pubs.acs.org/Langmuir © 2009 American Chemical Society
Dynamics of Liquid-Liquid Displacement Renate Fetzer,* Melanie Ramiasa, and John Ralston Ian Wark Research Institute, University of South Australia, Adelaide, SA 5095, Australia Received February 17, 2009. Revised Manuscript Received May 4, 2009 Capillary driven liquid-liquid displacement in a system with two immiscible liquids of comparable viscosity was investigated by means of optical high speed video microscopy. For the first time, the impact of substrate wettability on contact line dynamics in liquid-liquid systems was studied. On all substrates, qualitatively different dynamics, in two distinct velocity regimes, were found. Hydrodynamic models apply to the fast stage of initial spreading, while nonhydrodynamic dissipation dominates contact line motion in a final stage at low speed, where the molecular kinetic theory (MKT) successfully captured the dynamics. The MKT model parameter values showed no systematic dependence on substrate wettability. This unexpected result is interpreted in terms of local contact line pinning.
Introduction Industrial processes such as painting and coating involve the wetting of a solid surface by a liquid. Thus, the mechanism by which a liquid front advances on a solid surface in a gaseous surrounding has been the subject of increasing attention over the last 30 years. However, in many of the processes of technological interest, wetting occurs in systems constituted of two immiscible liquids in contact with a solid surface. In oil recovery, cleaning and pickering emulsion processes, for example, liquids spread or retreat while surrounded by another liquid phase. In these cases, the liquid-liquid displacement plays a crucial role in controlling, for instance, the efficiency of the recovery processes or the stabilization of the emulsion. Despite its enormous relevance, however, the dynamics of liquid-liquid displacement incorporates many unresolved issues and requires further studies; see, for instance, ref 1. In a gaseous surrounding, two main theoretical models have proven their capacity to describe contact line dynamics. Hydrodynamic models assume that viscous friction is the only significant dissipation force, while the molecular kinetic theory focuses on nonhydrodynamic dissipation at the three phase contact line. In both cases, the exact dependence of the microscopic model parameter values on system properties such as wettability and heterogeneity is still an open question. Especially in the case of liquid-liquid systems, where a competing dynamics between two immiscible liquid phases is expected, the behavior of the contact line motion is still unclear. One key property in liquid-liquid systems is the viscosity of the two fluids and their ratio. For very dissimilar viscosities, the less viscous fluid can be treated as inviscid and the system can be described in terms of liquid-vapor displacement, compare, for example, ref 2. Very early experimental studies over a wide range of viscosity ratios were performed to capture the respective impact by means of a hydrodynamic approach.3-5 Later, deviations from a purely hydrodynamic behavior were found for low contact line (1) Dussan, V. E. B. Ann. Rev. Fluid Mech. 1979, 11, 371. (2) Basu, S.; Nandakumar, K.; Masliyah, J. H. J. Colloid Interface Sci. 1996, 182, 82. (3) Mumley, T. E.; Radke, C. J.; Williams, M. C. J. Colloid Interface Sci. 1986, 109, 398. (4) Foister, R. T. J. Colloid Interface Sci. 1990, 136, 266. (5) Stokes, J. P.; Higgins, M. J.; Kushnick, A. P.; Bhattacharya, S.; Robbins, M. O. Phys. Rev. Lett. 1990, 65, 1885.
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speeds and capillary numbers Ca < 2 10-3.6,7 For capillary numbers below 10-4, viscous friction was found to be negligible and purely nonhydrodynamic dissipation described contact line dynamics successfully.8-10 We have studied the spreading of an oil droplet (dodecane) on a series of alkanethiol-coated gold surfaces in an aqueous surrounding phase (Milli-Q water). We chose to keep the liquids constant and modify the substrate wettability. In particular, the ratio of the respective fluid viscosities is fixed at 1.5. Thus, depending on the velocity regime studied, viscous dissipation of either both or none of the liquids is negligible. We investigated displacement dynamics at capillary numbers ranging from 2 10-5 to 2 10-3. We found a qualitative transition around Ca ≈ 2 10-4 from a hydrodynamic regime at high speeds to nonhydrodynamic behavior at low contact line velocities. Further, we discuss the significance of the microscopic parameters for both hydrodynamic and nonhydrodynamic models and their dependence on substrate wettability, hitherto unexplored.
Materials and Methods Liquids and Droplet Formation. For the experiments, dodecane (99%) was purchased from Sigma Aldrich (Sydney, Australia) and used in the present study without further purification. Ultrapure deionized water, obtained from a Milli-Q system, was used in all experiments. The viscosity of the liquids at 25 °C was 0.89 and 1.34 mPa 3 s for water and dodecane, respectively, while the water-dodecane interfacial tension was 52 mN/m (measured using the pendant drop technique). Dodecane droplets in water were produced using a microfluidic glass chip with a simple T-junction. The hydrophilic channel walls are preferentially wet by the water phase. This allows the formation of oil droplets at the junction by flowing water straight through the junction and feeding dodecane from the side. Placing the microfluidic device under water allows the dodecane droplets to detach easily from the outlet and to rise freely due to buoyancy. By adjusting the dimensions of the channels and the flow rate of the two fluids, the size of the droplets can be varied. A device (6) Zhou, M.-Y.; Sheng, P. Phys. Rev. Lett. 1990, 64, 882. (7) Sheng, P.; Zhou, M. Phys. Rev. A 1992, 45, 5694. (8) Kolev, V. L.; Kochijashky, I. I.; Danov, K. D.; Kralchevsky, P. A.; Broze, G.; Mehreteab, A. J. Colloid Interface Sci. 2003, 257, 357. (9) Kralchevsky, P. A.; Danov, K. D.; Kolev, V. L.; Gurkov, T. D.; Temelska, M. I.; Brenn, G. Ind. Eng. Chem. Res. 2005, 44, 1309. (10) Wang, X.; Nguyen, A. V.; Miller, J. D. Int. J. Miner. Process. 2006, 78, 122.
Published on Web 06/04/2009
DOI: 10.1021/la900584s
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Article with 300 μm wide and 50 μm deep channels was used, and flow rates of about 50 and 1 μL/min for water and dodecane, respectively were used; droplets about 300 μm in diameter were typically obtained. Sample Preparation and Characterization. Thiol-coated gold surfaces were used as substrates. Bare glass slides (microscope slides) were rinsed with ethanol and treated with air plasma. By thermal vapor deposition, first a 2.5 nm thick chromium layer (for secure anchoring of the gold) and then, second, 6 nm of gold were deposited onto the glass slides. Atomic force microscopy (AFM) revealed a root mean square (rms) roughness of 0.8 nm for the bare gold surfaces on 1 1 μm2 sized images. The metalcoated glass slides were again degreased with ethanol and cleaned under plasma, before immersing for 2 h in mixed thiol solutions (10-3 M) of 11-mercapto-1-undecanol [HS(CH2)11OH] and perfluorodecanethiol [HS(CH2)2(CF2)7CF3] in ethanol at room temperature. In order to obtain a range of substrates with different wettability, the molar ratio of the alkane thiols was varied between 15% and 67% of perfluorodecanethiol in the solution. After deposition of the thiol coating and prior to each further use, the samples were thoroughly rinsed and sonicated in ethanol. The thiol coatings showed a rms roughness of about 1.1-1.3 nm over an area of 1 1 μm2, independent of the layer composition. There were no detectable patches in the phase images using tapping mode AFM. Time-of-flight secondary-ion mass spectrometry (ToFSIMS) images of the surfaces, at a resolution of 100 nm2, showed no indication of segregation. We therefore conclude that the thiol layers were molecularly mixed. Static wettability and contact angle hysteresis were probed using the “captive bubble” configuration: the thiol substrate was immersed in water upside down, and a dodecane droplet was introduced with a microsyringe through a U-shaped needle and brought into contact with the solid surface from underneath. Advancing and receding contact angles of water displaced by the oil droplet were measured. The thiol-coated surfaces yielded reproducible static contact angle data with a hysteresis of about 30°, independent of the thiol composition. Experimental Apparatus. The experimental configuration for top view measurements of the spreading dynamics is shown in Figure 1a. It comprised a high-speed digital camera system, a water container, the sample of interest, the microfluidic device, various tubes, syringes, and automated pumps. The solid sample was horizontally submerged just below the water free surface and held in place above the microfluidic chip by dint of a specially designed Teflon piece. The camera was located above the optically transparent surface. Dodecane droplets were continuously produced in the microfluidic device as described above. In order to remove interfering droplets, another tube connected to a reverse dispensing syringe was introduced and placed above the outlet where the droplets emerged. This scavenger syringe guaranteed that only one droplet at a time rose freely until it hit the underside of the substrate, where it rested before finally spreading over the surface. The dynamics of droplet spreading were captured, from the moment each droplet touched the surface until it reached an equilibrium position, by a digital video recorder connected to a high speed camera and a microscope. The time between drop impact and rupture of the thin water film between the oil droplet and solid surface varied statistically in the range from 1 ms up to at least 45 ms. We could not detect any influence of drainage and rupture time on the spreading dynamics, indicating that the drop impact does not affect the subsequent spreading process. The spatial resolution at a frame rate of 3000 images per second was 512 512 pixels. All experiments were repeated several times with excellent reproducibility. Data Processing. From the optical images (cf. Figure 1b for typical pictures), the radius of the contact area between the oil droplet and solid surface was obtained, called contact radius thereafter. As shown in Figure 2, the initial growth of the contact radius depends strongly on substrate hydrophobicity, while the 8070 DOI: 10.1021/la900584s
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Figure 1. (a) Experimental arrangement for dynamic top-view measurements. (b) Typical series of top-view images. (c) Schematic (side view) of drop geometry during its spreading process.
Figure 2. Instantaneous contact radius of oil droplets versus time as the oil displaces water on thiol-coated gold surfaces. The experimental error in the radius data is less than 5% of the final value. The percentage gives the molar ratio of CF3-terminated thiols in the solution during deposition of the surface coating. Table 1. Results for the Model Parameters Gained from the Best Fit of the Respective Theories to Representative Data Sets (cf. Figures 3 and 5) % of CF3
VB [nL]
θm [deg]
ln (L/LS)
θMKT 0 [deg]
K0 [MHz]
λ [nm]
15 20 33 40 45 50 67
11.8 132 102 11.3 17.0 10.7 14.6
27.8 40.2 49.2 55.0 58.3 69.3
32.6 36.9 42.2 43.4 46.0 51.6
31.7 46.7 52.2 60.8 62.0 72.9 83.2
0.47 0.36 0.35 0.29 0.40 0.26 0.29
1.78 1.59 1.87 1.56 1.59 1.78 1.92
final contact radius is also determined by the droplet size; compare with Table 1 for respective drop volumes. In a subsequent step, the instantaneous contact angle for each consecutive image was of interest. Working with small droplets (typically 300 μm diameter), it can be assumed that effects of gravity on the drop shape are not significant. Moreover, the capillary number for the spreading droplets in these experiments is quite small, so that the effect of viscosity on the droplet shape can also be neglected. Therefore, during the course of the spreading process, the droplet remains in its quasistatic spherical shape. This was confirmed by side view Langmuir 2009, 25(14), 8069–8074
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images. As visualized in the schematic shown in Figure 1c, the instantaneous contact radius r can be expressed as a function of the instantaneous macroscopic water contact angle θ using the relationship characterizing the geometry of a spherical cap11 " r ¼
3VB sin3 θ π 2 þ 3cos θ - cos3 θ
#1=3 ð1Þ
The volume of the dodecane droplet, VB, was determined using the final contact radius and the final droplet diameter, both measured after relaxation to equilibrium. From these two values, the final contact angle was obtained and, using eq 1, VB could be determined. Knowing VB, eq 1 permits the instantaneous water contact angle for each consecutive contact radius to be computed. The velocity of the contact line was determined numerically (polynomial fit over five consecutive data points) by the first derivative of the contact radius with respect to time t, v = dr/dt. Thus, for every single droplet observed, the experimental values of both the dynamic contact angle and the contact line velocity as functions of time were determined and could be compared with the theoretical models.
Results and Discussion Hydrodynamic Regime. Data Analysis. Depending on the dominant dissipation mechanism, different approaches were developed to describe contact line dynamics in fluid-fluid displacement. In the hydrodynamic model, viscous shear is the only significant dissipation that counteracts the driving capillary force. As a consequence of the highest shear rates present in the liquid wedge close to the three phase contact line, the free fluid-fluid surface is bent and the instantaneous (apparent) macroscopic contact angle θ deviates from the microscopic one, θm. As shown by Cox,12 this approach, to lowest order in the capillary number Ca = vη1/γ, results in the following equation gðθ, εÞ ¼ gðθm , εÞ ( Ca lnðL=LS Þ
ð2Þ
where the plus sign holds for advancing liquid fronts and the minus sign for receding contact lines. The function g(θ,ε) is defined as Z gðθ, εÞ ¼
θ
dβ=f ðβ, εÞ
0
f ðβ, εÞ ¼ 2sin β½ε2 ðβ2 - sin2 βÞ þ 2εfβðπ -βÞ þ sin2 βg þ fðπ -βÞ2 - sin2 βg εðβ2 - sin2 βÞfðπ -βÞ þ sin β cos βg þ fðπ -βÞ2 - sin2 βgðβ - sin β cos βÞ
ð3Þ Here, v is the contact line speed, η1 is the bulk viscosity of the liquid under consideration, ε = η2/η1 is the ratio of the two fluid viscosities, and γ denotes the fluid-fluid interfacial tension. L characterizes a typical macroscopic length scale (e.g., the capillary length or the order of the droplet size), and LS denotes a microscopic cutoff length introduced to remove the singularity at the contact line, the diverging shear stress that evolves from the classical no-slip boundary condition. L is expected to be of molecular order. In the original hydrodynamic model, the microscopic contact angle θm was assumed constant and equal to the equilibrium contact angle θ0. (11) Fetzer, R.; Ralston, J. J. Phys. Chem. C 2009, 113, 8888. (12) Cox, R. G. J. Fluid Mech. 1986, 168, 169.
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Figure 3. Dynamic contact angle data of water displaced by dodecane droplets on thiol-coated gold surfaces. The best fit of the hydrodynamic model is presented by the solid lines. Respective fit parameters are given in Table 1.
For negligible viscosity η2 of the second fluid (e.g., if it is a gaseous phase) and for contact angles smaller than 135°, the Cox function g(θ,ε=0) can be approximated by θ3/9. In the case of liquid-liquid displacement with ε = η2/η1 of order 1, however, none of the viscosities is negligible. For a water front (η1 = 0.89 mPa 3 s) moving against dodecane (η2 = 1.34 mPa 3 s), eq 3 was solved numerically. The result was very well approximated by g(θ,ε=1.5) = 0.063θ2.52 for contact angles up to 60°. The following simplified hydrodynamic model is therefore used for dodecane-water displacement θ2:52 ¼ θm 2:52 ( Ca=0:063 lnðL=LS Þ
ð4Þ
to compare with dynamic contact angle data obtained for this system. The free fitting parameters are the microscopic contact angle θm and the logarithmic ratio of the two relevant length scales, ln(L/LS). Results and Discussion. In Figure 3, dynamic contact angle data of water are plotted against the respective contact line velocity for a typical set of data. The spreading of oil droplets in an aqueous medium starts at small water contact angles and high speeds and relaxes toward low speeds and the final maximum contact angle of water. The best fit of the hydrodynamic model for contact line motion in water-dodecane systems, eq 4, is represented by the solid lines in Figure 3. Above a contact line velocity of about 0.5-1 cm/s, the qualitative run of the data is very well described by hydrodynamics. Below this critical speed, nonhydrodynamic dissipation seems to control contact line dynamics (see section below). The fit parameters of the hydrodynamic model are summarized in Table 1. The results for θm are systematically smaller than the final water contact angle in the dynamic experiments. This result indicates that the final stage of contact line dynamics is nonhydrodynamic in nature. For the logarithmic constant ln(L/LS), we found values between 30 and 50, which does not fit the expectation: the macroscopic length scale L should be of the order of the droplet size (300 μm), whereas the microscopic cutoff length LS is expected to be of molecular order (angstrom to nanometer range). This suggests a ratio L/LS of about 5-6 orders of magnitude. Our results, however, translate to a ratio of 13-22 orders of magnitude between L and LS. This indicates that we cannot take our results literally and, although the dissipation is predominantly viscous in nature, some other friction mechanism (e.g., nonhydrodynamic contact line friction, roughness, or inertial effects) might, in addition, resist the contact line motion in DOI: 10.1021/la900584s
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the high velocity regime. One hint to what these additional effects might be is the fact that we observe some systematic trend in the data, which is not expected for purely viscous dissipation: the values for ln(L/LS) increase with increasing substrate hydrophobicity. Because we did not observe any systematic dependence of surface roughness on the coating composition, roughness alone can be excluded as the cause of the additional resistance. Inertial effects, on the other hand, are expected to become more pronounced for higher initial contact line speed. Because this is in agreement with the data, we suspect that inertia might resist the initial acceleration of the contact line and, thus, be (at least in part) responsible for the higher apparent hydrodynamic resistance in the initial regime. This argument is further supported by the Weber number We = Fv2R/γ. Inertia is known to hinder initial acceleration in capillary flow for Weber numbers larger than about 0.015.13 With R estimated by the droplet radius, We in our system indeed reaches values up to 0.05 on the most hydrophobic surfaces. Molecular Kinetic Regime. Data Analysis. In this section, analysis is focused on the motion of the contact line for speeds below 1-3 cm/s (depending on the hydrophobicity of the sample). As already observed in Figure 3, the hydrodynamic model does not capture the contact line dynamics for low velocities. To exclude the possibility that the apparent trend in the data is a matter of simply experimental error and scatter in the data, the prediction of the hydrodynamic model is compared with the primary data of contact radius versus time (cf. Figure 4). The solid line in Figure 4 was achieved by numerically integrating the equation of motion dθ = v(θ)/(dr/dθ)dt, where v(θ) is given by eq 4 (using the parameters θm and ln(L/LS) obtained from the best fit) and dr/dθ is determined from eq 1. From the plot shown in Figure 4, it becomes very clear that the contact line in this late regime of spreading extends well beyond any hydrodynamic prediction. In this low velocity regime, substrate heterogeneity and pinning of the contact line may become important and a statistical process of contact line motion is expected. The original approach to describe statistical events of local contact line displacements (either single atoms or molecules or clusters of them) is the molecular kinetic theory (MKT) derived by Blake and Haynes,14 based on the activated rate theory of Henry Eyring. In equilibrium, the frequency of thermally activated displacements at the contact line is given by K0 ¼
kB T -ΔG exp h kB T
ð5Þ
where ΔG is the activation free energy of the respective displacements, kBT is the thermal energy, and h is Planck’s constant. The unbalanced capillary force γ(cos θ0 - cos θ) alters the displacement rates with and against the direction of flow. Local displacements of mean distance λ result in an overall net contact line speed given by (
) λ2 γ ðcos θ0 - cos θÞ vðθÞ ¼ 2K0 λ sinh 2kB T
ð6Þ
Results. As shown by the solid lines in Figure 5, the molecular kinetic theory, eq 6, fits the data of liquid-liquid displacement in (13) Hoffman, R. L. J. Colloid Interface Sci. 1975, 50, 228. (14) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421.
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Figure 4. Data of increasing contact radius compared with the best fit of the hydrodynamic model. For long times (see inset as well), the data clearly exceed the theoretical prediction.
Figure 5. Best fit of the molecular kinetic theory to representative data sets in the low velocity regime. Fit parameters are given in Table 1.
the low velocity regime qualitatively quite well. The critical velocity, above which the MKT does not match the run of the data, was found to depend systematically on substrate hydrophobicity. For small, receding final water contact angles, the transition occurs at about 1 cm/s, whereas the MKT fits the data up to 3 cm/s for experiments with a final receding contact angle of about 70°. The respective fit parameters are summarized in Table 1. For the frequency of local displacements at the contact line, we find values of about 0.3-0.5 MHz and the jump distance ranges from 1.6 to 1.9 nm. Respective results for all investigated data sets are summarized in Figure 6. Both parameters λ and K0 are rather randomly distributed and do not show any clear dependence on the surface composition. These results are now compared with various expectations and interpretations of molecular processes that may take place at the contact line. Discussion. There are several approaches reported in literature which link the activation free energy ΔG (per unit area) for displacements at the three phase contact line to system properties such as solid-liquid interaction, capillary forces, or surface heterogeneity. In one of these attempts, ΔG in solid-liquid-vapor systems is correlated with the work of adhesion Wad = γ(1 + cos θ0).15,16 This approach is based on the assumption that adsorption-desorption processes of single atoms or molecules take place at the contact line.17 The jump (15) Vega, M. J.; Gouttiere, C.; Seveno, D.; Blake, T. D.; Voue, M.; De Coninck, J. Langmuir 2007, 23, 10628. (16) Ray, S.; Sedev, R.; Priest, C.; Ralston, J. Langmuir 2008, 24, 13007. (17) Blake, T. D.; De Coninck, J. Adv. Colloid Interface Sci. 2002, 96, 21.
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Figure 6. Model parameters λ and K0, gained from the best fit of the MKT to the low velocity regime, for all data sets on thiolcoated gold surfaces.
distance λ is expected to be of molecular order (typically below 1 nm), and the rate of local displacements K0, which is directly correlated with the activation free energy, should strongly depend on substrate hydrophobicity. This approach was confirmed for liquid-gas systems at rather large velocities.15,16,18 However, it is not supported by these present results in a water-oil system at low velocities. Values of λ larger than 1 nm are observed, and none of the parameters depend on substrate hydrophobicity. This is quite puzzling and leads to the question as to how ΔG should be correlated with system properties and solid-liquid interactions in this present study. One difference between the former experiments and the present study is the fact that we are dealing with liquid-liquid displacement processes. In liquid-liquid systems, the analogue to the work of adhesion in gaseous surroundings is the relative (1) = γ(1 + cos θ(1) substrate affinity Wad 0 ) of one liquid phase surrounded by another liquid. The liquid-liquid interfacial tension is γ, while θ(1) 0 is the advancing contact angle of liquid (1) against liquid (2). Accordingly, the affinity of liquid (2) to the (2) = γ(1 + cos θ(2) solid is given by Wad 0 ), where the advancing (1) contact angle of liquid (2) can be expressed via θ(2) 0 = 180° - θ0 + Δθ with Δθ representing the contact angle hysteresis. In the process of liquid-liquid displacement, the dynamics of both liquid phases compete against each other. For similar density and viscosity, none of the fluid phases is generally favored and the (1) or with activation free energy ΔG might correlate either with Wad (2) Wad , depending on which liquid dominates the dynamics at the contact line. A second distinct feature of our present experiments is the low velocities at the contact line in the regime where the molecular kinetic approach applies. For liquid-gas systems, it was shown recently11,19 that in a low velocity regime the motion of the three phase contact line is not governed by displacements via adsorption-desorption processes, but rather by a local pinning and depinning mechanism of the contact line. These pinning events should become important for slow contact line dynamics in all real systems that exhibit significant static contact angle hysteresis. The displacement distance should correlate with a typical length scale of substrate heterogeneities (which might easily exceed 1 nm), and the activation free energy should correspond to the strength of (18) Martic, G.; Blake, T. D.; De Coninck, J. Langmuir 2005, 21, 11201. (19) Rolley, E.; Guthmann, C. Phys. Rev. Lett. 2007, 98, 166105.
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Figure 7. Activation free energy ΔG/λ2 calculated from the displacement rate K0 using eq 5 and normalized to the respective values of λ2. The lines correspond to the relative affinity of water (water) (oil) Wad (dashed), the affinity of dodecane Wad (dotted), the static contact angle hysteresis H (solid black), and the local pinning energy P (solid gray).
the pinning sites. The latter was shown to correlate qualitatively with the static contact angle hysteresis H = γ(cos θr0 cos θa0), where θr,a 0 denote the static receding and advancing contact angles.19 In a similar approach,11 the activation free energy ΔG of local displacements at the three phase contact line could be related quantitatively to a microscopic pinning energy on surfaces which are heterogeneous on the molecular (nanometer) scale. For advancing/receding contact lines, the local pinning energy was estimated by P = γ(cos θa0 - cos θphob)/P = γ(cos θphil - cos θr0), where θphob,phil denotes the local wettability represents the of hydrophobic/hydrophilic defects and θa,r 0 advancing/receding macroscopic contact angle on the heterogeneous sample. For a quantitative comparison of our data with these various interpretations, we calculated via eq 5 the activation free energy ΔG of local contact line displacements from our results for K0. ΔG is then normalized to the respective values of λ2 and plotted against the final (receding) water contact angle θr0 in the liquidliquid system (cf. Figure 7). These data are compared with the various energies that might be relevant: the affinity (a) of water (water) , and (b) of dodecane in aqueous surrounded by dodecane, Wad (oil) surrounding, Wad , (c) the hysteresis H, and (d) the local pinning (water) is much larger energy P. As demonstrated in Figure 7, Wad than our data for the activation free energy (per unit area), while (oil) is in reasonable agreement with the the affinity of dodecane Wad data. These results suggest that the process of dodecane displacing water is dominated by the properties and interaction forces of the dodecane phase, a conclusion that is not very plausible. For our system, we observe a static contact angle hysteresis of 30° for all substrates. From the respective solid black line in Figure 7, we (oil) . This hints find that H describes the data at least as well as Wad that local contact line pinning might control liquid-liquid displacement in the slow velocity regime, an interpretation that seems more convincing than the suggestion that dodecane dominates over water. Finally, the local pinning energy P is estimated using θphil=15°. The respective solid gray line in Figure 7 (oil) and to the data. This, again, justifies the is very close to Wad idea that local pinning might have a strong influence on the dynamics of liquid-liquid displacement in a low velocity regime. Due to the large scatter in our data, however, no definite conclusion about the molecular mechanisms at the three phase contact line and the respective activation free energy can be drawn at this stage. DOI: 10.1021/la900584s
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Conclusion We have studied capillary driven liquid-liquid displacement in a system comprising two immiscible liquids of comparable viscosity, that is, dodecane droplets spreading on a solid surface, surrounded by water. Contact line dynamics and, for the first time, its dependence on substrate wettability were investigated. From optical high speed video microscopy, dynamic contact angle data were obtained and compared with various theoretical models. In the early stage of the spreading process, fast contact line motion at capillary numbers above 210-4 is governed by hydrodynamic models. The microscopic model parameter ln(L/LS) shows some dependence on substrate wettability, although the values are unrealistic. This may result from inertia resisting the initial acceleration of the contact line. In the second stage of slow relaxation toward equilibrium (Ca
