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Aqueous Wetting Films on Fused Quartz
Journal of Colloid and Interface Science 214, 156 –169 (1999) Article ID jcis.1999.6212, available online at http://www.idealibrary.com on
Aqueous Wetting Films on Fused Quartz Rene Reyes Mazzoco* and Peter C. Wayner Jr.† ,1 *Universidad de las Americas-Puebla Santa Catarina Martir, Cholula, Puebla, Mexico; and †The Isermann Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 Received March 31, 1998; accepted March 16, 1999
Using an image analyzing interferometer, IAI, the interfacial characteristics of an isothermal constrained vapor bubble, CVB, in a quartz cuvette were studied as a precursor to heat transfer research. The effects of pH and electrolyte concentration on the meniscus properties (curvature and adsorbed film thickness) and the stability of the aqueous wetting films were evaluated. The surface potential in the electric double layer was a function of the cleaning and hydroxylation of the quartz surface. The disjoining pressure isotherm for pure water was very close to that predicted by the Langmuir equation. For aqueous solutions of moderate electrolyte concentration, the Gouy–Chapman theory provided a good representation of the electrostatic effects in the film. The effect of temperature on the film properties of aqueous solutions and pure water was also evaluated: The meniscus curvature decreased with increasing temperature, while Marangoni effects, intermolecular forces, and local evaporation and condensation enhanced waves on the adsorbed film layer. Pure water wetting films were mechanically metastable, breaking into droplets and very thin films (less than 10 nm) after a few hours. Aqueous wetting films with pH 12.4 proved to be stable during a test of several months, even when subjected to temperature and mechanical perturbations. The mechanical stability of wetting films can explain the reported differences between the critical heat fluxes of pure water and aqueous solutions. The IAI-CVB technique is a simple and versatile experimental technique for studying the characteristics of interfacial systems. © 1999 Academic Press Key Words: water; thin liquid films; capillarity; disjoining pressure; Young–Laplace equation; DLVO theory.
INTRODUCTION
The study of intermolecular forces in aqueous wetting films is of fundamental importance for developing uses for very thin water films. Traditionally, interfacial studies have been related mainly to the surface science fields of wetting, adhesion, lubrication, spreading, and stability. However, the same information is also needed to understand and develop change-ofphase heat transfer systems. In thin films, the evaporative heat flux is a function of the interfacial force field and the interfacial temperature difference (1). For example, the rate of heat trans1
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fer in nucleate boiling close to the critical heat flux is also controlled by interfacial forces in the thin liquid film at the base of the bubble at the nucleation site (1–3). In this case, superheats can be very large when the thickness of the film approaches that of a monolayer. In heat pipes, heat transfer is controlled by evaporation and condensation in nonisothermal extended menisci. With heat pipes, the interfacial temperature differences tend to be very small. Herein, we are concerned with the interfacial aspects of the constrained isothermal airvapor bubble formed in the glass cuvette partially filled with water presented in Fig. 1. We call the generic system a constrained vapor bubble, CVB, which has many isothermal and nonisothermal uses. We note that the CVB can have many different shapes. As a precursor to nonisothermal microgravity experiments, the isothermal results presented below were obtained in the earth’s gravitational field. Whereas gravitational forces do not hinder the analysis of asymmetric isothermal systems with low Bond Numbers, a microgravity field significantly simplifies the study of nonisothermal systems by making the transport processes axisymmetric. In the nonisothermal pure vapor case with heat added at one end and removed at the other end, an evaporation:vapor-flow: condensation process with a very high thermal conductance occurs. The device is passive and stable in that the liquid is recycled by interfacial forces. The effective pressure field is obtained from the measured film thickness profile using the augmented Young–Laplace equation. Previously, isothermal (e.g., (4 – 6)) and nonisothermal (e.g., (1–3, 6 – 8)) thin film systems have been studied using apolar fluids. Since water is non-toxic and has a very high heat of vaporization, it is a very attractive heat transfer fluid. However, detailed experimental studies of an evaporating aqueous meniscus have not been done because water has proved to be an extremely complicated fluid (e.g., see recent discussions in (9 –12)). Herein, using the DLVO theory (see e.g., (13–15)), we discuss our initial results on an isothermal water-quartz CVB system. In the development of heat transfer, we find that there is an important natural convergence of at least four fundamental interfacial research areas, the interfacial aspects of an extended isothermal curved liquid film (e.g., (4, 6, 16)), the effect of interfacial phenomena on steady state evaporating thin films (e.g., (1, 3, 7)), the stability of isothermal thin films (see e.g.,
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FIG. 1. The constrained vapor bubble (CVB) with an image analyzing interferometer (IAI). Since the quartz cell is underfilled with liquid, a vapor-air bubble forms with a shape constrained by the glass walls. If heat is added at one end and removed at the other end, the resulting heat exchanger has a very high thermal conductance.
(11, 17–19)), and the effect of very high evaporative fluxes and interfacial phenomena on the stability of thin films (e.g., (2, 8, 10)). The CVB can be used to study the interfacial and transport aspects of these four areas. The objective of the present study is to obtain equilibrium data on interfacial forces as a function of temperature using pure water and aqueous solutions in the CVB cell described in the Experimental Section. Experimental techniques previously evaluated in our simpler apolar studies (4, 7) are used. We note that, in the future, the interfacial aspects of a closed CVB system would be initially characterized isothermally at the start of a heat transfer experiment. Then, without opening the cell, the temperature and pressure fields would be perturbed and compared. As described by kinetic theory, a small perturbation in the interfacial temperature difference gives a large interfacial mass flux (e.g., 20). The stability analysis of aqueous films was developed from heterocoagulation theory (21). Figure 2 shows the disjoining pressure isotherms for three unstable systems (lines 2– 4) and for a stable system (line 1). Low pH values and/or high concentrations of electrolyte produce the mechanical instability of wetting films of aqueous solutions which is represented by a negative slope in the disjoining pressure isotherm. For some values of the concentration of electrolyte and pH in aqueous solutions, the electrostatic component of the disjoining pressure is positive at all thicknesses providing stability to the wetting films of aqueous solutions (22). At room temperature, water wetting films are stable at a thickness lower than approx-
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imately 10 nm (a films) and metastable at a thickness greater than approximately 60 nm (b films). The range of water film thicknesses in between these two values corresponds to mechanically unstable films which break and collapse into droplets. To describe the presence of experimental wetting films of pure water that are thicker than predicted, Kitchener and Read (23) suggested the presence of a superimposed potential at the liquid–vapor interface, and Pashley and Kitchener (24) originated the concept of a structural component of the disjoining pressure. Derjaguin and Churaev (25) and Churaev (12) proposed an exponential behavior for the disjoining pressure caused by this effect. Vigil et al. (26) suggested that an additional repulsive component of the total disjoining pressure in aqueous wetting films on quartz is the result of the stearic interaction of silicilic acid protruding from the quartz surface. Using the Frumkin–Derjaguin theory of wetting, Derjaguin and Churaev (25) calculated the equilibrium contact angle of aqueous solutions of different pH and concentrations of electrolyte. Values of the van der Waals component of the disjoining pressure, P vdW, were calculated from the isotherms obtained by Derjaguin and Churaev (27), and the electrostatic component, P e, was calculated from Devereux and de Bruyn’s tables (28). These were combined to give the total disjoining pressure, P T. The potentials of the quartz and film surfaces were obtained from the results of electrokinetic measurements and measurements of the potentials of the solution– gas interfaces. These results showed that, by increasing the pH above 10 and lowering the concentration of KCl to 10 24 M, the equilibrium contact angle is lower than 5°, indicating a totally wetting system. The contact angle of aqueous solutions of constant ionic strength on quartz or glass is maximal at the isoelectric point of the substrate (pH 2) and decreases with increasing pH up to 12. This monotonic decrease in the value of the contact angle is explained through the spontaneous formation of an electric double layer (29). For concentrations of metal chlorides (Li, K, Na, Cs, Mg, Ba) of 10 22 M, the
FIG. 2. Disjoining pressure isotherms for unstable aqueous solutions and pure water film, lines 2– 4, and for a stable system, line 1.
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contact angle is low (around 10°); for concentrations above this value, the contact angle increases (30). This effect was explained by the collapse of the electric double layer at high ionic concentrations. The effect of surfactants (anionic sodium dodecyl sulfate, NaDS, or cationic cetyltrimethylammonium bromide, CTAB) adsorbed on the quartz surface proved that the contact angle of a solution of constant salt background (0.1 N NaCl) changes with the change in the quartz-solution surface potential. The variation in this potential provides positive values of P e at pH 12 and a value of P e equal to zero at the isoelectric point of the quartz surface (31). The adsorption state of water films on glass depends on the state of hydration of the glass surface. The contact angle of water on the inside surface of hydrated and dehydrated capillaries has been studied at increasing temperature levels. For both hydration states, the contact angle decreases with increasing temperature (32), in agreement with the variation of the intermolecular interaction parameters of the water-quartz system with temperature. The adsorption of water on quartz depends critically on the arrangement of the surface hydroxyl groups. The surface density of hydroxyl groups on quartz enhances the hydrogen-bonding network of the water and electrostatic interactions with electrolytes in solution. On fully hydroxylated quartz substrates (4.6 OH groups per 100 Å 2 (33)), water has a contact angle of 0°; on completely dehydroxylated quartz plates (0.4 OH groups per 100 Å 2), the contact angle of water on quartz is 45° (34). For aqueous solutions of simple electrolytes, the surface density of hydroxyl groups provides a result similar to that reported for water. The higher surface density of OH groups increases the absolute value of the quartz-solution surface potential, and consequently the value of P e. We augment the above-cited results using a new experimental setup for the study of interfacial effects which combines a constrained vapor bubble cell (CVB) with an image analyzing interferometer (IAI). The presented isothermal results are a precursor for unique nonisothermal studies which will use this particular CVB design as a passive heat exchanger controlled by interfacial phenomena. Using statistical modeling, we present new data on the effect of temperature along with the effects of pH and concentration of a simple electrolyte (KCl) on the meniscus properties (curvature and adsorbed film thickness). New data on the stability of these films are also presented. The theoretical framework for the analysis of aqueous films in the CVB is the augmented Young–Laplace equation and the DLVO theory. The relation between the cleaning method for quartz and the wetting character of the aqueous films is evaluated. The determination of the disjoining pressure isotherm of pure water confirmed previous results on quartz potential and experimental error caused by surface deformation. The Langmuir disjoining pressure isotherm is experimentally validated. This information is related to the study of heat transfer in thin films and in nucleate pool boiling.
THEORETICAL BACKGROUND
The study of an extended meniscus provides information about the intermolecular forces present in terms of capillarity. An expanded view of a meniscus formed in the corner of the CVB cell is shown in Fig. 1. In the following discussion, non-DLVO forces are neglected because thicknesses less than a few nanometers are not emphasized. As described by the DLVO theory (13–15), the stabilizing force in aqueous-solution films on quartz is the balance of electrostatic and van der Waals forces. The total disjoining pressure in the aqueous wetting films is calculated using P T 5 P vdW 1 P e.
[1]
The DLP theory (35) allows the calculation of van der Waals forces as a disjoining pressure, P vdW, between condensed media, P vdW 5
2A# , d3
[2]
in which A# , 0 represents a stable film. The electrostatic component due to the electric double layer, P e, is calculated from the solutions of the Poisson–Boltzmann equation, 2ee o
dc 2 5 ze r , dx 2
[3]
with specified boundary conditions in the electric double layer (EDL) of the liquid film. Figure 3 shows the variables in the EDL for a totally wetting liquid film. Pure water on clean hydroxylated quartz has low concentration of electrolyte (considering the OH 2 and H 1 ions) and high potential of the solid surface. For these conditions the Poisson–Boltzmann equation is reduced to the Langmuir equation (36) for the calculation of P e in b films of water: Pe 5
S D
ee o p kT 2 d 2 ze
2
.
[4]
High pH solutions in the presence of a hydroxylated quartz surface generate stable wetting films due to high surface potentials (c s), on the order of 2100 to 2150 mV. Low to moderate concentrations of simple electrolytes, 10 25 to 10 23 M, contribute to the stability of the wetting films (22). For moderate concentrations of electrolyte and high potentials of the solid surface, the Gouy–Chapman theory provides the variation of potential, c, and P e. For a 1:1 electrolyte,
c lv 5
S D
4kT ecs tanh e 4kT
e 2 kd o,
[5]
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AQUEOUS WETTING FILMS ON FUSED QUARTZ
in the thicker portion of the extended meniscus and the total disjoining pressure in the adsorbed film is obtained:
s lvK ` 5 P To.
[8]
An independent confirmation of the measured variation of curvature, K ` , with hydrostatic height difference, Dh, can be obtained by tilting the experimental setup, as shown in Fig. 1, and measuring the meniscus profile at two locations,
s lvDK ` 5 r gDh.
FIG. 3. Schematic view of the counterion density profile, r x , and electrostatic potential profile, c x , in terms of boundary conditions c s, c lv, and r s, r lv. The ionic densities r s and r lv are related to the bulk ionic density, r `.
where k is the inverse Debye length defined by
F
k 5 e2
O eer kTz G 2 `i i
i
1/ 2
.
[6]
o
Using pure water and Eq. [9], good accuracy in the measurements of Dh and DK are demonstrated below. Figures 5 and 6 show examples of the observed interference fringes naturally present in the extended meniscus and the average gray value distribution with the envelopes for the peak-to-valley interpolation. The gray values for the adsorbed film correspond to pixel numbers from 100 to 250. The first 100 points of the gray value distribution were added to the input data to average the variations in the adsorbed layer gray values. The value of d o was calculated by trial and error. The correct value of d o generates a constant gray value envelope for the gray values of the adsorbed layer. Following common practice (37), the order of the interference fringes was determined by comparing the gray value distributions using a green filter (l 5 548 nm) and a blue filter (l 5 436 nm). For the parabolic menisci profiles found in the isothermal CVB cell for d ( x) . 0.1 mm, K ` was calculated using Eq. [10] because the film thickness slope is very small.
The interaction pressure is calculated by
P e 5 kT r `
F S D G
e 2 c 2lvr ` e c lv cos h 21 , . kT kT
K` 5 2 [7]
EXPERIMENTAL SECTION
Image Analyzing Interferometer (IAI) and Constrained Vapor Bubble Cell The IAI is a relatively new microscopic image processing system based on interferometry, which was developed to measure nonuniform film thickness profiles. A schematic view of the system is presented in Fig. 1, and a complete description of the combined use and accuracy of the IAI and CVB concepts is given for apolar fluids in Das Gupta et al. (4). In essence, naturally occurring fringes due to the reflection of light from the liquid–vapor and liquid–solid interfaces are used to measure the meniscus shape. The shape gives the pressure field. Herein, we find that aqueous solutions are much more challenging than apolar liquids. Using the augmented Young–Laplace equation for the control volume in Fig. 4, the following equality between capillarity
[9]
S D d d 1/ 2 dx
2
[10]
Figure 7 shows the thickness profile and the square root of the thickness profile evaluated for the example in Fig. 6. For d ( x) . 0.1 m m, the square root of the thickness profile should have a constant slope when there are no viscous losses due to fluid
FIG. 4. Energy balance in the equilibrium meniscus relating capillarity at the thicker location, s lvK ` , to the disjoining pressure, P To, in the adsorbed layer region.
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FIG. 5. Interference fringes from the experiment with pure water with the experimental setup titled by an angle of 12° (cleaning method (B)).
FIG. 7. Thickness profile, d, and d 1/2 for a meniscus of pure water spreading on a clean quartz surface inclined at 12°.
Cleaning of the Cell flow (4). We find that the presentation of the square root explicitly shows four characteristics of the raw data, the adsorbed film region, the constant curvature region, the transition region, and the absence of viscous flow. For an evaporating or condensing nonisothermal system, the viscous flow rate can be calculated from the pressure gradient (curvature gradient).
FIG. 6. Gray value distribution with G max and G min envelopes for the meniscus of pure water spreading on a clean quartz surface inclined at 12°.
The geometry of the CVB cell (standard square quartz cuvette for spectrophotometric use with inside dimensions of 3 mm 3 3 mm 3 38 mm with only one opening) made cleaning of the internal surfaces difficult. We tested several methods for cleaning quartz previously reported in adsorption studies (24). We found that dichromate solution, nitric acid, and RCAsilicon-wafer cleaning did not produce water wetting films on the fused quartz cell. When the removal of the contamination initially on the quartz surface was insufficient, partially wetting water-quartz systems were obtained. Method (A). First a volumetric solution of 31 deionized water, 31 hydrochloric acid (with 37% vol. HCL), and 31 hydrogen peroxide (with 30% vol. H 2O 2) was used to remove inorganic contaminants. The cell remained in the hot solution (50°C) for 15 min the interior was flushed with a disposable Pasteur pipette. This part of the procedure was repeated with a new acidic solution for another 15 min. Then the cell was rinsed five times with deionized water. Then a volumetric solution of equal parts of ammonium hydroxide (with 29% vol. NH 4OH) and hydrogen peroxide (with 30% vol. H 2O 2) was used to remove organic contaminants from the cell. The solution was heated up to 70°C. The cell was immersed in the solution and flushed inside with a disposable pipette for 15 min. The procedure was repeated with a new ammoniac solution. Finally, the cell was rinsed four times with deionized water and filled. We used this cleaning method for the experiments based on the factorial experimental designs presented in Figs. 9 and 10. However, this cleaning method produced quartz-surface defor-
AQUEOUS WETTING FILMS ON FUSED QUARTZ
161
The solutions, of composition described in the experimental design, were prepared using Aldrich reactives of 99.99% purity. The handling of volumetric glassware and of reactives was performed following conventional instructions (39). In all the experiments, the liquid volume in the cell was one-third of the volume of the CVB cell. Constant Temperature Enclosure
FIG. 8. Constant temperature enclosure used for constant temperature measurements with the CVB cell.
mations that caused experimental error in the measurement of the meniscus thickness profile as explained below. Method (B). To reduce the experimental error found in the experimental designs studied, we changed the cleaning method for the study of pure water and an aqueous solution wetting film. This cleaning procedure consisted of a mild etching of the quartz surface by 30 s immersion in a 0.5% volume HF solution. By controlling the etching conditions, we found that it was possible to remove a layer of approximately 0.1 mm thickness from the surface. This removed the contaminants without affecting the optical properties of the cell (38). With cleaning method (B), the surface had comparatively small crevices (from the depth of penetration of the hydration layer) with constant dimensions and regular distribution. The optical noise caused by these crevices was eliminated by using a simple filter in the image processing of the gray values. As described by Gee et al. (34), subsequent boiling of the clean cell for 10 h in water increased the concentration of OH groups on the surface to 4.6 OH per 100 Å.
A thermally insulated box, which is described in Fig. 8, was used as a constant temperature enclosure. Two equal electric resistances connected in parallel were used as heaters with a DC current source. A visor for the microscope’s objective, on top of the CVB cell, was made of a dual-glass section inserted in the box, and adapted to the 1-mm working distance of the objective lens (Leitz 323) used. Eight K-thermocouples placed in two rows of four each were used to measure the temperature along the sides of the CVB cell. An average of the eight independent measurements was used as the temperature in the cell. Differences in temperature readings among these thermocouples were below 5/9°C (1°F), which was the resolution of the indicator. We note that nonequilibrium behavior could be detected more accurately using deviations in the measured curvature profile from the equilibrium profile. EXPERIMENTAL RESULTS
A factorial experimental design on two variables was used for the initial exploration of the influence of pH and concentration of electrolyte on wetting properties, meniscus curvature, and adsorbed film thickness. Using the standard nomenclature of factorial designs, the selected values for the experimental points for the study of potassium (KOH-KCl) solutions are shown in Fig. 9. The factorial experimental design for the
Preparation of Solutions We used nanopure water from a Milli-Q system fed with water from a distillation unit. The filters were controlled by a resistivity set point adjusted at 17.2 MV cm. We checked the conductivity of the water before each experiment. The values of conductivity were in all cases below 2 mm hos/cm and the pH was about 5. Organic material was removed in the charcoal filter of the Milli-Q system. The lack of persistence of bubbles agitating water inside a clean volumetric flask indicated that the water was free of organic material to the desired level.
FIG. 9. Factorial experimental design for the study of the effects of pH and concentration of electrolyte on wetting properties of aqueous solutions of potassium salts.
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provided the following regression formula for the curvature of the sodium solutions: K ` 5 1527 1 328.9 A 1 328.6 B.
[13]
Even though none of the effects was significant, the interaction effect disappeared from the regression formula. For the reduced range of pH values, a linear change of curvature values is observed. The same linear description of the curvature was obtained in one half of the experimental design for potassiumbased solutions. The regression formula for d o is also linear on pH and [KCl]: FIG. 10. Screening experimental design for the study of the effects of pH and concentration of electrolyte on wetting properties of aqueous solutions of sodium salts.
sodium solutions (NaOH-NaCl) was changed to avoid values of pH greater than 12, which would cause sodium interference on normal pH electrodes. The resultant screening design, shown in Fig. 10, is orthogonal. Analysis of K ` and d o Data from the Experimental Designs The tabular results for these experiments are given in ReyesMazzoco (40). Measurements were obtained at two locations in the cell. Following conventional nomenclature, the factors with values in the range [21,1] are named (A) pH, (B) [KCl] or [NaCl], and (A 3 B) for the interaction of the two factors. The regression formula for the curvature K ` , in m 21, of potassium solutions at the low stage scale value (lower capillary pressure) is K ` 5 1094.7 2 144.425 A 1 1.625 B 2 440.7 AB.
[11]
d o 5 612.2 2 114 A 1 149.3 B.
[14]
Thus, the same trend of curvature and d o values was obtained from both experimental designs. The concentration of the electrolyte and pH value define the film-meniscus properties of aqueous solutions. Values of pH around 12 and concentration of the electrolyte of 10 24 M are recommended for meniscus profiles of low curvature and high adsorbed layer thickness. The experimental error was mainly due to the effect on the optical measurements of damage to the quartz surface from the presence of alkali in the solutions. For this reason, we changed to cleaning method (B) for the evaluation of the disjoining pressure isotherm of pure water. Force Balance Confirmation of Curvature, K `, Measurements In Fig. 11, the difference in disjoining pressure, DP, evaluated using the measurement of meniscus curvature in water at two locations, is compared with the difference in hydrostatic head, r lgDh, between the two locations. Clearly, both measurements are very similar, indicating that the experimental determinations of curvature, K ` , had a very low experimental
Despite the lack of significance of the F test, the regression analysis showed that the interaction effect was the most important contribution to the value of the curvature of the menisci of the solutions. This was an indication that the liquid film properties were controlled simultaneously by the pH and the concentration of the electrolyte in potassium solutions. The regression formula for d o, in Å, is
d o 5 396.7 2 100 A 2 5 B 1 165 AB.
[12]
These results showed the same conclusion as the analysis of the curvature values above. Although the F test showed no significant factor, the interaction of pH (defined by [KOH]) and [KCl] had the highest contribution in defining the film thickness. The analysis of variance for the curvature values obtained at the higher value of the stage scale (higher capillary pressure)
FIG. 11. Capillarity difference (DK ` s lv) versus hydrostatic head difference ( r gDh) for pure water at 298 K.
AQUEOUS WETTING FILMS ON FUSED QUARTZ
FIG. 12. Disjoining pressure isotherm for water at 298 K: P T Experimental 5 K ` s lv (1); P Langmuir Eq. (2), from Eq. [4]. The experimental error bars are 620% of the d o values.
error. Therefore, the use of Eq. [9] with pure water confirmed the accuracy of the results. Disjoining Pressure Isotherm for Water at 298 K The experimental data for P T(d) for pure water is compared with the theoretical prediction of P e(d) obtained using the Langmuir equation, Eq. [4], in Fig. 12. The experimental results are in good agreement with the theoretical prediction. Relatively, the determination of K ` contains little experimental error. Thus, the scatter in the experimental data came from the sensitivity of the measurement technique for d o due to variations in the surface conditions. Figure 12 also provides a 20% estimate of the scatter. Water wetting films had adsorbed layer thicknesses of around 100 nm. This liquid layer spread over most of the surfaces in the CVB cell as a metastable film. We observed the instability of these films by their breakage after 8 to 24 h. The films were replaced by droplets on a quartz surface with an apparent organic contamination. Figure 13 illustrates the process of decomposition of a water wetting film. The bulk contact angle for the droplet in the upper part of the picture was approximately 19.1°. Kitchener and Read (23) found similar effects due to organic contamination using the bubble against the plate (BAP) technique.
163
thermocouples surrounding the CVB cell. The temperature fluctuations around the CVB cell were reduced to less than one degree Fahrenheit. The bulk isothermal conditions in the box had very small temperature gradients, if any. Surface waves of small depth appeared at temperatures relatively close to the ambient temperature (305.5 K). The waves grew in amplitude and frequency with increasing temperature and moved toward the meniscus. The waves were symmetric along the cell’s larger axis and oscillated in front of the meniscus. For higher temperatures, contact line regions appeared to exist in the valleys of the waves. The K ` value of the extended meniscus decreased with increasing temperatures while the thickness of the adsorbed layer increased. Figures 14 and 15 show the interference fringes and gray value distributions for the experiments with pure water at 350 K. Analysis of the minimum gray value at a pixel number around 200 indicated that it was the zero-order destructive interference fringe. Temperature gradients are evident during the process of bringing the constant temperature enclosure to a new constant temperature level. The meniscus conditions were measured after steady state (constant temperature readings and a constant value of the meniscus curvature) was maintained for at least 1 h. Even though liquid waves could be sustained by very small temperature gradients, this steady state is close to an equilibrium state. The waves on the adsorbed film surface appeared to be driven by Marangoni effects and intermolecular forces with local evaporation and condensation in the crests and valleys of the waves. These observations support the description by Bankoff (41) of the breakage of thin liquid films due to the destabilizing effects of thermocapillarity, vapor recoil, and van der Waals forces. Eventually, the evaporation and condensa-
Effect of Temperature on the Adsorbed Layer Thickness, d o, with Water Wetting Films For these experiments, the temperature inside the insulated box was controlled by electrical resistance heaters in the box, and monitored until constant readings were obtained from the
FIG. 13. Contamination on the fused quartz surface inside the CVB cell. A droplet sits on a layer of contamination in front of the water fringes.
164
FIG. 14.
MAZZOCO AND WAYNER
Interference fringes for an experiment with pure water at 350 K.
tion processes cause the formation of thin film regions that can be analyzed using models given in (2) and (42). Effect of Temperature on the Constant Curvature Region In Fig. 16, the results for the variation of P T, obtained from measured values of K ` , are presented as a function of temper-
FIG. 16. Variation of the total disjoining pressure of pure water wetting films with increasing temperature level.
ature. We found that the disjoining pressure decreased with increasing temperature. In Fig. 17, the values of d o, calculated using the Langmuir equation, are presented. For these calculations, the values of the relative permittivity of water, e (T), were obtained from Hill (43), and the values of s lv(T) were calculated using the results of Jasper (44). The experimental data are shown in Table 1. The change in the experimental values of P T is described by the following linear approximation: P T~T! 5 115 2 0.32~T 2 290!.
FIG. 15. Gray value distribution for an experiment with pure water at 350 K.
[15]
FIG. 17. Calculated values of the adsorbed film thickness, d o, at different temperature levels. Here, d o is calculated from P T Experimental and the Langmuir equation, Eq. [4].
AQUEOUS WETTING FILMS ON FUSED QUARTZ
165
TABLE 1 Experimental Values of K ` (T), e(T), and s lv(T) for Water T (K)
K` (m 21)
e
s lv (mN/m 2)
298.3 305.6 312.8 326.7 338.3 350.0
1595.3 1579.2 1557.3 1525.6 1510.4 1537.9
78.6 76.0 73.5 68.6 64.5 60.4
72.1 71.0 70.0 67.9 66.2 64.5
Thus, the capillary meniscus became flatter and the conceptual adsorbed film thickness increased with increasing temperature. A schematic view of these effects is presented in Fig. 18. Effects of pH and Concentration on the Meniscus Properties High pH values and low-to-moderate concentrations of electrolyte provide low contact angles for aqueous solutions spreading on quartz (25, 30). From the experimental design tests with potassium solutions, we found that the lowest curvature values with d o values around 600 Å were obtained with a solution of pH 12 and [KCl] 5 1 3 10 24. Thus, we tested the mechanical stability of an aqueous solution of pH 12.4 and [KCl] 5 1 3 10 24 by maintaining the CVB cell under observation for more than five months. During this time, experiments on the effect of temperature and the effect of inclination angle on the films were performed. None of these perturbations caused a change in the nature of these completely wetting
FIG. 18. Schematic view of the change in the meniscus profile with an increase in the temperature.
FIG. 19. Experimental values of P T and d o for pH 12.4 and [KCl] 5 10 24 M. The calculated values of c lv are based on Eq. [7].
films. Therefore, contamination of the quartz surface was not detected. The presence of the alkali in the solution caused corrosion of the quartz walls in a noticeable manner, which affected the measurements of d o and K ` . Therefore, it was not possible to confirm the force balance using two locations and Eq. [9]. The experimental measurements of the total disjoining pressure (P T 5 s lv K ` ) and the adsorbed film thickness for the experiments with the aqueous solutions are shown in Fig. 19 for two disjoining pressure levels, 130 and 460 Pa. The values very close to P T 5 130 Pa were obtained with the cell inclined at an angle of 6°. Other values of P T around 130 Pa, which were obtained with other angles of inclination (0°, 12°, and 15°), are also included in this figure. The values of P T around 460 Pa were obtained with the cell in a vertical position. As indicated by the vertical spread of the data, measurements of P T showed a very low amount of scatter. Instead, the measurements of d o had a large variation which was caused by the presence of surface waves and the corrosion of the quartz surface by the strong alkali. The Gouy–Chapman theory, Eqs. [5]–[7], was used to calculate c lv values. For these aqueous-solution films, P T of the films was equal to the P e component. For values of P T 5 130 Pa and P T 5 460 Pa, the values of c lv calculated from Eq. [7] are 20.8 and 21.58 mV, respectively. On the other hand, considering the scatter in the experimental data for d o, the c lv calculated from the potential profile using Eqs. [5] and [6] were in the range of 21 mV to 21.6 3 10 25 mV. Since the value of c lv in Eq. [5] depends on the value of d o in an exponential term, we find that the calculated values are very sensitive to d o. The experiments with pure water confirmed the value of the solid
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FIG. 21. Gray value distribution for the experiment with a solution of pH 12.4 and [KCl] 5 10 24 M at 305.5 K.
FIG. 20. Interference fringes for the experiment with a solution of pH 12.4 and [KCl] 5 10 24 M at 305.5 K.
surface potential, c s ' 2100 mV. Since the same cleaning procedure was used, the same value of the surface potential was assumed for the calculations with the aqueous solution. Thus, the values of c lv calculated from Eq. [7] corresponded to the expected liquid–vapor interfacial potential for the concentration of ionic species in the solution, but we couldn’t confirm this using the above assumptions and Eq. [5]. Calculated values of c lv from the potential profile for aqueous wetting films could also be altered by other effects. The corrosion of the quartz surface modified the total concentration of the solution (consequently, the Debye length, k) and increased the error in the d o measurement. Finally, dissolved silica coagulates into particles of sizes that deviate from the assumptions in the Gouy– Chapman theory, altering the theoretical potential profile. Considering these complications, we believe that we can still conclude that these aqueous-solution films were mechanically stable and that the parameters in the EDL can be calculated from the interaction pressure, P e, in the Gouy–Chapman theory. Effect of Temperature on the Aqueous Solution Wetting Films We observed perturbations in the adsorbed liquid layer of the aqueous solution menisci with increasing constant temperature levels similar to those described for pure water films. We noticed a wave distribution in the proximity of the meniscus which was more uniform in the case of the aqueous solution than in the case of pure water. The waves presented in Figs. 20 and 21 reached the solid surface at the highest gray value close to pixel number 70, and formed rivulets. We believe that the
driving forces for the proposed recirculating heat flux represented by these waves were capillarity pressure, and, probably, thermocapillarity due to extremely small temperature gradients. The values of P T of the extended meniscus decreased linearly with increasing temperature levels. The values of the experimentally measured curvature at different temperature levels are shown in Table 2. The values of s lv for this dilute aqueous solution are calculated from the correlation for water given by Jasper (44). Figure 22 shows the values of P T calculated using the measured values of K ` given in Table 2. The change in P T with temperature is P T 5 130 2 0.44~T 2 290!.
[16]
We find that the rate of change of the disjoining pressure of these menisci with increasing temperature is higher than with pure water. The scatter in the experimental data in Fig. 22 is more pronounced than the scatter in the experimental data for pure water in Fig. 16, due to surface damage by the basic solution.
TABLE 2 Experimental K ` and s lv(T) Values for an Aqueous Solution of pH 12.4 and [KCl] 5 10 24 M Temperature (K)
Low K ` (m 21)
High K ` (m 21)
s lv (mN/m 2)
298.3 305.6 338.9 355.6 373.3
1708.0 1802.6 1735.8 1596.8 1641.0
2223.8 2396.6 2438.6 2342.5 1958.2
72.1 70.6 63.7 60.2 56.6
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AQUEOUS WETTING FILMS ON FUSED QUARTZ
FIG. 23. Comparison of the thickness profiles experimentally measured by Lam and Schechter (44) for an aqueous solution on borosilicate crown glass (E) with one for an aqueous solution on fused quartz in the CVB cell (—). FIG. 22. Variation of the total disjoining pressure with increasing temperature level for a solution of pH 12.4 and [KCl] 5 10 24 M.
High Total Disjoining Pressure Values The curvature and adsorbed film thickness of the menisci formed on the end (3 mm 3 3 mm) wall of the CVB cell oriented in a vertical position were measured. The results from three consecutive measurements of the highest values of P T are given in Table 3. These measurements and the calculated values of c lv are shown in Fig. 19. In a related study, Lam and Schechter (45) measured film thickness versus lateral distance for a 1 3 10 24 M KBr solution spreading on a borosilicate-crown-glass disc 1 mm wide: Figure 23 gives the reported values at two disjoining pressures. These data show rates of change of the film thickness much lower than predictions based on solutions to the extended Young–Laplace equation by Kralchevsky et al. for variable interfacial tension (46) and by Hirasaki for constant interfacial tension (5). In Fig. 7, we demonstrated that our values agreed very well with those calculated using the extended Young– Laplace equation. In addition, the meniscus profile for an aqueous solution presented in Fig. 23 also differs from the profile measurements by Lam and Schechter (45). However, TABLE 3 High Disjoining Pressure Measurements K` (m 21)
PT (Pa)
do (nm)
Elapsed time (days)
6399.3 6369.0 6468.9
461.4 459.2 466.4
32 32 36
1 3 4
the measurements from the CVB cell were focused on the meniscus shape and a small segment of the flat adsorbed liquid film, whereas the measurements in Lam and Schechter focused on the adsorbed flat film. Differences in the substrate material and the aqueous solution for these two sets of experimental data did not account for the differences in the shape of the meniscus profile. They might be the result of the damage to the solid surface by the cleaning method. Effect of Film Stability on Critical Heat Flux The solution films were stable, whereas the pure water films were unstable. These characteristics can be related to the difference between the critical heat fluxes, q0 CHF, in distilled and tap water. Costello and Frea (47) experimentally found that q0 CHF with tap water was equal to that predicted by hydrodynamic theory, whereas q0 CHF for distilled water was about 40% less than that predicted. Using the description of Dhir (48) for conditions close to the CHF, the instability of the pure water microlayer accelerates the dewetting process, thereby merging vapor stems and reducing q0 CHF. On the other hand, tap water boiling on surfaces with scale does not have the same degree of instability and, therefore, a higher critical heat flux. We note that the various surface conditions discussed above make consistent measurements and correlations difficult to attain in change-of-phase heat transfer studies. Future use of a wellcharacterized CVB heat transfer cell should eliminate these experimental difficulties and also lead to the development of small CVB heat exchangers based on interfacial phenomena. CONCLUSIONS ● The IAI-CVB technique is a simple and versatile experimental technique for studying the characteristics of interfacial systems.
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● A totally wetting metastable water-quartz system and a stable aqueous solution-quartz system were obtained by cleaning the CVB cell with a solution 0.5% vol. HF. ● The experimental thickness profile in the extended meniscus confirmed the validity of the augmented Young–Laplace equation. ● For aqueous solutions, d o and K ` are functions of the pH and the electrolyte concentration. ● For aqueous solutions of moderate electrolyte concentration, the Gouy–Chapman theory provided a good representation of the electrostatic effects in the film. ● For water at 298 K, the experimental disjoining pressure isotherm agrees with the electrostatic disjoining pressure calculated using the Langmuir equation. Thick films of water (b films) are controlled mainly by electrostatic effects. ● The disjoining pressure of the water and aqueous solution menisci decrease with increasing temperature. ● The waves on the surface of the adsorbed water film observed with increasing temperature lead to film breakage by thermocapillarity, vapor recoil, and disjoining pressure effects. ● The stability of aqueous solution thin films and the metastability of water films can explain the reported differences in the maximum heat flux of tap water versus pure water.
APPENDIX: NOMENCLATURE
A# e g h k K T x z d e eo P c r s
modified Hamaker constant electronic charge gravitational constant hydrostatic height Boltzmann constant curvature temperature distance inside the film valence of the ion film thickness dielectric constant permittivity of free space disjoining pressure electrostatic potential density, ionic and fluid surface tension
Subscripts and Superscripts CHF e l lv o s T vdW `
critical heat flux electrostatic liquid liquid–vapor adsorbed layer region solid surface total van derWaals thick film limit
ACKNOWLEDGMENTS This material is based on work partially supported by the National Science Foundation, under grant CTS-9123006, and by Fulbright/CONACYT, grant 15922189. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the NSF or Fulbright/CONACYT. Special thanks to Ivana Jovanovic and Dawn O’Loughlin, undergraduate students of the Chemical Engineering Department, who performed the experiments associated with Eqs. [11]–[14] as part of their participation in a NSF program for the Summer of 1994.
REFERENCES 1. Potash, M. L., Jr., and Wayner, P. C., Jr., Int. J. Heat Mass Transfer 15, 1851 (1972). 2. Stephan, P., and Hammer, J., Warme-und Stoffubertragung 30, 119 (1994). 3. Wayner, P. C., Jr., J. Heat Transfer 116, 938 (1994). 4. Das Gupta, S., Plawsky, J. L., and Wayner, P. C., Jr., AIChE J. 41, 2140 (1995). 5. Hirasaki, G. J., in “Interfacial Phenomena in Petroleum Recovery.” Dekker, New York, 1990. [as referenced in Schechter, R. S., Lam, A. C., J. Colloid Interface Sci. 146, 206 (1991).] 6. Brochard-Wyart, F., di Meglio, J. M., Quere, D., and de Gennes, P. G., Langmuir 7, 335 (1991). 7. Das Gupta, S., Kim, I. Y., and Wayner, P. C., Jr., J. Heat Transfer 116, 1007 (1994). 8. Bankoff, S. G., J. Heat Transfer 116, 10 (1994). 9. Ducker, W. A., Xu, Z., and Israelachvili, J. N., Langmuir 10, 3279 (1994). 10. Lipson, S. G., Physica Scripta T67, 63 (1996). 11. Sharma, A., and Jameel, A. T., J. Colloid Interface Sci. 161, 190 (1993). 12. Churaev, N. V., Adv. Colloid Interface Sci. 58, 87 (1995). 13. Derjaguin, B. V., and Landau, L. D., Acta Physicochim. URSS 14, 633 (1941). 14. Verwey, E. J. W., and Overbeek, J. Th. G., Trans. Faraday Soc. 42B, 117 (1946). 15. Israelachvili, J. N., “Intermolecular and Surface Forces,” 2nd ed., Chap. 12. Academic Press, San Diego, 1991. 16. Renk, F., Wayner, P. C., Jr., and Homsy, G. M., J. Colloid Interface Sci. 67, 408 (1978). 17. Joo, S. W., Davis, S. H., and Bankoff, S. G., Phys. Fluids A 3, 231 (1990). 18. Ruckenstein, E., and Jain, R. K., Faraday Trans. 70, 132 (1974). 19. Sharma, A., Langmuir 9, 861 (1993). 20. Carey, V. P., “Liquid–Vapor Phase-Change Phenomena.” Hemisphere, Washington, DC, 1992. 21. Derjaguin, B. V., Disc. Faraday Soc. 18, 85 (1954). 22. Derjaguin, B. V., and Churaev, N. V., in “Fluid Interfacial Phenomena” (C. A. Croxton, Ed.), Chap. 15. Wiley, New York, 1986. 23. Kitchener, J. A., and Read, A. D., “The Thickness of Wetting Films,” monograph in “Wetting.” Soc. Chem. Industry, New York, 1967. 24. Pashley, R. M., and Kitchener, J. A., J. Colloid Interface Science 71, 491 (1979). 25. Derjaguin, B. V., and Churaev, N. V., Langmuir 3, 607 (1987). 26. Vigil, G., Zhenghe, X., Steinberg, S., and Israelachvili, J., J. Colloid Interface Sci. 165, 367 (1994). 27. Derjaguin, B. V., and Churaev, N. V., J. Colloid Interface Sci. 49, 249 (1974). 28. Devereux, O. F., and de Bruyn, P. L., “Interaction of Plane-Parallel Double Layers.” MIT Press, Cambridge, MA, 1963. 29. Gribanova, E. V., Molchanova, L. I., Grigorov, O. N., and Popova, V. N., Kolloidnyi Z. 38, 557 (1976). [translated from]
AQUEOUS WETTING FILMS ON FUSED QUARTZ 30. Gribanova, E. V., Mashonskaya, L. I., and Cherkashina, L. M., Kolloidnyi Z. 50, 818 (1988). [translated from] 31. Zorin, Z. M., Romanov, V. P., and Churaev, N. V., Kolloidnyi Z. 41, 1066 (1979). [translated from] 32. Gribanova, E. V., Adv. Colloid Interface Sci. 39, 235 (1992). 33. Iler, R. K., “The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry.” Wiley-Interscience, New York, 1979. 34. Gee, M. L., Healy, T. W., and White, L. R., J. Colloid Interface Sci. 140, 450 (1990). 35. Dzyaloskinskii, I. E., Lifshitz, E. M., and Pitaevskii, L. P., Adv. Phys. 10, 165 (1961). 36. Langmuir, I., Chem. Phys. J. 6, 873 (1938). 37. Tung, C. Y., “Evaporative Heat Transfer in the Contact Line Region of a Mixture,” Ph.D. thesis, Rensselaer Polytechnic Institute, Chemical Engineering Dept., Troy, NY, 1982. 38. Doremus, R. H., Glass Research Center at Rensselaer, personal communication, 1995.
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39. Gershon, J. S., and Ballinger, J. T., Eds., “Chemical Technicians’ Ready Reference Handbook,” Chapter 25. McGraw–Hill, New York, 1990. 40. Reyes-Mazzoco, R., “Effect of Interfacial Forces on Change of Phase Heat Transfer,” Ph.D. thesis, Chemical Engineering Dept., Rensselaer Polytechnic Institute, Troy, NY, 1996. 41. Bankoff, S. G., J. Heat Transfer 116, 10 (1994). 42. Reyes, R., and Wayner, P. C., Jr., J. Heat Transfer 117, 779 (1995). 43. Hill, N. E., J. Phys. Chem. Solid State Phys. 3, 238 (1970). 44. Jasper, J. J., J. Phys. Chem. Ref. Data. 1, 841 (1972). 45. Lam, A. C., and Schechter, R. S., J. Colloid Interface Sci. 146, 206 (1991). 46. Kralchevsky, P. A., and Ivanov, I. B., Chem. Phys. Lett. 121, 116 (1985). 47. Costello, C. P., and Frea, W. J., Chem. Eng. Prog. Symp. Series 61, 258 (1965). 48. Dhir, V. K., “Some Observations from Maximum Heat Flux Data Obtained on Surfaces Having Different Degrees of Wettability,” pp. 185– 192. Pool and External Flow Boiling. ASME, New York, 1992.
Aqueous Wetting Films on Fused Quartz Rene Reyes Mazzoco* and Peter C. Wayner Jr.† ,1 *Universidad de las Americas-Puebla Santa Catarina Martir, Cholula, Puebla, Mexico; and †The Isermann Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 Received March 31, 1998; accepted March 16, 1999
Using an image analyzing interferometer, IAI, the interfacial characteristics of an isothermal constrained vapor bubble, CVB, in a quartz cuvette were studied as a precursor to heat transfer research. The effects of pH and electrolyte concentration on the meniscus properties (curvature and adsorbed film thickness) and the stability of the aqueous wetting films were evaluated. The surface potential in the electric double layer was a function of the cleaning and hydroxylation of the quartz surface. The disjoining pressure isotherm for pure water was very close to that predicted by the Langmuir equation. For aqueous solutions of moderate electrolyte concentration, the Gouy–Chapman theory provided a good representation of the electrostatic effects in the film. The effect of temperature on the film properties of aqueous solutions and pure water was also evaluated: The meniscus curvature decreased with increasing temperature, while Marangoni effects, intermolecular forces, and local evaporation and condensation enhanced waves on the adsorbed film layer. Pure water wetting films were mechanically metastable, breaking into droplets and very thin films (less than 10 nm) after a few hours. Aqueous wetting films with pH 12.4 proved to be stable during a test of several months, even when subjected to temperature and mechanical perturbations. The mechanical stability of wetting films can explain the reported differences between the critical heat fluxes of pure water and aqueous solutions. The IAI-CVB technique is a simple and versatile experimental technique for studying the characteristics of interfacial systems. © 1999 Academic Press Key Words: water; thin liquid films; capillarity; disjoining pressure; Young–Laplace equation; DLVO theory.
INTRODUCTION
The study of intermolecular forces in aqueous wetting films is of fundamental importance for developing uses for very thin water films. Traditionally, interfacial studies have been related mainly to the surface science fields of wetting, adhesion, lubrication, spreading, and stability. However, the same information is also needed to understand and develop change-ofphase heat transfer systems. In thin films, the evaporative heat flux is a function of the interfacial force field and the interfacial temperature difference (1). For example, the rate of heat trans1
To whom correspondence should be addressed. E-mail: [email protected]. Fax: (518) 276-4030. 0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
fer in nucleate boiling close to the critical heat flux is also controlled by interfacial forces in the thin liquid film at the base of the bubble at the nucleation site (1–3). In this case, superheats can be very large when the thickness of the film approaches that of a monolayer. In heat pipes, heat transfer is controlled by evaporation and condensation in nonisothermal extended menisci. With heat pipes, the interfacial temperature differences tend to be very small. Herein, we are concerned with the interfacial aspects of the constrained isothermal airvapor bubble formed in the glass cuvette partially filled with water presented in Fig. 1. We call the generic system a constrained vapor bubble, CVB, which has many isothermal and nonisothermal uses. We note that the CVB can have many different shapes. As a precursor to nonisothermal microgravity experiments, the isothermal results presented below were obtained in the earth’s gravitational field. Whereas gravitational forces do not hinder the analysis of asymmetric isothermal systems with low Bond Numbers, a microgravity field significantly simplifies the study of nonisothermal systems by making the transport processes axisymmetric. In the nonisothermal pure vapor case with heat added at one end and removed at the other end, an evaporation:vapor-flow: condensation process with a very high thermal conductance occurs. The device is passive and stable in that the liquid is recycled by interfacial forces. The effective pressure field is obtained from the measured film thickness profile using the augmented Young–Laplace equation. Previously, isothermal (e.g., (4 – 6)) and nonisothermal (e.g., (1–3, 6 – 8)) thin film systems have been studied using apolar fluids. Since water is non-toxic and has a very high heat of vaporization, it is a very attractive heat transfer fluid. However, detailed experimental studies of an evaporating aqueous meniscus have not been done because water has proved to be an extremely complicated fluid (e.g., see recent discussions in (9 –12)). Herein, using the DLVO theory (see e.g., (13–15)), we discuss our initial results on an isothermal water-quartz CVB system. In the development of heat transfer, we find that there is an important natural convergence of at least four fundamental interfacial research areas, the interfacial aspects of an extended isothermal curved liquid film (e.g., (4, 6, 16)), the effect of interfacial phenomena on steady state evaporating thin films (e.g., (1, 3, 7)), the stability of isothermal thin films (see e.g.,
156
AQUEOUS WETTING FILMS ON FUSED QUARTZ
FIG. 1. The constrained vapor bubble (CVB) with an image analyzing interferometer (IAI). Since the quartz cell is underfilled with liquid, a vapor-air bubble forms with a shape constrained by the glass walls. If heat is added at one end and removed at the other end, the resulting heat exchanger has a very high thermal conductance.
(11, 17–19)), and the effect of very high evaporative fluxes and interfacial phenomena on the stability of thin films (e.g., (2, 8, 10)). The CVB can be used to study the interfacial and transport aspects of these four areas. The objective of the present study is to obtain equilibrium data on interfacial forces as a function of temperature using pure water and aqueous solutions in the CVB cell described in the Experimental Section. Experimental techniques previously evaluated in our simpler apolar studies (4, 7) are used. We note that, in the future, the interfacial aspects of a closed CVB system would be initially characterized isothermally at the start of a heat transfer experiment. Then, without opening the cell, the temperature and pressure fields would be perturbed and compared. As described by kinetic theory, a small perturbation in the interfacial temperature difference gives a large interfacial mass flux (e.g., 20). The stability analysis of aqueous films was developed from heterocoagulation theory (21). Figure 2 shows the disjoining pressure isotherms for three unstable systems (lines 2– 4) and for a stable system (line 1). Low pH values and/or high concentrations of electrolyte produce the mechanical instability of wetting films of aqueous solutions which is represented by a negative slope in the disjoining pressure isotherm. For some values of the concentration of electrolyte and pH in aqueous solutions, the electrostatic component of the disjoining pressure is positive at all thicknesses providing stability to the wetting films of aqueous solutions (22). At room temperature, water wetting films are stable at a thickness lower than approx-
157
imately 10 nm (a films) and metastable at a thickness greater than approximately 60 nm (b films). The range of water film thicknesses in between these two values corresponds to mechanically unstable films which break and collapse into droplets. To describe the presence of experimental wetting films of pure water that are thicker than predicted, Kitchener and Read (23) suggested the presence of a superimposed potential at the liquid–vapor interface, and Pashley and Kitchener (24) originated the concept of a structural component of the disjoining pressure. Derjaguin and Churaev (25) and Churaev (12) proposed an exponential behavior for the disjoining pressure caused by this effect. Vigil et al. (26) suggested that an additional repulsive component of the total disjoining pressure in aqueous wetting films on quartz is the result of the stearic interaction of silicilic acid protruding from the quartz surface. Using the Frumkin–Derjaguin theory of wetting, Derjaguin and Churaev (25) calculated the equilibrium contact angle of aqueous solutions of different pH and concentrations of electrolyte. Values of the van der Waals component of the disjoining pressure, P vdW, were calculated from the isotherms obtained by Derjaguin and Churaev (27), and the electrostatic component, P e, was calculated from Devereux and de Bruyn’s tables (28). These were combined to give the total disjoining pressure, P T. The potentials of the quartz and film surfaces were obtained from the results of electrokinetic measurements and measurements of the potentials of the solution– gas interfaces. These results showed that, by increasing the pH above 10 and lowering the concentration of KCl to 10 24 M, the equilibrium contact angle is lower than 5°, indicating a totally wetting system. The contact angle of aqueous solutions of constant ionic strength on quartz or glass is maximal at the isoelectric point of the substrate (pH 2) and decreases with increasing pH up to 12. This monotonic decrease in the value of the contact angle is explained through the spontaneous formation of an electric double layer (29). For concentrations of metal chlorides (Li, K, Na, Cs, Mg, Ba) of 10 22 M, the
FIG. 2. Disjoining pressure isotherms for unstable aqueous solutions and pure water film, lines 2– 4, and for a stable system, line 1.
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MAZZOCO AND WAYNER
contact angle is low (around 10°); for concentrations above this value, the contact angle increases (30). This effect was explained by the collapse of the electric double layer at high ionic concentrations. The effect of surfactants (anionic sodium dodecyl sulfate, NaDS, or cationic cetyltrimethylammonium bromide, CTAB) adsorbed on the quartz surface proved that the contact angle of a solution of constant salt background (0.1 N NaCl) changes with the change in the quartz-solution surface potential. The variation in this potential provides positive values of P e at pH 12 and a value of P e equal to zero at the isoelectric point of the quartz surface (31). The adsorption state of water films on glass depends on the state of hydration of the glass surface. The contact angle of water on the inside surface of hydrated and dehydrated capillaries has been studied at increasing temperature levels. For both hydration states, the contact angle decreases with increasing temperature (32), in agreement with the variation of the intermolecular interaction parameters of the water-quartz system with temperature. The adsorption of water on quartz depends critically on the arrangement of the surface hydroxyl groups. The surface density of hydroxyl groups on quartz enhances the hydrogen-bonding network of the water and electrostatic interactions with electrolytes in solution. On fully hydroxylated quartz substrates (4.6 OH groups per 100 Å 2 (33)), water has a contact angle of 0°; on completely dehydroxylated quartz plates (0.4 OH groups per 100 Å 2), the contact angle of water on quartz is 45° (34). For aqueous solutions of simple electrolytes, the surface density of hydroxyl groups provides a result similar to that reported for water. The higher surface density of OH groups increases the absolute value of the quartz-solution surface potential, and consequently the value of P e. We augment the above-cited results using a new experimental setup for the study of interfacial effects which combines a constrained vapor bubble cell (CVB) with an image analyzing interferometer (IAI). The presented isothermal results are a precursor for unique nonisothermal studies which will use this particular CVB design as a passive heat exchanger controlled by interfacial phenomena. Using statistical modeling, we present new data on the effect of temperature along with the effects of pH and concentration of a simple electrolyte (KCl) on the meniscus properties (curvature and adsorbed film thickness). New data on the stability of these films are also presented. The theoretical framework for the analysis of aqueous films in the CVB is the augmented Young–Laplace equation and the DLVO theory. The relation between the cleaning method for quartz and the wetting character of the aqueous films is evaluated. The determination of the disjoining pressure isotherm of pure water confirmed previous results on quartz potential and experimental error caused by surface deformation. The Langmuir disjoining pressure isotherm is experimentally validated. This information is related to the study of heat transfer in thin films and in nucleate pool boiling.
THEORETICAL BACKGROUND
The study of an extended meniscus provides information about the intermolecular forces present in terms of capillarity. An expanded view of a meniscus formed in the corner of the CVB cell is shown in Fig. 1. In the following discussion, non-DLVO forces are neglected because thicknesses less than a few nanometers are not emphasized. As described by the DLVO theory (13–15), the stabilizing force in aqueous-solution films on quartz is the balance of electrostatic and van der Waals forces. The total disjoining pressure in the aqueous wetting films is calculated using P T 5 P vdW 1 P e.
[1]
The DLP theory (35) allows the calculation of van der Waals forces as a disjoining pressure, P vdW, between condensed media, P vdW 5
2A# , d3
[2]
in which A# , 0 represents a stable film. The electrostatic component due to the electric double layer, P e, is calculated from the solutions of the Poisson–Boltzmann equation, 2ee o
dc 2 5 ze r , dx 2
[3]
with specified boundary conditions in the electric double layer (EDL) of the liquid film. Figure 3 shows the variables in the EDL for a totally wetting liquid film. Pure water on clean hydroxylated quartz has low concentration of electrolyte (considering the OH 2 and H 1 ions) and high potential of the solid surface. For these conditions the Poisson–Boltzmann equation is reduced to the Langmuir equation (36) for the calculation of P e in b films of water: Pe 5
S D
ee o p kT 2 d 2 ze
2
.
[4]
High pH solutions in the presence of a hydroxylated quartz surface generate stable wetting films due to high surface potentials (c s), on the order of 2100 to 2150 mV. Low to moderate concentrations of simple electrolytes, 10 25 to 10 23 M, contribute to the stability of the wetting films (22). For moderate concentrations of electrolyte and high potentials of the solid surface, the Gouy–Chapman theory provides the variation of potential, c, and P e. For a 1:1 electrolyte,
c lv 5
S D
4kT ecs tanh e 4kT
e 2 kd o,
[5]
159
AQUEOUS WETTING FILMS ON FUSED QUARTZ
in the thicker portion of the extended meniscus and the total disjoining pressure in the adsorbed film is obtained:
s lvK ` 5 P To.
[8]
An independent confirmation of the measured variation of curvature, K ` , with hydrostatic height difference, Dh, can be obtained by tilting the experimental setup, as shown in Fig. 1, and measuring the meniscus profile at two locations,
s lvDK ` 5 r gDh.
FIG. 3. Schematic view of the counterion density profile, r x , and electrostatic potential profile, c x , in terms of boundary conditions c s, c lv, and r s, r lv. The ionic densities r s and r lv are related to the bulk ionic density, r `.
where k is the inverse Debye length defined by
F
k 5 e2
O eer kTz G 2 `i i
i
1/ 2
.
[6]
o
Using pure water and Eq. [9], good accuracy in the measurements of Dh and DK are demonstrated below. Figures 5 and 6 show examples of the observed interference fringes naturally present in the extended meniscus and the average gray value distribution with the envelopes for the peak-to-valley interpolation. The gray values for the adsorbed film correspond to pixel numbers from 100 to 250. The first 100 points of the gray value distribution were added to the input data to average the variations in the adsorbed layer gray values. The value of d o was calculated by trial and error. The correct value of d o generates a constant gray value envelope for the gray values of the adsorbed layer. Following common practice (37), the order of the interference fringes was determined by comparing the gray value distributions using a green filter (l 5 548 nm) and a blue filter (l 5 436 nm). For the parabolic menisci profiles found in the isothermal CVB cell for d ( x) . 0.1 mm, K ` was calculated using Eq. [10] because the film thickness slope is very small.
The interaction pressure is calculated by
P e 5 kT r `
F S D G
e 2 c 2lvr ` e c lv cos h 21 , . kT kT
K` 5 2 [7]
EXPERIMENTAL SECTION
Image Analyzing Interferometer (IAI) and Constrained Vapor Bubble Cell The IAI is a relatively new microscopic image processing system based on interferometry, which was developed to measure nonuniform film thickness profiles. A schematic view of the system is presented in Fig. 1, and a complete description of the combined use and accuracy of the IAI and CVB concepts is given for apolar fluids in Das Gupta et al. (4). In essence, naturally occurring fringes due to the reflection of light from the liquid–vapor and liquid–solid interfaces are used to measure the meniscus shape. The shape gives the pressure field. Herein, we find that aqueous solutions are much more challenging than apolar liquids. Using the augmented Young–Laplace equation for the control volume in Fig. 4, the following equality between capillarity
[9]
S D d d 1/ 2 dx
2
[10]
Figure 7 shows the thickness profile and the square root of the thickness profile evaluated for the example in Fig. 6. For d ( x) . 0.1 m m, the square root of the thickness profile should have a constant slope when there are no viscous losses due to fluid
FIG. 4. Energy balance in the equilibrium meniscus relating capillarity at the thicker location, s lvK ` , to the disjoining pressure, P To, in the adsorbed layer region.
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FIG. 5. Interference fringes from the experiment with pure water with the experimental setup titled by an angle of 12° (cleaning method (B)).
FIG. 7. Thickness profile, d, and d 1/2 for a meniscus of pure water spreading on a clean quartz surface inclined at 12°.
Cleaning of the Cell flow (4). We find that the presentation of the square root explicitly shows four characteristics of the raw data, the adsorbed film region, the constant curvature region, the transition region, and the absence of viscous flow. For an evaporating or condensing nonisothermal system, the viscous flow rate can be calculated from the pressure gradient (curvature gradient).
FIG. 6. Gray value distribution with G max and G min envelopes for the meniscus of pure water spreading on a clean quartz surface inclined at 12°.
The geometry of the CVB cell (standard square quartz cuvette for spectrophotometric use with inside dimensions of 3 mm 3 3 mm 3 38 mm with only one opening) made cleaning of the internal surfaces difficult. We tested several methods for cleaning quartz previously reported in adsorption studies (24). We found that dichromate solution, nitric acid, and RCAsilicon-wafer cleaning did not produce water wetting films on the fused quartz cell. When the removal of the contamination initially on the quartz surface was insufficient, partially wetting water-quartz systems were obtained. Method (A). First a volumetric solution of 31 deionized water, 31 hydrochloric acid (with 37% vol. HCL), and 31 hydrogen peroxide (with 30% vol. H 2O 2) was used to remove inorganic contaminants. The cell remained in the hot solution (50°C) for 15 min the interior was flushed with a disposable Pasteur pipette. This part of the procedure was repeated with a new acidic solution for another 15 min. Then the cell was rinsed five times with deionized water. Then a volumetric solution of equal parts of ammonium hydroxide (with 29% vol. NH 4OH) and hydrogen peroxide (with 30% vol. H 2O 2) was used to remove organic contaminants from the cell. The solution was heated up to 70°C. The cell was immersed in the solution and flushed inside with a disposable pipette for 15 min. The procedure was repeated with a new ammoniac solution. Finally, the cell was rinsed four times with deionized water and filled. We used this cleaning method for the experiments based on the factorial experimental designs presented in Figs. 9 and 10. However, this cleaning method produced quartz-surface defor-
AQUEOUS WETTING FILMS ON FUSED QUARTZ
161
The solutions, of composition described in the experimental design, were prepared using Aldrich reactives of 99.99% purity. The handling of volumetric glassware and of reactives was performed following conventional instructions (39). In all the experiments, the liquid volume in the cell was one-third of the volume of the CVB cell. Constant Temperature Enclosure
FIG. 8. Constant temperature enclosure used for constant temperature measurements with the CVB cell.
mations that caused experimental error in the measurement of the meniscus thickness profile as explained below. Method (B). To reduce the experimental error found in the experimental designs studied, we changed the cleaning method for the study of pure water and an aqueous solution wetting film. This cleaning procedure consisted of a mild etching of the quartz surface by 30 s immersion in a 0.5% volume HF solution. By controlling the etching conditions, we found that it was possible to remove a layer of approximately 0.1 mm thickness from the surface. This removed the contaminants without affecting the optical properties of the cell (38). With cleaning method (B), the surface had comparatively small crevices (from the depth of penetration of the hydration layer) with constant dimensions and regular distribution. The optical noise caused by these crevices was eliminated by using a simple filter in the image processing of the gray values. As described by Gee et al. (34), subsequent boiling of the clean cell for 10 h in water increased the concentration of OH groups on the surface to 4.6 OH per 100 Å.
A thermally insulated box, which is described in Fig. 8, was used as a constant temperature enclosure. Two equal electric resistances connected in parallel were used as heaters with a DC current source. A visor for the microscope’s objective, on top of the CVB cell, was made of a dual-glass section inserted in the box, and adapted to the 1-mm working distance of the objective lens (Leitz 323) used. Eight K-thermocouples placed in two rows of four each were used to measure the temperature along the sides of the CVB cell. An average of the eight independent measurements was used as the temperature in the cell. Differences in temperature readings among these thermocouples were below 5/9°C (1°F), which was the resolution of the indicator. We note that nonequilibrium behavior could be detected more accurately using deviations in the measured curvature profile from the equilibrium profile. EXPERIMENTAL RESULTS
A factorial experimental design on two variables was used for the initial exploration of the influence of pH and concentration of electrolyte on wetting properties, meniscus curvature, and adsorbed film thickness. Using the standard nomenclature of factorial designs, the selected values for the experimental points for the study of potassium (KOH-KCl) solutions are shown in Fig. 9. The factorial experimental design for the
Preparation of Solutions We used nanopure water from a Milli-Q system fed with water from a distillation unit. The filters were controlled by a resistivity set point adjusted at 17.2 MV cm. We checked the conductivity of the water before each experiment. The values of conductivity were in all cases below 2 mm hos/cm and the pH was about 5. Organic material was removed in the charcoal filter of the Milli-Q system. The lack of persistence of bubbles agitating water inside a clean volumetric flask indicated that the water was free of organic material to the desired level.
FIG. 9. Factorial experimental design for the study of the effects of pH and concentration of electrolyte on wetting properties of aqueous solutions of potassium salts.
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provided the following regression formula for the curvature of the sodium solutions: K ` 5 1527 1 328.9 A 1 328.6 B.
[13]
Even though none of the effects was significant, the interaction effect disappeared from the regression formula. For the reduced range of pH values, a linear change of curvature values is observed. The same linear description of the curvature was obtained in one half of the experimental design for potassiumbased solutions. The regression formula for d o is also linear on pH and [KCl]: FIG. 10. Screening experimental design for the study of the effects of pH and concentration of electrolyte on wetting properties of aqueous solutions of sodium salts.
sodium solutions (NaOH-NaCl) was changed to avoid values of pH greater than 12, which would cause sodium interference on normal pH electrodes. The resultant screening design, shown in Fig. 10, is orthogonal. Analysis of K ` and d o Data from the Experimental Designs The tabular results for these experiments are given in ReyesMazzoco (40). Measurements were obtained at two locations in the cell. Following conventional nomenclature, the factors with values in the range [21,1] are named (A) pH, (B) [KCl] or [NaCl], and (A 3 B) for the interaction of the two factors. The regression formula for the curvature K ` , in m 21, of potassium solutions at the low stage scale value (lower capillary pressure) is K ` 5 1094.7 2 144.425 A 1 1.625 B 2 440.7 AB.
[11]
d o 5 612.2 2 114 A 1 149.3 B.
[14]
Thus, the same trend of curvature and d o values was obtained from both experimental designs. The concentration of the electrolyte and pH value define the film-meniscus properties of aqueous solutions. Values of pH around 12 and concentration of the electrolyte of 10 24 M are recommended for meniscus profiles of low curvature and high adsorbed layer thickness. The experimental error was mainly due to the effect on the optical measurements of damage to the quartz surface from the presence of alkali in the solutions. For this reason, we changed to cleaning method (B) for the evaluation of the disjoining pressure isotherm of pure water. Force Balance Confirmation of Curvature, K `, Measurements In Fig. 11, the difference in disjoining pressure, DP, evaluated using the measurement of meniscus curvature in water at two locations, is compared with the difference in hydrostatic head, r lgDh, between the two locations. Clearly, both measurements are very similar, indicating that the experimental determinations of curvature, K ` , had a very low experimental
Despite the lack of significance of the F test, the regression analysis showed that the interaction effect was the most important contribution to the value of the curvature of the menisci of the solutions. This was an indication that the liquid film properties were controlled simultaneously by the pH and the concentration of the electrolyte in potassium solutions. The regression formula for d o, in Å, is
d o 5 396.7 2 100 A 2 5 B 1 165 AB.
[12]
These results showed the same conclusion as the analysis of the curvature values above. Although the F test showed no significant factor, the interaction of pH (defined by [KOH]) and [KCl] had the highest contribution in defining the film thickness. The analysis of variance for the curvature values obtained at the higher value of the stage scale (higher capillary pressure)
FIG. 11. Capillarity difference (DK ` s lv) versus hydrostatic head difference ( r gDh) for pure water at 298 K.
AQUEOUS WETTING FILMS ON FUSED QUARTZ
FIG. 12. Disjoining pressure isotherm for water at 298 K: P T Experimental 5 K ` s lv (1); P Langmuir Eq. (2), from Eq. [4]. The experimental error bars are 620% of the d o values.
error. Therefore, the use of Eq. [9] with pure water confirmed the accuracy of the results. Disjoining Pressure Isotherm for Water at 298 K The experimental data for P T(d) for pure water is compared with the theoretical prediction of P e(d) obtained using the Langmuir equation, Eq. [4], in Fig. 12. The experimental results are in good agreement with the theoretical prediction. Relatively, the determination of K ` contains little experimental error. Thus, the scatter in the experimental data came from the sensitivity of the measurement technique for d o due to variations in the surface conditions. Figure 12 also provides a 20% estimate of the scatter. Water wetting films had adsorbed layer thicknesses of around 100 nm. This liquid layer spread over most of the surfaces in the CVB cell as a metastable film. We observed the instability of these films by their breakage after 8 to 24 h. The films were replaced by droplets on a quartz surface with an apparent organic contamination. Figure 13 illustrates the process of decomposition of a water wetting film. The bulk contact angle for the droplet in the upper part of the picture was approximately 19.1°. Kitchener and Read (23) found similar effects due to organic contamination using the bubble against the plate (BAP) technique.
163
thermocouples surrounding the CVB cell. The temperature fluctuations around the CVB cell were reduced to less than one degree Fahrenheit. The bulk isothermal conditions in the box had very small temperature gradients, if any. Surface waves of small depth appeared at temperatures relatively close to the ambient temperature (305.5 K). The waves grew in amplitude and frequency with increasing temperature and moved toward the meniscus. The waves were symmetric along the cell’s larger axis and oscillated in front of the meniscus. For higher temperatures, contact line regions appeared to exist in the valleys of the waves. The K ` value of the extended meniscus decreased with increasing temperatures while the thickness of the adsorbed layer increased. Figures 14 and 15 show the interference fringes and gray value distributions for the experiments with pure water at 350 K. Analysis of the minimum gray value at a pixel number around 200 indicated that it was the zero-order destructive interference fringe. Temperature gradients are evident during the process of bringing the constant temperature enclosure to a new constant temperature level. The meniscus conditions were measured after steady state (constant temperature readings and a constant value of the meniscus curvature) was maintained for at least 1 h. Even though liquid waves could be sustained by very small temperature gradients, this steady state is close to an equilibrium state. The waves on the adsorbed film surface appeared to be driven by Marangoni effects and intermolecular forces with local evaporation and condensation in the crests and valleys of the waves. These observations support the description by Bankoff (41) of the breakage of thin liquid films due to the destabilizing effects of thermocapillarity, vapor recoil, and van der Waals forces. Eventually, the evaporation and condensa-
Effect of Temperature on the Adsorbed Layer Thickness, d o, with Water Wetting Films For these experiments, the temperature inside the insulated box was controlled by electrical resistance heaters in the box, and monitored until constant readings were obtained from the
FIG. 13. Contamination on the fused quartz surface inside the CVB cell. A droplet sits on a layer of contamination in front of the water fringes.
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FIG. 14.
MAZZOCO AND WAYNER
Interference fringes for an experiment with pure water at 350 K.
tion processes cause the formation of thin film regions that can be analyzed using models given in (2) and (42). Effect of Temperature on the Constant Curvature Region In Fig. 16, the results for the variation of P T, obtained from measured values of K ` , are presented as a function of temper-
FIG. 16. Variation of the total disjoining pressure of pure water wetting films with increasing temperature level.
ature. We found that the disjoining pressure decreased with increasing temperature. In Fig. 17, the values of d o, calculated using the Langmuir equation, are presented. For these calculations, the values of the relative permittivity of water, e (T), were obtained from Hill (43), and the values of s lv(T) were calculated using the results of Jasper (44). The experimental data are shown in Table 1. The change in the experimental values of P T is described by the following linear approximation: P T~T! 5 115 2 0.32~T 2 290!.
FIG. 15. Gray value distribution for an experiment with pure water at 350 K.
[15]
FIG. 17. Calculated values of the adsorbed film thickness, d o, at different temperature levels. Here, d o is calculated from P T Experimental and the Langmuir equation, Eq. [4].
AQUEOUS WETTING FILMS ON FUSED QUARTZ
165
TABLE 1 Experimental Values of K ` (T), e(T), and s lv(T) for Water T (K)
K` (m 21)
e
s lv (mN/m 2)
298.3 305.6 312.8 326.7 338.3 350.0
1595.3 1579.2 1557.3 1525.6 1510.4 1537.9
78.6 76.0 73.5 68.6 64.5 60.4
72.1 71.0 70.0 67.9 66.2 64.5
Thus, the capillary meniscus became flatter and the conceptual adsorbed film thickness increased with increasing temperature. A schematic view of these effects is presented in Fig. 18. Effects of pH and Concentration on the Meniscus Properties High pH values and low-to-moderate concentrations of electrolyte provide low contact angles for aqueous solutions spreading on quartz (25, 30). From the experimental design tests with potassium solutions, we found that the lowest curvature values with d o values around 600 Å were obtained with a solution of pH 12 and [KCl] 5 1 3 10 24. Thus, we tested the mechanical stability of an aqueous solution of pH 12.4 and [KCl] 5 1 3 10 24 by maintaining the CVB cell under observation for more than five months. During this time, experiments on the effect of temperature and the effect of inclination angle on the films were performed. None of these perturbations caused a change in the nature of these completely wetting
FIG. 18. Schematic view of the change in the meniscus profile with an increase in the temperature.
FIG. 19. Experimental values of P T and d o for pH 12.4 and [KCl] 5 10 24 M. The calculated values of c lv are based on Eq. [7].
films. Therefore, contamination of the quartz surface was not detected. The presence of the alkali in the solution caused corrosion of the quartz walls in a noticeable manner, which affected the measurements of d o and K ` . Therefore, it was not possible to confirm the force balance using two locations and Eq. [9]. The experimental measurements of the total disjoining pressure (P T 5 s lv K ` ) and the adsorbed film thickness for the experiments with the aqueous solutions are shown in Fig. 19 for two disjoining pressure levels, 130 and 460 Pa. The values very close to P T 5 130 Pa were obtained with the cell inclined at an angle of 6°. Other values of P T around 130 Pa, which were obtained with other angles of inclination (0°, 12°, and 15°), are also included in this figure. The values of P T around 460 Pa were obtained with the cell in a vertical position. As indicated by the vertical spread of the data, measurements of P T showed a very low amount of scatter. Instead, the measurements of d o had a large variation which was caused by the presence of surface waves and the corrosion of the quartz surface by the strong alkali. The Gouy–Chapman theory, Eqs. [5]–[7], was used to calculate c lv values. For these aqueous-solution films, P T of the films was equal to the P e component. For values of P T 5 130 Pa and P T 5 460 Pa, the values of c lv calculated from Eq. [7] are 20.8 and 21.58 mV, respectively. On the other hand, considering the scatter in the experimental data for d o, the c lv calculated from the potential profile using Eqs. [5] and [6] were in the range of 21 mV to 21.6 3 10 25 mV. Since the value of c lv in Eq. [5] depends on the value of d o in an exponential term, we find that the calculated values are very sensitive to d o. The experiments with pure water confirmed the value of the solid
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FIG. 21. Gray value distribution for the experiment with a solution of pH 12.4 and [KCl] 5 10 24 M at 305.5 K.
FIG. 20. Interference fringes for the experiment with a solution of pH 12.4 and [KCl] 5 10 24 M at 305.5 K.
surface potential, c s ' 2100 mV. Since the same cleaning procedure was used, the same value of the surface potential was assumed for the calculations with the aqueous solution. Thus, the values of c lv calculated from Eq. [7] corresponded to the expected liquid–vapor interfacial potential for the concentration of ionic species in the solution, but we couldn’t confirm this using the above assumptions and Eq. [5]. Calculated values of c lv from the potential profile for aqueous wetting films could also be altered by other effects. The corrosion of the quartz surface modified the total concentration of the solution (consequently, the Debye length, k) and increased the error in the d o measurement. Finally, dissolved silica coagulates into particles of sizes that deviate from the assumptions in the Gouy– Chapman theory, altering the theoretical potential profile. Considering these complications, we believe that we can still conclude that these aqueous-solution films were mechanically stable and that the parameters in the EDL can be calculated from the interaction pressure, P e, in the Gouy–Chapman theory. Effect of Temperature on the Aqueous Solution Wetting Films We observed perturbations in the adsorbed liquid layer of the aqueous solution menisci with increasing constant temperature levels similar to those described for pure water films. We noticed a wave distribution in the proximity of the meniscus which was more uniform in the case of the aqueous solution than in the case of pure water. The waves presented in Figs. 20 and 21 reached the solid surface at the highest gray value close to pixel number 70, and formed rivulets. We believe that the
driving forces for the proposed recirculating heat flux represented by these waves were capillarity pressure, and, probably, thermocapillarity due to extremely small temperature gradients. The values of P T of the extended meniscus decreased linearly with increasing temperature levels. The values of the experimentally measured curvature at different temperature levels are shown in Table 2. The values of s lv for this dilute aqueous solution are calculated from the correlation for water given by Jasper (44). Figure 22 shows the values of P T calculated using the measured values of K ` given in Table 2. The change in P T with temperature is P T 5 130 2 0.44~T 2 290!.
[16]
We find that the rate of change of the disjoining pressure of these menisci with increasing temperature is higher than with pure water. The scatter in the experimental data in Fig. 22 is more pronounced than the scatter in the experimental data for pure water in Fig. 16, due to surface damage by the basic solution.
TABLE 2 Experimental K ` and s lv(T) Values for an Aqueous Solution of pH 12.4 and [KCl] 5 10 24 M Temperature (K)
Low K ` (m 21)
High K ` (m 21)
s lv (mN/m 2)
298.3 305.6 338.9 355.6 373.3
1708.0 1802.6 1735.8 1596.8 1641.0
2223.8 2396.6 2438.6 2342.5 1958.2
72.1 70.6 63.7 60.2 56.6
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AQUEOUS WETTING FILMS ON FUSED QUARTZ
FIG. 23. Comparison of the thickness profiles experimentally measured by Lam and Schechter (44) for an aqueous solution on borosilicate crown glass (E) with one for an aqueous solution on fused quartz in the CVB cell (—). FIG. 22. Variation of the total disjoining pressure with increasing temperature level for a solution of pH 12.4 and [KCl] 5 10 24 M.
High Total Disjoining Pressure Values The curvature and adsorbed film thickness of the menisci formed on the end (3 mm 3 3 mm) wall of the CVB cell oriented in a vertical position were measured. The results from three consecutive measurements of the highest values of P T are given in Table 3. These measurements and the calculated values of c lv are shown in Fig. 19. In a related study, Lam and Schechter (45) measured film thickness versus lateral distance for a 1 3 10 24 M KBr solution spreading on a borosilicate-crown-glass disc 1 mm wide: Figure 23 gives the reported values at two disjoining pressures. These data show rates of change of the film thickness much lower than predictions based on solutions to the extended Young–Laplace equation by Kralchevsky et al. for variable interfacial tension (46) and by Hirasaki for constant interfacial tension (5). In Fig. 7, we demonstrated that our values agreed very well with those calculated using the extended Young– Laplace equation. In addition, the meniscus profile for an aqueous solution presented in Fig. 23 also differs from the profile measurements by Lam and Schechter (45). However, TABLE 3 High Disjoining Pressure Measurements K` (m 21)
PT (Pa)
do (nm)
Elapsed time (days)
6399.3 6369.0 6468.9
461.4 459.2 466.4
32 32 36
1 3 4
the measurements from the CVB cell were focused on the meniscus shape and a small segment of the flat adsorbed liquid film, whereas the measurements in Lam and Schechter focused on the adsorbed flat film. Differences in the substrate material and the aqueous solution for these two sets of experimental data did not account for the differences in the shape of the meniscus profile. They might be the result of the damage to the solid surface by the cleaning method. Effect of Film Stability on Critical Heat Flux The solution films were stable, whereas the pure water films were unstable. These characteristics can be related to the difference between the critical heat fluxes, q0 CHF, in distilled and tap water. Costello and Frea (47) experimentally found that q0 CHF with tap water was equal to that predicted by hydrodynamic theory, whereas q0 CHF for distilled water was about 40% less than that predicted. Using the description of Dhir (48) for conditions close to the CHF, the instability of the pure water microlayer accelerates the dewetting process, thereby merging vapor stems and reducing q0 CHF. On the other hand, tap water boiling on surfaces with scale does not have the same degree of instability and, therefore, a higher critical heat flux. We note that the various surface conditions discussed above make consistent measurements and correlations difficult to attain in change-of-phase heat transfer studies. Future use of a wellcharacterized CVB heat transfer cell should eliminate these experimental difficulties and also lead to the development of small CVB heat exchangers based on interfacial phenomena. CONCLUSIONS ● The IAI-CVB technique is a simple and versatile experimental technique for studying the characteristics of interfacial systems.
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● A totally wetting metastable water-quartz system and a stable aqueous solution-quartz system were obtained by cleaning the CVB cell with a solution 0.5% vol. HF. ● The experimental thickness profile in the extended meniscus confirmed the validity of the augmented Young–Laplace equation. ● For aqueous solutions, d o and K ` are functions of the pH and the electrolyte concentration. ● For aqueous solutions of moderate electrolyte concentration, the Gouy–Chapman theory provided a good representation of the electrostatic effects in the film. ● For water at 298 K, the experimental disjoining pressure isotherm agrees with the electrostatic disjoining pressure calculated using the Langmuir equation. Thick films of water (b films) are controlled mainly by electrostatic effects. ● The disjoining pressure of the water and aqueous solution menisci decrease with increasing temperature. ● The waves on the surface of the adsorbed water film observed with increasing temperature lead to film breakage by thermocapillarity, vapor recoil, and disjoining pressure effects. ● The stability of aqueous solution thin films and the metastability of water films can explain the reported differences in the maximum heat flux of tap water versus pure water.
APPENDIX: NOMENCLATURE
A# e g h k K T x z d e eo P c r s
modified Hamaker constant electronic charge gravitational constant hydrostatic height Boltzmann constant curvature temperature distance inside the film valence of the ion film thickness dielectric constant permittivity of free space disjoining pressure electrostatic potential density, ionic and fluid surface tension
Subscripts and Superscripts CHF e l lv o s T vdW `
critical heat flux electrostatic liquid liquid–vapor adsorbed layer region solid surface total van derWaals thick film limit
ACKNOWLEDGMENTS This material is based on work partially supported by the National Science Foundation, under grant CTS-9123006, and by Fulbright/CONACYT, grant 15922189. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the NSF or Fulbright/CONACYT. Special thanks to Ivana Jovanovic and Dawn O’Loughlin, undergraduate students of the Chemical Engineering Department, who performed the experiments associated with Eqs. [11]–[14] as part of their participation in a NSF program for the Summer of 1994.
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39. Gershon, J. S., and Ballinger, J. T., Eds., “Chemical Technicians’ Ready Reference Handbook,” Chapter 25. McGraw–Hill, New York, 1990. 40. Reyes-Mazzoco, R., “Effect of Interfacial Forces on Change of Phase Heat Transfer,” Ph.D. thesis, Chemical Engineering Dept., Rensselaer Polytechnic Institute, Troy, NY, 1996. 41. Bankoff, S. G., J. Heat Transfer 116, 10 (1994). 42. Reyes, R., and Wayner, P. C., Jr., J. Heat Transfer 117, 779 (1995). 43. Hill, N. E., J. Phys. Chem. Solid State Phys. 3, 238 (1970). 44. Jasper, J. J., J. Phys. Chem. Ref. Data. 1, 841 (1972). 45. Lam, A. C., and Schechter, R. S., J. Colloid Interface Sci. 146, 206 (1991). 46. Kralchevsky, P. A., and Ivanov, I. B., Chem. Phys. Lett. 121, 116 (1985). 47. Costello, C. P., and Frea, W. J., Chem. Eng. Prog. Symp. Series 61, 258 (1965). 48. Dhir, V. K., “Some Observations from Maximum Heat Flux Data Obtained on Surfaces Having Different Degrees of Wettability,” pp. 185– 192. Pool and External Flow Boiling. ASME, New York, 1992.