
Colloidal Forces between Bitumen Droplets
Figure 1. Illustration of a doublet breaking up in a wall shear flow. The doublet is composed of a fixed droplet (attached to the wall) and a “free” droplet (not attached to the wall). A shear flow is applied in the y direction to breakup the doublet. G is the shear rate, a is the droplet radius, and h is the separation distance between the two drops. (xb, yb, zb) is the position of the “free” droplet at the onset of a breakup. All the coordinates are scaled by a. F2y, and F2z are two components of the drag force in the y and z directions. F2y, F2z, and Fcoll (colloidal force) are balanced in the normal direction (through droplet centers) at the onset of a breakup.
measurement technique, differential electrophoresis.14 In this case the known force is the “electrophoretic displacement force”, which is only present when two particles have different zeta potentials. This may limit its application to a general colloidal system. The HFB technique can be applied to suspension systems as well. The reasons we chose the bitumen-inwater emulsion are 2-fold. First, understanding the stability mechanism of bitumen-in-water emulsion is of paramount importance in the oil sand industry since the stability (or instability) of the emulsion directly affects the recovery of bitumen from oil sand (a mixture of bitumen and sand). Second, latex particles, though commonly regarded as “model colloids”, rarely behave according to the classical DLVO theory, due to the “hairy” structure on the surface15-17 and the heterogeneous distribution of surface charges.14,18 By contrast, a bitumen droplet surface is partially smooth despite the existence of a few isolated “bumps” of 50-100 nm in horizontal diameter and 0-20 nm or more in thickness.8 Since the interactions between smooth bitumen droplet surfaces do follow the classical DLVO theory, some of the HFB results can be verified by a proven theory and the validity of the method can then be confirmed. The HFB method is a very sensitive technique owing to the employment of a micrometer-sized droplet as a force “sensor”. The lower limit for force detection is around 10-13 N (or 0.1 pN), which corresponds to an energy minimum of 0.5kT. The detailed operation range will be given in the Experimental Section. Theory 1. Basic Principles of the HFB Technique. The best configuration of a doublet for attractive force measurement is illustrated in Figure 1. At the onset of a doublet breakup in this configuration, the colloidal force between the two droplets is approximately equal to the hydrodynamic drag exerted on the “free” droplet. The drag force is closely related to the fluid flow velocity in the system, which can be described by the Stokes equation for a creeping flow (14) Velegol, D.; Anderson, J. L.; Garoff, S. Langmuir 1996, 12, 4103. (15) Chow, R. S.; Takamura, K. J. Colloid Interface Sci. 1988, 125, 226. (16) Wu, X.; van de Ven, T. G. M. Langmuir 1996, 12, 3859. (17) Suresh, L.; Walz, J. Y. J. Colloid Interface Sci. 1996, 183, 199. (18) Velegol, D.; Anderson, J. L.; Garoff, S. Langmuir 1996, 12, 675.
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Figure 2. F2y as a function of z when y f ∞. The filled circles are literature values. Both y and z are defined according to the coordinate system shown in Figure 1. z is scaled by droplet radius, a, and F2y is scaled by 6πµGa2.
and the continuity equation:
µ∇2v(r) ) ∇p
(1)
∇‚v(r) ) 0
(2)
where µ is the fluid viscosity, v(r) is the fluid flow velocity at position r, and p is the pressure. The integral solution of the Stokes equation can be written as 2
v(r) ) v°(r) +
∫S G(r,k)‚f(k) dSi(k) ∑ i)1 i
(3)
where v°(r) is an undisturbed fluid flow field in the absence of the doublet, 1 and 2 stand for fixed and “free” droplets, f(k) is the force density at point k on the droplet surface Si(k), and G(r,k) is the Oseen tensor. The total force exerted by the “free” droplet on the fluid, or vice versa, can be expressed as,
F2 )
∫S f(k) dS2(k) i
(4)
The detailed procedure of solving these equations was described in ref 11. As will be shown later, the most important component of the drag is in the y direction since the colloidal force is mainly balanced by this component (F2y). When the “free” droplet is far from the fixed one, the F2y values should reduce to the results calculated by Goldman et al.21 for a single sphere moving along a wall in a wall shear flow. The agreement between these two calculations is shown in Figure 2. No-slip boundary conditions on the wall and droplet surfaces were assumed in the calculation. For liquid droplets with slipping interfaces, the possible error in the result can be estimated by comparing the friction coefficients in the Stokes law for a solid particle: Fdrag ) 6πµau (19) Hadamard, J. C. R. Acad. Sci. 1911, 152, 1735. (20) Chow, R. S.; Takamura, K. J. Colloid Interface Sci. 1988, 125, 212. (21) Goldman, A. J.; Cox, R. G.; Brenner, H. Chem. Eng. Sci. 1967, 22, 653.
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surface roughness may vary the exact position of the secondary minimum,16,17 the condition of yb < 2.04 will still hold for any detectable attractive forces in the minimum. For this reason, arbitrary yb values around the position of h ) 9 nm were chosen in the calculation. The above-mentioned analysis makes zb the sole variable among the three coordinates. It is determined from the droplet velocity after the breakup using a hydrodynamic theory for a single particle moving in a wall shear flow.21 According to Figure 3, if zb ) 1.01, F2y can be considered a constant of 1.17 (dimensionless value scaled by 6πµGa2, G being the shear rate). If zb > 1.01, F2y is numerically calculated based on the theory described above. The results can be approximated by a linear function for any zb values between 1.01 and 2.0,
F2y ) 1.16 + 1.19 (zb - 1) Figure 3. F2y as a function of yb and zb. The symbols of circles, squares, inverted triangles, and triangles represent the drag forces when zb < 1.01, zb ) 1.1, 1.5, and 2.0, respectively. Both yb and zb are scaled by a, and F2y is scaled by 6πµGa2.
and in the drag force equation for a liquid drop19
µl 2 + µ 3 Fdrag ) 6πµau µl +1 µ
The theory also gives the drag force in the z direction, F2z. It is always around 0.1 for any xb, yb, and zb values of interest. From the geometry shown in Figure 1, the maximum value of the attractive colloidal force between two droplets, Fcoll, can be expressed as follows assuming the forces are balanced in the normal direction, i.e., through the droplet centers, at a breakup,
(5)
where a is the particle or droplet radius, u is the particle or droplet velocity, and µl is the viscosity of the liquid in the droplet. At room temperature, the viscosities of bitumen and water are 400 Pa‚s 20 and 10-3 Pa‚s. This makes eq 5 deviate from the Stokes drag law only by 10-4%. Hence, bitumen droplets can be practically treated as solid particles. For low-viscosity liquid droplets without rigid surfactant layer on the interface, a correction factor must be applied to the calculated F2. Liquid droplets might also deform when a large force is exerted on them. However, the droplet deformation was found to be negligible in the present system where typical surface forces are in the order of 10-12 N.8 The drag force at a breakup is dependent on the “free” droplet position (xb, yb, zb). All the coordinates are scaled by the droplet radius, a, and the origin is placed on the bottom of the fixed droplet (cf. Figure 1). Among these three coordinates, xb ) 0, otherwise the drag force in the x direction becomes nonzero and automatically aligns the doublet with the flow prior to the breakup. This may not be true if the droplet is pushed by a “tangential force” caused by rough surfaces. However, calculation shows that the variation of F2y is within 1% as xb varies from -0.2 to 0.2, a range much wider than any deviations observed in the experiment. Therefore, xb is always treated as zero. The drag force, F2y, for various yb and zb values is plotted in Figure 3. The values of zb were kept below 2.0 because the doublet breakup becomes less observable when the “free” droplet is far from the wall. Figure 3 shows that F2y is almost independent of yb, especially when yb < 2.04. In that region, the variation of F2y becomes less than 1%. In a typical experimental system containing 6 µm droplets in a 0.1 M KCl solution, yb < 2.04 is equivalent to h < 120 nm or more depending on zb (h being the separation distance defined in Figure 1). This condition is always satisfied since the interaction range for any attractive forces is usually much shorter than 120 nm, e.g., the secondary energy minimum for smooth droplets is located around h ) 9 nm at a salt concentration of 0.1 M. Although
(6)
Fcoll ) F2y(zb)
yb
xy2b + (zb - 1)2
+ F2z
zb - 1
xyb2 + (zb - 1)2
(7)
When zb f 1 (practically zb < 1.01), Fcoll is equal to F2y and becomes a constant of 1.17. For any larger zb values, Fcoll seems to depend on both yb and zb. In fact, because yb is always around 2 and the above-mentioned uncertainty of yb due to the surface roughness is usually 2 orders of magnitude smaller, the error caused by using an approximate value for yb is negligible. As a result, Fcoll is only a function of zb and can be calculated following the above-mentioned procedure. 2. Bitumen Surface Model. Force measurement is usually not an end in itself. More important information about surface structure and other colloidal properties can be deduced from the interaction forces using a force model for a specific colloidal surface. According to freeze-fracture scanning electron microscopy (SEM) analysis from the previous work,8 the bitumen droplet surface comprises isolated “bumps” of 50-100 nm in horizontal diameter. The average spacing between any two “bumps” is about 200 nm. Various surface models, such as hemispheres on smooth surface and rippled structure, were used, in the literature,22-28 to calculate interaction forces between rough surfaces. Most of these models were applied specifically to certain colloidal systems. Several general models using a distribution function of material density on particle surface22,23 only describe the average force between two particles over all possible configurations. They cannot be used to interpret the HFB data, which reflect a given configuration involving a limited number (22) Czarnecki, J.; Dabros, T. J. Colloid Interface Sci. 1980, 78, 25. (23) Czarnecki, J.; Itschenskij, V. J. Colloid Interface Sci. 1984, 98, 590. (24) Czarnecki, J.; Warszynski, P. Colloids Surf. 1987, 22, 207. (25) Herman, M. C.; Papadopoulos, K. D. J. Colloid Interface Sci. 1990, 136, 385. (26) Elimelech, M.; O’Melia, C. R. Langmuir 1990, 6, 1153. (27) Shulepov, S. Y.; Frens, G. J. Colloid Interface Sci. 1996, 182, 388. (28) Bhattacharjee, S.; Ko, C.-H.; Elimelech, M. Langmuir 1998, 14, 3365.
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Figure 4. Illustration of the disk-sphere model for doublet interaction force calculation. Each bitumen droplet was considered as a smooth sphere with a single disk-shaped protrusion attached. The disk radius is r for both droplets. The thickness values are L1 and L2, respectively. The total thickness is L ) L1 + L2. The separation distance between the two droplet core surfaces is h.
of protrusions directly facing each other. Because of the relatively large spacing between any two “bumps”, force calculation shows that the “bump” closest to the center of the gap region between two spheres contributes at least 90% of the total protrusion interaction forces. Hence, only one “bump” on each sphere is considered in the following protrusion model. The “bumps” on bitumen droplets were modeled as two flat disks for simplicity (cf. Figure 4). The thickness values of the disks are L1 and L2, respectively. The total disk thickness, L, defined as L ) L1 + L2, is a parameter to be determined from the experimental data. The disk radius, r, was assumed to be identical for both disks. According to the previous SEM analysis,8 r is in the range of 25-50 nm. Here, it is fixed at the average value, 37.5 nm. The resulting error in the determined L value is about 1020%. In this disk-sphere model, it is assumed that the disk is at the center of the sphere surface in the gap region. “Off-center” cases do exist in the experiment. The effects of various asymmetrical configurations are currently being investigated. Preliminary analysis shows that the interaction forces are relatively insensitive to the position of the disk if it shifts from the center by less than 1.5r. Beyond this point, the error in the determined L value gradually increases to about 40%. As will be shown later, even for the simple symmetrical configuration, an uncertainty of a factor of 2 in the individual disk thickness, L1 or L2, is unavoidable. For this reason, the idealized model was considered adequate for the system that prohibits the accurate measurement of the individual disk thickness anyhow. The interactions between disks and spheres are exclusively DLVO-type forces, which will be verified later. The electric double-layer force can be expressed as the sum of sphere-sphere and plate-plate interactions29 -1 -κh
Fel ) Bπaκ e
2
+ Bπr [e
-κ(h-L)
-κh
-e
]
(8)
where B ) 32 tanh2(eøo/4kT)0κ2(kT/e)2, e is the electronic charge, øo is the surface potential of the droplets and the protrusion, which is assumed to be identical to the zeta potential of the droplet, -85 mV, 0 is the permittivity of vacuum, is the dielectric constant of water, κ is the reciprocal Debye length, and h is the separation distance defined in Figure 4. The second term in brackets eliminates the overestimation of the double-layer force between two spheres containing uncharged surfaces behind the disks. The disk-sphere interactions were neglected because of the fast decaying feature of the double-layer force. For the van der Waals forces, three contributions from sphere-sphere, disk-sphere and disk-disk were taken (29) van de Ven, T. G. M. Colloidal Hydrodynamics; Academic Press: London, 1989.
into account. The forces were calculated according to Hamaker’s approach with modifications for the retardation effect. The first contribution was formulated using Derjaguin approximation.29 The second contribution was formulated assuming a plate-half space interaction.1 This was justified by the fact that r , a always holds. The third contribution, Fvdw,d-d, was calculated using numerical integration over the space occupied by the two disks (cf. Appendix). The total van der Waals forces can be expressed as follows
As-sa f1(ps-s) 12h2 f2(h - L1) f2(h) f2(h - L2) f2(h) - 3 + - 3 + Ad-sr2 (h - L1)3 h (h - L2)3 h Fvdw,d-d (9)
Fvdw ) -
[
]
where
f1(p) ) f1(p) )
1 + 3.54p (1 + 1.77p)2
pe1
0.98 0.434 0.067 + p p2 p3
p>1
and
f2(s) ) 0.168 - 0.093
3
(πsλ ) + 0.019(πsλ )
4
(πsλ )
- 0.005
Here, As-s and Ad-s are the Hamaker constants of bitumen-water-bitumen and protrusion-water-bitumen. f1(p) and f2(s) are functions accounting for the retardation effects in a sphere-sphere system30 and a flat plate-plate system,31 respectively. λ is the retardation wavelength (fixed at 100 nm) and ps-s ) 2πh/λ. Fvdw,d-d can also be calculated based on the following formula, which deviates from the numerical results by less than 10% for all h values
Fvdw,d-d )
[
-Ad-dr2
f2(h - L) 3
(h - L)
-
f2(h - L1) (h - L1)
3
-
f2(h - L2) 3
(h - L2)
+
]
f2(h) h3
(10) where Ad-d is the Hamaker constant of protrusion-waterprotrusion. As-s will be determined from the experimental data. The values of Ad-s and Ad-d depend on the compositions of the protrusion, which may vary from 100% water to 100% bitumen depending on the extent of hydration of the protrusion. Two extreme cases of 100% water and 100% bitumen will be used to interpret the force data. They are called case A and case B, respectively. In case A, eqs 9 and 10 reduce to
Fvdw ) -
As-sa 12h2
f1(ps-s)
(11)
In case B, because As-s ) Ad-s ) Ad-d, eqs 9 and 10 (30) Schenkel, J. H.; Kitchener, J. A. Trans. Faraday Soc. 1960, 56, 161. (31) van Silfhout, A. Proc. Konigs. Akad. Wetensh. B. 1966, 69, 501.
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Figure 5. Typical force profiles calculated based on the disksphere model in both case A and case B. The solid curve on the left represents the force profile assuming L ) 0 nm. The solid curve on the right was calculated assuming L ) 10 nm in case B. The dotted curve on the left was calculated assuming L ) 10 nm in case A. Other parameters are a ) 3 µm, r ) 37.5 nm, and As-s ) 3.2 × 10-21 J. The force barriers were plotted in the inset with the same symbols. The force unit in the inset is 1 nN or 10-9 N.
Figure 6. Setup of a hydrodynamic force balance. Solid lines with arrows represent the flow of video signals. Dotted lines with arrows represent the directions of the controlling signals sent through the joystick or the computer keyboard.
reduce to
Fvdw ) -
As-sa 2
12h
[
f1(ps-s) - As-sr2
f2(h - L) (h - L)
3
-
]
f2(h) h3
(12)
Note that case A represents “hollow” disks with charged surfaces rather than two smooth spheres without any disks. The electric double-layer force (eq 8) remains unchanged in both cases. Combining eqs 8, 11, and 12, we can plot the forcedistance profiles assuming a typical L value in both case A and case B (cf. Figure 5). The force profile of smooth sphere-sphere interactions (L ) 0) was also shown for comparison. The force barriers were plotted in the inset. By comparing the solid curves in Figure 5, i.e., the force profiles of L ) 0 and 10 nm of case B, one can see that both the force barrier and the secondary minimum are reduced when protrusions are present. These findings are in agreement with literature results.17 The reduction of the force or energy barrier is caused by the relatively large van der Waals attraction between two protrusions at a close distance. Hence, the force profile of case A, which neglects all van der Waals interactions between the two protrusions, does not show any reduction of the force barrier (cf. Figure 5 inset). In the HFB experiment, even the reduced force barrier is 3 orders of magnitude higher than the maximum hydrodynamic force obtainable using the current apparatus, therefore the study is only restricted to the secondary minimum. In terms of the depth of the secondary minimum (or maximum attractive force), the force curves of cases A and B show far less differences as compared to the force barriers. This small difference in the attractive force allows one to determine the thickness of the protrusion to certain degrees of accuracy without knowing its exact chemical compositions or Hamaker constant. The actual value of the total disk thickness, L, for each breakup measurement was obtained by fitting the experimental force data with the maximum attractive force values calculated from eqs 8, 11, and 12. According to these equations, the total colloidal force is independent
Figure 7. A close-up view of the sample cell. Note that this picture represents the actual orientation of the instrument. The view in Figure 1 should be inverted.
of the individual thickness L1 or L2. Hence, from the experimental force data, it is not possible to differentiate one disk with a thickness L opposing a sphere with smooth surface in the gap region or two disks with a thickness 1/ L each. This uncertainty of a factor of 2 in the individual 2 disk thickness probably overshadows other errors mentioned above. Experimental Section 1. Materials. Syncrude coker-feed bitumen was mixed with 0.1 M KCl solution and placed in a Fisher FS6 ultrasonic water bath at 50-60 °C for 80 s to create 4-8 µm bitumen droplets. The salt solution also contained 30% D2O to generate a slight buoyancy force for the bitumen droplets (density difference ∼10 kg/m3). The pH of the solution was not adjusted and was determined to be 7. 2. Apparatus. The hydrodynamic force balance is actually a “surface collision apparatus”6 (later called “microcollider”8) running in a different mode. The setup is illustrated in Figure 6. The bitumen-in-water emulsion was placed in a sample cell, which was mounted on a x,y axes motorized stage (Newport UTM50CC.5HA). A steel cylinder with a flat glass surface glued to one end was immersed into the emulsion to form a gap of 120 µm between the glass surface (top plate) and the parallel bottom plate of the sample cell (cf. Figure 7). Since the top plate is fixed, when the bottom plate moves with the motorized stage, a wall shear flow is created in the gap. The shear rate and flow direction are controllable either through a joystick or by a Pentium computer. Droplet movement was observed under an optical
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Figure 8. A typical shear rate profile in a breakup experiment. The breakup time can be found from the video frame. It was used to locate the breakup shear rate, Gb, which was subsequently used to calculate the drag force. The z-coordinate of the “free” droplet was determined in the constant shear zone indicated in the upper-right corner. microscope (Zeiss AXIOTECH) and was recorded by a video camera (Sony DXC-950) and a VCR (Sony SVO-9500MD). The VCR is controlled by the same computer, so the motion of the stage can be synchronized with the recording. The computer also contains a frame grabber (Imaging Technology IC-PCI/AM-CLR) to measure droplet positions and speeds. 3. Procedure. In a 0.1 M KCl solution, bitumen droplets usually adhere to a glass surface if the separation distance is very small. Shortly after the introduction of the bitumen emulsion to the cell, one can observe some droplets firmly attached to the top plate. One of these droplets could be used as the fixed droplet. A droplet with a radius difference of less than 10% (referred to as the “free” droplet) was then located in the gap (cf. Figure 7) and was manipulated to the vicinity of the fixed droplet by a controlled shear flow. The “free” droplet usually floats slowly to the top plate under the buoyancy force. Once the “free” droplet was close to the top plate, a collision between these two droplets was generated using a weak shear flow (∼2 s-1). Subsequently, a weaker shear flow (∼0.5 s-1) was generated to test the mobility of the newly formed doublet in x and y directions. In this system, bitumen droplets have much lower affinity to other bitumen droplets than to the glass surface, probably due to the lower Hamaker constant of bitumen-water-bitumen compared to that of bitumen-water-silica.32 Therefore, bitumen doublets are almost exclusively secondary doublets and the mobility of the “free” droplet should only be in the x direction. Mobility in both directions indicates no doublet formation probably because the “free” droplet is still far from the top plate. Another droplet collision should be generated after some additional waiting time, and the mobility would be retested. Mobility in neither direction usually indicates that the “free” droplet is attached to the top plate as well. The common cause is that the “free” droplet was allowed to float too close to the top plate. A breakup experiment should not proceed with this pair of droplets. The screening procedure is subjected to changes if different types of forces, e.g., adhesive force, are to be investigated. Once a secondary doublet was detected, a computer command was immediately sent to move the motorized stage at a preprogrammed acceleration in the breakup direction (y direction). The motor speed increases in small steps, which creates a stepwise increase of the shear rate. The steps are usually small, so no oscillation of the flow occurs in the system. A typical shear rate vs time curve is plotted in Figure 8. At time zero, the address of a recording videocassette was acquired by the computer. After the doublet breakup, the videocassette was played backward frame by frame (1 frame ) 1/30 s) to locate the frame of the breakup (32) Sanders, R. S.; Chow, R. S.; Masliyah, J. H. J. Colloid Interface Sci. 1995, 174, 230.
Figure 9. Snapshots of the breakup process. Two 5 µm bitumen droplets are shown in the figure. The one on the left is the fixed droplet and the one on the right is the “free” droplet. The shear flow direction is from left to right. The breakup frame is defined as one frame before any detectable motion of the “free” droplet. It thus looks identical to any frames before breakup and can only be located by playing the videocassette backward. (cf. Figure 9). The elapsed time shown on a VCR was used to find the breakup shear rate, Gb (cf. Figure 8). The z coordinate of the “free” droplet after the breakup was determined from the droplet velocity, measured from a series of digitized frames, and the known shear rate, taken from a constant shear zone in Figure 8. The detailed procedure and theory of determining z coordinates are described in the literature.6,21 After the “free” droplet position had been determined, the drag forces in y and z directions, F2y and F2z, were calculated by solving eqs 1-4. The dimensionless attractive force, Fcoll, was then calculated from eq 6. This value multiplied by 6πµGba2 yielded the final colloidal force between two droplets near an energy minimum. The operation range of the current apparatus is 0.1-10 pN for an aqueous system. The lower limit of 0.1 pN is determined by the experimental error to be discussed below. It is actually quite close to the “natural limit” of all force measurements, at which the random force component becomes a significant part of the measured force. To be reasonably accurate, we only demonstrate the determination of larger forces, i.e., from 0.2 to 5.2 pN. The upper limit of 10 pN is instrument dependent. It can be further raised if a modified sample cell is installed.
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Table 1. Determined Forces and Data Interpretation Using the Disk-Sphere Model a no. (µm) 1 2 3 4 5 6 7 8 9 10 11 12 13
3.9a 3.6a 3.2a 3.7 2.2 3.7 3.7 3.7 2.6 2.2a 3.0 2.5 3.5
Zb
determined force and its error (pN)
