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Wettability of a surface subjected to high frequency mechanical vibrations
Ultrasonics Sonochemistry xxx (2016) xxx–xxx
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Wettability of a surface subjected to high frequency mechanical vibrations R. Galleguillos-Silva ⇑, Y. Vargas-Hernández, L. Gaete-Garretón Laboratorio de Ultrasonidos, Departamento de Física, Universidad de Santiago de Chile, Av. Ecuador 3493, Estación Central, Santiago, Chile
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 30 August 2016 Accepted 13 September 2016 Available online xxxx Keywords: Wettability Ultrasounds Contact angle
a b s t r a c t Ultrasonic radiation can modify some physical properties in liquid/solid interactions, such as wettability. The dependence of solid surface wettability on its vibrational state was studied. Experiments with an interface formed by distilled water deposited on a titanium alloy and surrounded by air were carried out. It is shown that it is possible to control the apparent wettability of a given liquid/solid/gas system by applying sonic-ultrasonic vibrations of controlled amplitude at the interface. The system studied is composed of a drop of distilled water deposited on a flat titanium surface in air. The contact angle was used as an indicator of apparent wettability. It is shown that the apparent wettability of a surface is linearly dependent on the peak vibration velocity and independent of the vibration frequency. Higher vibration speed lowers the contact angle and therefore causes greater surface wettability. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Understanding and characterization of the wettability of a surface by a liquid is a process of great scientific as well as industrial importance. The wetting of solid surfaces by liquids is the governing phenomenon in processes such as lubrication, coatings, printing, detergency, separations process, and manufacture of composite materials [1–4]. Wettability is the ability of a liquid to maintain contact with a solid surface, resulting from the molecular interaction of the solid with the liquid. The degree of wettability is determined by the balance of forces of adhesion and cohesion between the surfaces involved in the interface. The greater the wettability the greater are the adhesion forces between the solid and liquid. This proposal, called the force treatment of the wettability process, is supported by several scientists like Extrand [5] and Lichao Gao [6], who proposed that the force per unit length gives a more clear understanding of the wettability phenomena and the hysteresis produced when the advancing and receding contact angle are measured. This last point of view allows the vector sum leading to the well-known Young relationship. It should be noted that a vector sum like that shown in Fig. 1 must be made only if the forces are applied at one point, in this case the point where the three interfaces, solid, liquid, and gas meet. There are other scientists like Wenzel [7] ⇑ Corresponding author. E-mail address: [email protected] (R. Galleguillos-Silva).
and Cassie [8] who introduce other points of view, suggesting that the balance of surface energies are the governing mechanism describing the wettability phenomena. It is interesting to point out that the controversy between the two points of view is alive until our days. However, the great interest of this controversy will not be treated in this paper because the experimental emphasis of this research leaves it out of its scope. In spite of the controversy, the contact angle and its relationship with wettability is a technique installed in both the industrial and scientific fields. Numerous methods have been developed to measure the forces involved in the phenomenon of wettability, e.g., Wilhelmy plate and Du Nouy ring [9]. These methods allow measuring the cohesive strength of a liquid and a surface at equilibrium as well as in a dynamic way. Moreover, each material has a specific energy and expresses different surface adhesion forces when in contact with a liquid, the magnitude of these forces depends not only on the nature of both, but also on the history of wetting, porosity, and chemical properties. This makes it difficult to know all the real surface energies and their balance of forces. In addition, there are other problems with the surface wetting, since there is not a perfectly smooth surface, and regardless of the polishing efforts that are made, a surface will always have some degree of roughness, making it difficult to assess the real dimensions of a wetted surface. For instance, if a solid surface is roughened so that a unit plane geometrical area has an actual surface area r times that of the ‘‘smooth” surface,
http://dx.doi.org/10.1016/j.ultsonch.2016.09.011 1350-4177/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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Fig. 1. Schematic of contact angle for a drop of liquid placed on a solid surface.
the measured contact angle obtained from cos0 ¼ ð1=rÞ cos h will be termed ‘‘apparent contact angle”. This denomination may be considered somewhat arbitrary, however, the surface area of a solid liquid interface is unique and can always be identified with its plane geometrical area [10]. The difficulties described above make it hard to know all the real surface energies and their balance of forces in a wetting process. In this context the contact angle technique represents a very suitable method to assess the wettability of a surface in contact with a liquid, providing a measure of the balance of forces between a liquid drop and a surface without a detailed consideration of the complex microscopic interactions involved. In the discussion of our results we analyze the vibratory energy present in our experiments, showing that there is enough energy to produce the increase in wettability reported in this work. The well-known classical technique of contact angle measurement involves depositing a drop of liquid on a flat and horizontal solid surface; depending on the properties of the materials, the liquid acquires a shape that approximates a spherical cap. From this approximation, considering the force scheme shown in Fig. 1, the contact angle can be measured. This angle is defined geometrically as the angle formed by a liquid at the three-phase boundary where liquid, gas, and solid intersect. From the scheme of forces shown in Fig. 1 it is easy to obtain the so called Young’s equation [11–13] representing the balance between the adhesion and cohesion forces.
cSG ¼ cSL þ cLG cos h
ð1Þ
where cSG ; cSL ; cLG are the surface tensions of the solid/gas, solid/ liquid and liquid/gas interfaces, respectively. As already mentioned, this relation is valid only if the surface is ideal, that is rigid, flat, smooth, chemically homogeneous, insoluble, and unreactive. A real surface contact angle has upper and lower limits, called contact angle forward and backward. This phenomenon is mainly related to the roughness of the surface [14–16], and implies that there is no single contact angle, but rather a range that depends on the energy barriers associated with the surface finish of the material [17]. Despite these phenomena that hinder the determination of a single contact angle value for each material system (solid, liquid and gas), this parameter is one of the most commonly used for the quantification of wettability between a surface and a liquid [12]. In a liquid in contact with a surface it has been found that the lower the contact angle, the greater the surface wettability, and vice versa. Besides the dependence of wettability from the parameters listed before, repeatable variations of the wettability on vibrating surfaces have been found. Some experimental studies showing a relationship between the wettability of a surface and its vibratory state have been reported [1,17]. In the first article, vibrations were used to overcome the energy barrier and improve the wettability of epoxy resins on aramid fibers. In the second one vertical vibrations were used to allow a drop to overcome the energy barrier, reaching
its GEM (global energy minimum) state determining the apparent contact angle. In those reports no full data about the dependence between the wettability and the ultrasonic parameters used in the research were included. In this research a contribution including experimental data about the effect of low ultrasonic frequencies on the wettability of a titanium surface by water is attempted. An experimental study of wettability variations due to vertical vibrations of a solid surface is presented, one of the aims of this research is to find a relationship (if there is one) between the wettability of an acoustically excited surface and its vibratory state, using the contact angle as an indicator of surface wettability. Although in this research the surface was titanium, the liquid was water and the atmosphere was air, the method can be applied to other sets of materials. The acoustic variables considered (vibration state) were the vibration frequency and amplitude. To avoid problems with an excessive attenuation and to keep the possibility of wide surface applications, the frequency range considered in this research lies between 5 and 40 kHz, which is the frequency range more often used to design high power ultrasonic devices for industrial and scientific applications. The data reported in this paper may be used to obtain a first approach to determine the energy balance in the variations of wettability phenomena, advancing in this way in the understanding of the problem. Also, the furnished data could be useful in establishing the method of using vibrations to improve the wettability in different industrial processes as well as in scientific experiments. It should be noted that carrying out this experimental study required a great effort, including the design and construction of seven high power ultrasonic sources and their electronic control systems. It should also be pointed out that although the wettability of a solid surface by a liquid is an old problem (200 years), many questions remain unanswered [17] and some are still being debated [6,12]. We have chosen an experimental approach using acoustics to address the effect of vibrations on wettability. For this research the authors use their expertise in acoustic science, allowing the determination on line and in real time of the vibration state of a surface under vibration. Several techniques and equipment were used to do it, as described in the following lines. This paper is the first report on the influence of acoustical parameters on surface wettability using the measurement of the contact angle. The knowledge of the relationship between the wettability and the acoustic parameters can allow the application of acoustic energy to different industrial process in which wettability is important. Matters such as the relation between acoustic energy and the work per unit area in the system and its interactions are out of the scope of this paper, and will be treated later in a research especially devoted to the topic that is under way.
2. Materials and methods The experimental setup requires a flat, solid, smooth, clean and horizontal surface. A drop of liquid is carefully deposited on the surface and its contact angle is measured. The experimental setup allows the generation of vertical vibrations on the surface, with arbitrary amplitude at different vibration frequencies. Because it is difficult to obtain a system providing large amplitudes for different frequencies simultaneously, an ensemble of transducers was designed and constructed, each one for a specific vibration frequency, working in resonance. In this way, high amplitudes at seven different frequencies were available for the experiments. During the experiments the variation of the contact angle caused by different vibration amplitudes of the surface was measured for each available frequency. Fig. 2 is a diagram of the experimental configuration, showing an ultrasonic transducer that
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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Fig. 2. Schematic of the active part of the experimental system, the ultrasonic transducer placed vertically, a high-speed camera, and a lighting system.
Fig. 3. Set of transducers used for the research.
provides high amplitude vibration at a given working frequency, an illumination source, and a high speed camera. On the right side of the image, a photographic detail of the assembly is shown. The following lines give a more detailed description of the experimental setup. 2.1. Liquid and surface For this research distilled water and a titanium alloy (Ti-6Al-4V) for solid surface were used. The tip of each transducer it is coated by an alloy sheet 0.45 mm thick. The sheets were fabricated from a single solid bar, were cut with a precision disc cutter machine (Buehler IsoMet 1000). After cutting, the sheets were polished with diamond paste (Struers DP-Paste, HQ 1/4 lm). Before gluing the discs on the transducer tip, a cleaning protocol was executed, consisting in immersing the disc in a beaker with acetone, placing the beaker in an ultrasonic cleaning bath with water, activated to produce cavitation in both liquids during 3 min; finally the discs were carefully removed from the vessel and were left drying in air on a clean cloth. The clean plate was fixed to the transducer tip with epoxy glue. The center of the disc is the place where the droplet was deposited for the experiments. Experiments were performed in an air atmosphere, and the laboratory conditions were 20 °C and atmospheric pressure. 2.2. Generation of controlled vibrations Seven high power transducers with the resonance frequencies of 6.06 kHz, 10.79 kHz, 16.67 kHz, 22.04 kHz, 24.89 kHz, 30.50 kHz and 38.19 kHz were designed, fabricated and characterized. Stepped horn type transducers were selected because of their high efficiency working at the resonant frequencies [18], allowing high amplitudes at the tip of each transducer to perform the experiments. Fig. 3 is a picture of the set of high power transducers used in this research. Each transducer, due to its operating principle and differences in design and manufacturing tolerances has different vibration amplitudes for a given excitation voltage. Experiments have shown that the vibration amplitude and current in a stepped horn piezoelectric transducer are linearly correlated [19]. This is an experimental fact that comes from the linearity of the relationship between these two variables appearing in the piezoelectric matrix
representing reciprocal transducers [20]. Therefore, it is possible to characterize the behavior of each transducer by recording the vibration amplitude and the electric current. The functional relationship between these variables allows determining the amplitude of vibration of the transducer tip, i.e., the displacement can be calculated by measuring the current fed to the transducer during the experiments when the transducer tip displacement cannot be measured directly. This characterization procedure was performed with each one of the electromechanical transducers used in the study. It is interesting to point out that this method allows knowing simultaneously the vibration amplitude of the surface of interest while the contact angle measurement is performed. The excitation of the transducers was made using an Agilent 33220A function generator, an AE Techron 7224 power amplifier (broad band), and a phase indicator specially designed and constructed for this research. The electronic circuit capable of measuring the phase shift between voltage and fed current to the transducer is shown in Fig. 4. The system furnishes a DC voltage output proportional to the phase shift. The circuit for measuring phase shift, shown in Fig. 4, is based on an Ex-Or gate. First, the voltage and current signals are transformed into two TTL signal. Then the signals are compared using an Ex-Or gate. A new TTL signal, whose duty cycle is proportional to the phase shift, is generated, and this signal is integrated to obtain a DC voltage proportional to the phase shift. The phase meter, between current and voltage, was used as an indicator of resonance, since the system is considered at resonance when the phase difference has a zero or minimum value [21]. An inductor was connected in parallel to each transducer to reduce the capacitive effect of the piezoelectric stacking, and this value was calculated from the equivalent transducer circuit near the resonance from the impedance versus frequency diagram of each transducer. The vibration amplitude measurement was performed using a laser Doppler vibrometer system with an analog interferometer (Polytec OFV 512) and a signal demodulator (Polytec OFV 3001). With this system the vibration velocity peak was measured for each case, and the displacement amplitude was calculated and then correlated with its feed current.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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R. Galleguillos-Silva et al. / Ultrasonics Sonochemistry xxx (2016) xxx–xxx Table 1 Critical atomization amplitude for each frequency used. It is important to mention that if the atomization threshold is correlated with the energy radiated per unit area, the behavior of this relation becomes monotonously increasing, because the energy depends on the square of the product of the amplitude and the angular frequency. Vibration frequency (kHz)
Critical amplitude (lm)
6.06 10.79 16.67 22.04 24.89 30.50 38.19
10.30 7.50 5.20 5.00 4.20 3.68 2.92
numerous microdrops, making it impossible to measure the contact angle. Considering each of the aspects described in the experimental procedure, it is necessary to take the following steps for each measurement:
Fig. 4. Schematic of the electronic circuit for measuring the phase between voltage and current.
The electric current is measured by a high frequency Hall Effect current probe, Tektronix TM502A, coupled with a Tektronix TDS320 oscilloscope. 2.3. Photography For each contact angle measurement, an image is acquired using a Phantom Miro M310 high speed camera. The shutter time used is 10 ls and the camera was manually operated. A Carl Zeiss Makroplanar 50 mm f/2.0 lens plus a 65-mm extension tube were used. With this system an effective focal length of 30 mm is achieved. The illumination system is configured using a single 3W LED 30 mm from the drop, without using a diffuser, as shown in Fig. 2. For each acquired image, the corresponding values of frequency, current fed to the transducer, and test number were recorded.
(1) A drop of distilled water is deposited, using a pipette, in the center of the prepared surface, at nil vibration amplitude. (2) An image is recorded for measuring the contact angle. (3) The vibration amplitude of the transducer tip is recorded. (4) The vibration amplitude is increased monotonically, to avoid problems of hysteresis at the contact angle. The amount of amplitude to be increased was chosen as one tenth of the critical amplitude, shown in Table 1. (5) Steps 2–5 are repeated for each vibration amplitude below the critical limit, to complete the characterization of the entire behavior of the contact angle. For the method outlined in the introduction, the measurement of the contact angle was made as follows: (1) On the image, a horizontal line was drawn parallel to the plane of the solid surface, as explained above. (2) Then a tangent to the surface of the liquid phase passing through image point P in Fig. 1 was drawn. (3) The lines, based on a Cartesian plane, were used to measure the angle between them. The intersection angle is the contact angle. For each frequency a minimum of 20 data were recorded at different vibration amplitudes. This was done by performing the experiment three times, using different drops, and plotting all the data.
2.4. Experimental procedure 3. Results Before performing each experiment, the system was prepared by making a revision of the following aspects: – The horizontality of the ultrasonic transducer’s radiant face was checked with a circular bubble level. – The transducer’s radiating surface was cleaned with a soft cloth and ethyl alcohol of 99.9% purity, waiting for 5 min to allow the solvent to evaporate. – The voltage amplitude of the generator was adjusted to 0 V, and the operating frequency for the power transducer in use was checked. Because the phenomenon of ultrasonic atomization obstructs the measurement of the contact angle, it had be avoided. For this the atomizing thresholds for each frequency in the study was measured. In each experiment the peak excitation amplitudes remained below this threshold. Table 1 shows the critical atomization amplitude for each vibration frequency used in this study. Above this limit, the water drop on the surface starts dividing into
Using the methodology described above, the contact angles were measured for each frequency and different vibration amplitudes. As already stated, the amplitudes were increased from zero, always below the atomization threshold, in steps of one tenth of the critical amplitude until a value close to this limit. The results are shown in the Fig. 5, where each line represent an ensemble of points corresponding to different contact angles vs. vibration amplitude for each vibration frequency. To offer a better understanding of the working methodology, Fig. 6a is, as an example, a photograph of a drop of distilled water placed on a titanium surface without vibration, and lines that determine the contact angle, h, have been drawn. Fig. 6b shows the drop of water when the transducer tip is subjected to vertical vibrations. The contact angle in Fig. 6b is remarkably smaller than in Fig. 6a. In this example, the transducer is vibrating with an amplitude of 5 lm at a frequency of 11 kHz. This smaller contact angle shows the system’s apparent increase in wettability when it is subjected to ultrasonic vibrations.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
Contact Angle (rad)
1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,0
1,5
3 3,0
4,5
6,0
7,5
9,0
10,5 12,0 13,5
Peak Amplitude (µm) Fig. 5. Contact angle versus peak vibration amplitude curves for different frequencies.
In all the curves the contact angle decreased as the vibration amplitude of the transducer tip was increased. This behavior shows an increase of the apparent wettability of the surface with increasing vibration amplitude for all frequencies. The data distribution suggests a linear correlation between the contact angle and the vibration amplitude, and applying a least squares method we get the straight lines of Fig. 5. The slopes of the straight lines in Fig. 5 decrease as the vibration frequency increases. Looking for the possible relationship between the wettability and the vibration frequency, a graph of the slopes of the curves of Fig. 5 vs. the frequency was plotted. The points of Fig. 7 are lined up, showing an inverse dependence between the slopes and the vibration frequencies. In other words, for a given vibration amplitude, the contact angle decreases with increasing frequency, showing an increase of the surface wettability. When the measured contact angle is plotted vs. the peak vibration velocity, a relationship between these two variables is found. Fig. 8 shows the resulting graph of contact angle versus vibration velocity for the different frequencies studied. In this graph a similar behavior between different frequencies is seen. Assuming a linear correlation between data, the slopes of the lines are similar to one another. It is important to note that the 6 kHz line behavior does not follow the general trend, with this line having a lower slope. This behavior is shown in Fig. 9, where the slope of the contact angle versus the peak vibration velocity is plotted for different frequencies. The slopes for all the frequencies are almost the same, except for the 6 kHz slope, for which it is lower than those for the other frequencies studied. A possible reason for this difference
-0,02 -0,04 -0,06 -0,08 -0,10 -0,12 -0,14 -0,16 -0,18 5
10
15
20
25
30
35
40
Frequency (kHz)
Fig. 7. Ratio of contact angle and peak vibration amplitude vs. frequency.
1,3
6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
1,2 1,1
Contact angle (rad)
1,3
Contact angle / Peak amplitude (rad/microns)
R. Galleguillos-Silva et al. / Ultrasonics Sonochemistry xxx (2016) xxx–xxx
1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
Peak speed (m/s) Fig. 8. Contact angle vs. peak speed for different frequencies.
would be the presence of capillary waves, hindering the measurement of the contact angle. Fig. 10 shows capillary waves with a wavelength of 250 lm for this frequency. It should be noted that the length of a capillarity wave is about one-tenth the drop diameter at this frequency, affecting the measurement processes. As frequency increases, the impact of these capillarity surface waves decreases. Despite the behavior at 6 kHz, the general trend of the curves shows that the apparent wettability is proportional to the peak vibration velocity, at least for a frequency range from 11 kHz to
Fig. 6. Pictures showing the effect of vibrations on the apparent contact angle of a water drop on titanium surface: a) Vibration-free. b) Subject to vibration.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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Contact Angle / speed amplitude (rad/(m/s))
6
0,0 -0,1 -0,2 -0,3 -0,4 -0,5 -0,6 -0,7 -0,8 -0,9 -1,0 -1,1 -1,2 5
10
15
20
25
30
35
40
Frequency (kHz) Fig. 9. Ratio of contact angle and peak vibration speed vs. frequency.
Fig. 10. Drop of water on a solid surface vibrating at a frequency of 6 kHz below the atomization threshold, showing the presence of capillary waves on the liquid surface.
38 kHz, with an average proportionality constant of 0.707 rad/ (m/s). The intercept value represents the contact angle without vibrations, i.e. at rest, and has an average value of 1.189 rad. With a correlation coefficient of R = 0.84. From this, an empirical relationship between these two variables can be written as:
happarent ¼ 1:189 0:707m
ð2Þ
where happarent is the apparent contact angle, measured in radians, and m is the peak vibration velocity measured in m/s. This expression is independent of the vibration frequency at least in the range from 11 kHz to 38 kHz and corresponds only to the variation of the wettability for the Water/Ti-6Al-4V/Air interface under the specified laboratory conditions. The behavior during testing shows a dramatic increase of the apparent wettability with increasing vibration velocity. Expression (2) allows the determination of the upper wettability limit; the velocity can be increased until the value of h became zero, and beyond this value expression (2) loses its meaning. This expression facilitates the application of the technique, but does not imply that they can consider other more general relations. 4. Discussion The onset of atomization was selected as the control parameter; the threshold of atomization decreases as the frequency increases, and this has been experimentally demonstrated and reported elsewhere [22]. The atomization displacement amplitude threshold
was found to be inversely and monotonically dependent on frequency. This relationship may be quite different if the velocity amplitude or the kinetic energy threshold were considered. We have conducted experiments to test the hypothesis that it is possible to produce atomization without cavitation. Preliminary results seem to confirm this hypothesis, although the final results have been delayed due to the experimental complexity of the problem. At present there are two theories about atomization: one of them is the capillary theory, explaining that atomization appears because with increasing vibration amplitude capillary waves produced on a vibrating surface become unstable and the wave crests become separated, producing droplets [23–26]. The other hypothesis proposes that the atomization is produced because the supersonic jets generated in a cavitation regime cut the crests of capillary waves, thus producing atomization [25]. The contact angle versus peak vibration amplitude, in Fig. 5, shows a linear trend with a small dispersion for each frequency studied. As frequency increases, the slope of each wettability curve obtained experimentally decreases. This shows that the wettability predictably increases with increasing vibration amplitude for the studied system. It is also possible to obtain maximum limits of contact angle for each frequency. The results found in this research for the wettability angle dependence on the vibration velocity are similar to those reported by Tammar S. Meiron, et al. [17] using frequencies (between 30 and 80 Hz), well below those used in this study. A variation is seen for the curves drawn for each frequency in the value of the intercept with the ordinate axis. This value corresponds to the contact angle when the vibration amplitude is zero, and in theory it should have the same value for all experiments. However, the intercept depends not only on the materials involved, but also on the system’s temperature, wet history, surface finish, and the properties of the gas in contact with the drop. These facts may explain why, in spite of the care in the preparation of the surfaces, it was difficult to maintain exactly the same conditions for all experiments. These variations in the experimental conditions were considered as the explanation of the dispersion of the obtained data. It should be pointed out that in our data the 6 kHz curve appear to have a behavior different from that of the other explored frequencies, a discrepancy that was interpreted as probably caused by the early onset of capillary waves, as shown in the image of Fig. 10. A somewhat surprising result is the non-dependence of the wettability increase on frequency, which shows that the problem of wettability, as had been assumed, is an energy problem, since energy can be obtained using the vibration velocity amplitude. For instance, effects on wettability were reported in Ref. [17] for millimeter vibration amplitudes and frequencies between 30 and 80 Hz. In contrast, in this research the vibration amplitudes used are micrometric and the frequencies are in the kHz range. This could be an important factor to consider, because the velocity depends linearly on the frequency, and the acceleration depends on the square of this magnitude. For instance, in Ref. [17] the maximum velocity reported is 0.43 m/s at 30 Hz, while in the data of the present paper, for a frequency of 30 kHz the maximum velocity was almost the same (0.49 m/s). However, the accelerations are quite different; 81.7 m/s2 for 30 Hz, and 9571 m/s2 for 30 kHz. As frequency increases, the slope of each curve decreases, showing the relationship between the contact angle and the vibration amplitude. This shows that, predictably, the wettability increases with increasing amplitude of vibration for the system studied. This does not allow making a theoretical model of the phenomena because, besides the usefulness of such a curves, the slope of the vibration amplitude curves has not meaning from dynamic or energy theories.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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cSL ¼ jcLG cSG j
ð3Þ
and Young’s equation (1) it is easy to obtain the relationship
cos h ¼ 1 þ 2
cSG cLG
ð4Þ
replacing the value of liquid surface free energy, cLG ¼ 0; 0720½J=m2 and the contact angle for the system at rest, hSessile drop ¼ 1:18297½rad, Eq. (4) gives for cSG the value:
cSG ¼ 0; 0496½J=m2 Then, if we assume that the mechanical vibrations produces an ‘‘apparent” effect on the surface tension cLG only, it is possible to calculate the new value (cLG ) for each contact angle measured and plot the evolution of this parameter as a function of the vibration speed. Then cLG has the form
cLG ¼
2 0; 0496 ½J=m2 cos h þ 1
ð5Þ
Fig. 11 shows, for the experimental system described and for all vibration frequencies measured in this research, the evolution of the apparent surface tension with peak speed. The behavior of this curve, in Fig. 11, shows a clear trend, independent of the vibration frequency. Due to the large data dispersion it is difficult to define a functional relationship between the variables, although from Fig. 11 a decreasing dependence of the surface tension of this liquid on the velocity amplitude of ultrasonic vibration can be established. Finally, a simple calculation considering the energy present in the waveguide and the transmission coefficient of acoustic energy from the titanium to the water shows that the energy available for the process is thousands times higher than necessary to produce the wettability effects reported in this paper.
80 75
Liquid Surface Tension (mJ/m^2)
The wettability behavior is represented by the slope and intercept of a straight line plotted with the acquired data. The intercept is the contact angle for a drop at rest and the slope shows the change under different vibration velocities. To avoid hysteresis problems in the measurements, the amplitude increase during the experiments was monotonic. The obtained relationships show that the wettability can be described as an energy problem, because the data related to this magnitude can be interpreted more easily and straightforwardly than the data related to acceleration. If the more important mechanism of wettability is dynamic, the behavior can change abruptly when the g value is overcome. However, we reached several thousand g without a detectable effect. This proposes a fascinating problem to study the balance of energy supplied to the drop by the vibrations; of course the problem has a complex dynamics because in a first stage the energy was communicated to the liquid and then, after this transient time interval that can be estimated at about 0.7 ls, the energy from the surface is radiated by the drop. In this problem the energy balance can be calculated by determining the exact shape of the drop, calculating the potential energy content, and comparing with the initial energy. Afterwards the differences in energy can be compared with the values obtained from the Young and Wenzel equation, producing an advance in the vibratory wettability theory. Our present experimental sept-up does not allow making such a determination, and the problem will be tackled in coming research. On the other hand, if we consider some approximations, it is possible to calculate the surface free energy in the liquid for each vibrational state. Considering the Antonow relationship [27]:
70 65 60 55
6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
50 45 40 35 30 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Peak Speed (m/s) Fig. 11. Surface tension of the water vs. peak speed for different frequencies.
5. Conclusions It was confirmed that an increase in the wettability of a surface occurs when it is activated by mechanical vibrations at low ultrasonic frequencies. Interestingly, the improvement in the wettability seems to be independent of the exciting frequency. An empirical relationship is obtained between the growth of the wettability for a vibrating surface and the velocity amplitude of the vibration (Eq. (2)). The results reported in this paper may lead to the improvement of important industrial methods like those reported in [1], because the curves obtained can be used to choose the working frequencies for industrial process in which one can avoid some negative effects of large vibration amplitudes, for instance. Acknowledgements This research was financially supported by CONICYT – Chile under FONDEF Project D09I1235. References [1] L. Liu, Y.D. Huang, Z.Q. Zhang, X.B. Yang, Effect of Ultrasound on Wettability Between Aramid Fibers and Epoxy Resin, Wiley InterScience, 2005, http://dx. doi.org/10.1002/app.22859. [2] George B. Sigal, Milan Mrksich, George M. Whitesides, Effects of surface wettability on the adsorption of proteins and detergents, J. Am. Chem. Soc. 120 (1998) 3464–3473. [3] Yuan Li, Zhaozhu Zhang, Xiaotao Zhu, Xuehu Men, Bo Ge, Xiaoyan Zhou, Fabrication of a superhydrophobic coating with high adhesive effect to substrates and tunable wettability, Appl. Surf. Sci. 328 (2015) 475–481. [4] Xiaming Luo, Limin He, Hongping Wang, Haipeng Yan, Yahua Qin, An experimental study on the motion of water droplets in oil under ultrasonic irradiation, Ultrason. Sonochem. 28 (2016) 110–117. [5] C.W. Extrand, Contact angles and hysteresis on surfaces with chemically heterogeneous islands, Langmuir 19 (2003) 3793–3796. [6] Lichao Gao, Thomas J. McCarthy, How Wenzel and Cassie were wrong, Langmuir 23 (7) (2007) 3762–3765. [7] R.N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28 (1936) 988. [8] A.B.D. Cassie, S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40 (1944) 546–551. [9] Elias I. Franses, Osman A. Basaran, Chien-Hsiang Chang, Techniques to measure dynamic surface tension, in: Colloid Interface Sci. 1 (1996) 296–303. [10] A.B.D. Cassie, Contact angles, Discuss. Faraday Soc. 3 (1948). [11] Thomas. Young, An essay on the cohesion of fluids, Phil. Trans. R. Soc. Lond. 95 (1805) 65–87. [12] H. Erbil Yildrim, The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: a review, Surf. Sci. Rep. 69 (2014) 325–365.
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[13] K.L. Mittal (Ed.), Advances in Contact Angle, Wettability and Adhesion, Scrivener Publishing, 1983. [14] R.E. Johnson, R.H. Dettre, Wettability and Contact Angles, Surface and Colloid Science, Wiley-Interscience, New York, 1969. [15] A. Marmur, Thermodynamic aspects of contact angle hysteresis, Adv. Colloid Interface Sci. 50 (1994). [16] E. Chibowski, Surface free energy of a solid from contact angle hysteresis, Adv. Colloid Interface Sci. 103 (2003). [17] S. Tammar Meiron, Abraham Marmur, I. Sam Saguy, Contact angle measurement on rough surfaces, Colloid Interface Sci. 274 (2004) 637–644. [18] E.A. Neppiras, The prestressed piezoelectric sandwich transducers, in: Proceedings International Conference Ultrasonic. pp. 295-302 (1973). [19] V. Salinas, Y. Vargas, O. Lousnard, L. Gaete, Influence of the viscosity on the formation of bubble structures in a 20 kHz field, Ultrason. Sonochem. 22 (2015) 227–234.
[20] F.V. Hunt, Electroacoustics, The Analysis of Transduction and its Historical Background, American Institute of Physics for the Acoustical Society of America, 1982. [21] Y. Kuang, Y. Jin, S. Cochran, Z. Hung, Resonance tracking and vibration stablilization for high power ultrasonic transducers, Ultrasonics 54 (2014) 187–194. [22] D. Briceño-Gutierrez, V. Salinas-Barrera, Y. Vargas-Hernández, L. GaeteGarretón, C. Zanelli-Iglesias, On the ultrasonic atomization of liquids, Phys. Procedia 63 (2015) 37–41. [23] R.W. Good, A.L. Loomis, Phil. Mag. S. 7, vol. 4 N° (1927). [24] R. Lang, Ultrasonic atomization of liquids, J. Acoust. Soc. Am. 34 (1962) 1. [25] Kiran A. Ramisetty, Aniruddha B. Pandit, Parag R. Gogate, Investigations into ultrasound induced atomization, Ultrason. Sonochem. (2013) 254–264. [26] Dragan Sarkovic, Vukota Babovic, On the statistics of ultrasonically produced water droplets, in: Z. Naturforsch 60 (2005) 489–493. [27] Frank M. Etzler, Surface free energy of solids: a comparison of models, in: Contact Angle, Wettability and Adhesion, vol. 4, pp. 215–236, 2006.
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Ultrasonics Sonochemistry journal homepage: www.elsevier.com/locate/ultson
Wettability of a surface subjected to high frequency mechanical vibrations R. Galleguillos-Silva ⇑, Y. Vargas-Hernández, L. Gaete-Garretón Laboratorio de Ultrasonidos, Departamento de Física, Universidad de Santiago de Chile, Av. Ecuador 3493, Estación Central, Santiago, Chile
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 30 August 2016 Accepted 13 September 2016 Available online xxxx Keywords: Wettability Ultrasounds Contact angle
a b s t r a c t Ultrasonic radiation can modify some physical properties in liquid/solid interactions, such as wettability. The dependence of solid surface wettability on its vibrational state was studied. Experiments with an interface formed by distilled water deposited on a titanium alloy and surrounded by air were carried out. It is shown that it is possible to control the apparent wettability of a given liquid/solid/gas system by applying sonic-ultrasonic vibrations of controlled amplitude at the interface. The system studied is composed of a drop of distilled water deposited on a flat titanium surface in air. The contact angle was used as an indicator of apparent wettability. It is shown that the apparent wettability of a surface is linearly dependent on the peak vibration velocity and independent of the vibration frequency. Higher vibration speed lowers the contact angle and therefore causes greater surface wettability. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Understanding and characterization of the wettability of a surface by a liquid is a process of great scientific as well as industrial importance. The wetting of solid surfaces by liquids is the governing phenomenon in processes such as lubrication, coatings, printing, detergency, separations process, and manufacture of composite materials [1–4]. Wettability is the ability of a liquid to maintain contact with a solid surface, resulting from the molecular interaction of the solid with the liquid. The degree of wettability is determined by the balance of forces of adhesion and cohesion between the surfaces involved in the interface. The greater the wettability the greater are the adhesion forces between the solid and liquid. This proposal, called the force treatment of the wettability process, is supported by several scientists like Extrand [5] and Lichao Gao [6], who proposed that the force per unit length gives a more clear understanding of the wettability phenomena and the hysteresis produced when the advancing and receding contact angle are measured. This last point of view allows the vector sum leading to the well-known Young relationship. It should be noted that a vector sum like that shown in Fig. 1 must be made only if the forces are applied at one point, in this case the point where the three interfaces, solid, liquid, and gas meet. There are other scientists like Wenzel [7] ⇑ Corresponding author. E-mail address: [email protected] (R. Galleguillos-Silva).
and Cassie [8] who introduce other points of view, suggesting that the balance of surface energies are the governing mechanism describing the wettability phenomena. It is interesting to point out that the controversy between the two points of view is alive until our days. However, the great interest of this controversy will not be treated in this paper because the experimental emphasis of this research leaves it out of its scope. In spite of the controversy, the contact angle and its relationship with wettability is a technique installed in both the industrial and scientific fields. Numerous methods have been developed to measure the forces involved in the phenomenon of wettability, e.g., Wilhelmy plate and Du Nouy ring [9]. These methods allow measuring the cohesive strength of a liquid and a surface at equilibrium as well as in a dynamic way. Moreover, each material has a specific energy and expresses different surface adhesion forces when in contact with a liquid, the magnitude of these forces depends not only on the nature of both, but also on the history of wetting, porosity, and chemical properties. This makes it difficult to know all the real surface energies and their balance of forces. In addition, there are other problems with the surface wetting, since there is not a perfectly smooth surface, and regardless of the polishing efforts that are made, a surface will always have some degree of roughness, making it difficult to assess the real dimensions of a wetted surface. For instance, if a solid surface is roughened so that a unit plane geometrical area has an actual surface area r times that of the ‘‘smooth” surface,
http://dx.doi.org/10.1016/j.ultsonch.2016.09.011 1350-4177/Ó 2016 Elsevier B.V. All rights reserved.
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Fig. 1. Schematic of contact angle for a drop of liquid placed on a solid surface.
the measured contact angle obtained from cos0 ¼ ð1=rÞ cos h will be termed ‘‘apparent contact angle”. This denomination may be considered somewhat arbitrary, however, the surface area of a solid liquid interface is unique and can always be identified with its plane geometrical area [10]. The difficulties described above make it hard to know all the real surface energies and their balance of forces in a wetting process. In this context the contact angle technique represents a very suitable method to assess the wettability of a surface in contact with a liquid, providing a measure of the balance of forces between a liquid drop and a surface without a detailed consideration of the complex microscopic interactions involved. In the discussion of our results we analyze the vibratory energy present in our experiments, showing that there is enough energy to produce the increase in wettability reported in this work. The well-known classical technique of contact angle measurement involves depositing a drop of liquid on a flat and horizontal solid surface; depending on the properties of the materials, the liquid acquires a shape that approximates a spherical cap. From this approximation, considering the force scheme shown in Fig. 1, the contact angle can be measured. This angle is defined geometrically as the angle formed by a liquid at the three-phase boundary where liquid, gas, and solid intersect. From the scheme of forces shown in Fig. 1 it is easy to obtain the so called Young’s equation [11–13] representing the balance between the adhesion and cohesion forces.
cSG ¼ cSL þ cLG cos h
ð1Þ
where cSG ; cSL ; cLG are the surface tensions of the solid/gas, solid/ liquid and liquid/gas interfaces, respectively. As already mentioned, this relation is valid only if the surface is ideal, that is rigid, flat, smooth, chemically homogeneous, insoluble, and unreactive. A real surface contact angle has upper and lower limits, called contact angle forward and backward. This phenomenon is mainly related to the roughness of the surface [14–16], and implies that there is no single contact angle, but rather a range that depends on the energy barriers associated with the surface finish of the material [17]. Despite these phenomena that hinder the determination of a single contact angle value for each material system (solid, liquid and gas), this parameter is one of the most commonly used for the quantification of wettability between a surface and a liquid [12]. In a liquid in contact with a surface it has been found that the lower the contact angle, the greater the surface wettability, and vice versa. Besides the dependence of wettability from the parameters listed before, repeatable variations of the wettability on vibrating surfaces have been found. Some experimental studies showing a relationship between the wettability of a surface and its vibratory state have been reported [1,17]. In the first article, vibrations were used to overcome the energy barrier and improve the wettability of epoxy resins on aramid fibers. In the second one vertical vibrations were used to allow a drop to overcome the energy barrier, reaching
its GEM (global energy minimum) state determining the apparent contact angle. In those reports no full data about the dependence between the wettability and the ultrasonic parameters used in the research were included. In this research a contribution including experimental data about the effect of low ultrasonic frequencies on the wettability of a titanium surface by water is attempted. An experimental study of wettability variations due to vertical vibrations of a solid surface is presented, one of the aims of this research is to find a relationship (if there is one) between the wettability of an acoustically excited surface and its vibratory state, using the contact angle as an indicator of surface wettability. Although in this research the surface was titanium, the liquid was water and the atmosphere was air, the method can be applied to other sets of materials. The acoustic variables considered (vibration state) were the vibration frequency and amplitude. To avoid problems with an excessive attenuation and to keep the possibility of wide surface applications, the frequency range considered in this research lies between 5 and 40 kHz, which is the frequency range more often used to design high power ultrasonic devices for industrial and scientific applications. The data reported in this paper may be used to obtain a first approach to determine the energy balance in the variations of wettability phenomena, advancing in this way in the understanding of the problem. Also, the furnished data could be useful in establishing the method of using vibrations to improve the wettability in different industrial processes as well as in scientific experiments. It should be noted that carrying out this experimental study required a great effort, including the design and construction of seven high power ultrasonic sources and their electronic control systems. It should also be pointed out that although the wettability of a solid surface by a liquid is an old problem (200 years), many questions remain unanswered [17] and some are still being debated [6,12]. We have chosen an experimental approach using acoustics to address the effect of vibrations on wettability. For this research the authors use their expertise in acoustic science, allowing the determination on line and in real time of the vibration state of a surface under vibration. Several techniques and equipment were used to do it, as described in the following lines. This paper is the first report on the influence of acoustical parameters on surface wettability using the measurement of the contact angle. The knowledge of the relationship between the wettability and the acoustic parameters can allow the application of acoustic energy to different industrial process in which wettability is important. Matters such as the relation between acoustic energy and the work per unit area in the system and its interactions are out of the scope of this paper, and will be treated later in a research especially devoted to the topic that is under way.
2. Materials and methods The experimental setup requires a flat, solid, smooth, clean and horizontal surface. A drop of liquid is carefully deposited on the surface and its contact angle is measured. The experimental setup allows the generation of vertical vibrations on the surface, with arbitrary amplitude at different vibration frequencies. Because it is difficult to obtain a system providing large amplitudes for different frequencies simultaneously, an ensemble of transducers was designed and constructed, each one for a specific vibration frequency, working in resonance. In this way, high amplitudes at seven different frequencies were available for the experiments. During the experiments the variation of the contact angle caused by different vibration amplitudes of the surface was measured for each available frequency. Fig. 2 is a diagram of the experimental configuration, showing an ultrasonic transducer that
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Fig. 2. Schematic of the active part of the experimental system, the ultrasonic transducer placed vertically, a high-speed camera, and a lighting system.
Fig. 3. Set of transducers used for the research.
provides high amplitude vibration at a given working frequency, an illumination source, and a high speed camera. On the right side of the image, a photographic detail of the assembly is shown. The following lines give a more detailed description of the experimental setup. 2.1. Liquid and surface For this research distilled water and a titanium alloy (Ti-6Al-4V) for solid surface were used. The tip of each transducer it is coated by an alloy sheet 0.45 mm thick. The sheets were fabricated from a single solid bar, were cut with a precision disc cutter machine (Buehler IsoMet 1000). After cutting, the sheets were polished with diamond paste (Struers DP-Paste, HQ 1/4 lm). Before gluing the discs on the transducer tip, a cleaning protocol was executed, consisting in immersing the disc in a beaker with acetone, placing the beaker in an ultrasonic cleaning bath with water, activated to produce cavitation in both liquids during 3 min; finally the discs were carefully removed from the vessel and were left drying in air on a clean cloth. The clean plate was fixed to the transducer tip with epoxy glue. The center of the disc is the place where the droplet was deposited for the experiments. Experiments were performed in an air atmosphere, and the laboratory conditions were 20 °C and atmospheric pressure. 2.2. Generation of controlled vibrations Seven high power transducers with the resonance frequencies of 6.06 kHz, 10.79 kHz, 16.67 kHz, 22.04 kHz, 24.89 kHz, 30.50 kHz and 38.19 kHz were designed, fabricated and characterized. Stepped horn type transducers were selected because of their high efficiency working at the resonant frequencies [18], allowing high amplitudes at the tip of each transducer to perform the experiments. Fig. 3 is a picture of the set of high power transducers used in this research. Each transducer, due to its operating principle and differences in design and manufacturing tolerances has different vibration amplitudes for a given excitation voltage. Experiments have shown that the vibration amplitude and current in a stepped horn piezoelectric transducer are linearly correlated [19]. This is an experimental fact that comes from the linearity of the relationship between these two variables appearing in the piezoelectric matrix
representing reciprocal transducers [20]. Therefore, it is possible to characterize the behavior of each transducer by recording the vibration amplitude and the electric current. The functional relationship between these variables allows determining the amplitude of vibration of the transducer tip, i.e., the displacement can be calculated by measuring the current fed to the transducer during the experiments when the transducer tip displacement cannot be measured directly. This characterization procedure was performed with each one of the electromechanical transducers used in the study. It is interesting to point out that this method allows knowing simultaneously the vibration amplitude of the surface of interest while the contact angle measurement is performed. The excitation of the transducers was made using an Agilent 33220A function generator, an AE Techron 7224 power amplifier (broad band), and a phase indicator specially designed and constructed for this research. The electronic circuit capable of measuring the phase shift between voltage and fed current to the transducer is shown in Fig. 4. The system furnishes a DC voltage output proportional to the phase shift. The circuit for measuring phase shift, shown in Fig. 4, is based on an Ex-Or gate. First, the voltage and current signals are transformed into two TTL signal. Then the signals are compared using an Ex-Or gate. A new TTL signal, whose duty cycle is proportional to the phase shift, is generated, and this signal is integrated to obtain a DC voltage proportional to the phase shift. The phase meter, between current and voltage, was used as an indicator of resonance, since the system is considered at resonance when the phase difference has a zero or minimum value [21]. An inductor was connected in parallel to each transducer to reduce the capacitive effect of the piezoelectric stacking, and this value was calculated from the equivalent transducer circuit near the resonance from the impedance versus frequency diagram of each transducer. The vibration amplitude measurement was performed using a laser Doppler vibrometer system with an analog interferometer (Polytec OFV 512) and a signal demodulator (Polytec OFV 3001). With this system the vibration velocity peak was measured for each case, and the displacement amplitude was calculated and then correlated with its feed current.
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R. Galleguillos-Silva et al. / Ultrasonics Sonochemistry xxx (2016) xxx–xxx Table 1 Critical atomization amplitude for each frequency used. It is important to mention that if the atomization threshold is correlated with the energy radiated per unit area, the behavior of this relation becomes monotonously increasing, because the energy depends on the square of the product of the amplitude and the angular frequency. Vibration frequency (kHz)
Critical amplitude (lm)
6.06 10.79 16.67 22.04 24.89 30.50 38.19
10.30 7.50 5.20 5.00 4.20 3.68 2.92
numerous microdrops, making it impossible to measure the contact angle. Considering each of the aspects described in the experimental procedure, it is necessary to take the following steps for each measurement:
Fig. 4. Schematic of the electronic circuit for measuring the phase between voltage and current.
The electric current is measured by a high frequency Hall Effect current probe, Tektronix TM502A, coupled with a Tektronix TDS320 oscilloscope. 2.3. Photography For each contact angle measurement, an image is acquired using a Phantom Miro M310 high speed camera. The shutter time used is 10 ls and the camera was manually operated. A Carl Zeiss Makroplanar 50 mm f/2.0 lens plus a 65-mm extension tube were used. With this system an effective focal length of 30 mm is achieved. The illumination system is configured using a single 3W LED 30 mm from the drop, without using a diffuser, as shown in Fig. 2. For each acquired image, the corresponding values of frequency, current fed to the transducer, and test number were recorded.
(1) A drop of distilled water is deposited, using a pipette, in the center of the prepared surface, at nil vibration amplitude. (2) An image is recorded for measuring the contact angle. (3) The vibration amplitude of the transducer tip is recorded. (4) The vibration amplitude is increased monotonically, to avoid problems of hysteresis at the contact angle. The amount of amplitude to be increased was chosen as one tenth of the critical amplitude, shown in Table 1. (5) Steps 2–5 are repeated for each vibration amplitude below the critical limit, to complete the characterization of the entire behavior of the contact angle. For the method outlined in the introduction, the measurement of the contact angle was made as follows: (1) On the image, a horizontal line was drawn parallel to the plane of the solid surface, as explained above. (2) Then a tangent to the surface of the liquid phase passing through image point P in Fig. 1 was drawn. (3) The lines, based on a Cartesian plane, were used to measure the angle between them. The intersection angle is the contact angle. For each frequency a minimum of 20 data were recorded at different vibration amplitudes. This was done by performing the experiment three times, using different drops, and plotting all the data.
2.4. Experimental procedure 3. Results Before performing each experiment, the system was prepared by making a revision of the following aspects: – The horizontality of the ultrasonic transducer’s radiant face was checked with a circular bubble level. – The transducer’s radiating surface was cleaned with a soft cloth and ethyl alcohol of 99.9% purity, waiting for 5 min to allow the solvent to evaporate. – The voltage amplitude of the generator was adjusted to 0 V, and the operating frequency for the power transducer in use was checked. Because the phenomenon of ultrasonic atomization obstructs the measurement of the contact angle, it had be avoided. For this the atomizing thresholds for each frequency in the study was measured. In each experiment the peak excitation amplitudes remained below this threshold. Table 1 shows the critical atomization amplitude for each vibration frequency used in this study. Above this limit, the water drop on the surface starts dividing into
Using the methodology described above, the contact angles were measured for each frequency and different vibration amplitudes. As already stated, the amplitudes were increased from zero, always below the atomization threshold, in steps of one tenth of the critical amplitude until a value close to this limit. The results are shown in the Fig. 5, where each line represent an ensemble of points corresponding to different contact angles vs. vibration amplitude for each vibration frequency. To offer a better understanding of the working methodology, Fig. 6a is, as an example, a photograph of a drop of distilled water placed on a titanium surface without vibration, and lines that determine the contact angle, h, have been drawn. Fig. 6b shows the drop of water when the transducer tip is subjected to vertical vibrations. The contact angle in Fig. 6b is remarkably smaller than in Fig. 6a. In this example, the transducer is vibrating with an amplitude of 5 lm at a frequency of 11 kHz. This smaller contact angle shows the system’s apparent increase in wettability when it is subjected to ultrasonic vibrations.
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6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
Contact Angle (rad)
1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,0
1,5
3 3,0
4,5
6,0
7,5
9,0
10,5 12,0 13,5
Peak Amplitude (µm) Fig. 5. Contact angle versus peak vibration amplitude curves for different frequencies.
In all the curves the contact angle decreased as the vibration amplitude of the transducer tip was increased. This behavior shows an increase of the apparent wettability of the surface with increasing vibration amplitude for all frequencies. The data distribution suggests a linear correlation between the contact angle and the vibration amplitude, and applying a least squares method we get the straight lines of Fig. 5. The slopes of the straight lines in Fig. 5 decrease as the vibration frequency increases. Looking for the possible relationship between the wettability and the vibration frequency, a graph of the slopes of the curves of Fig. 5 vs. the frequency was plotted. The points of Fig. 7 are lined up, showing an inverse dependence between the slopes and the vibration frequencies. In other words, for a given vibration amplitude, the contact angle decreases with increasing frequency, showing an increase of the surface wettability. When the measured contact angle is plotted vs. the peak vibration velocity, a relationship between these two variables is found. Fig. 8 shows the resulting graph of contact angle versus vibration velocity for the different frequencies studied. In this graph a similar behavior between different frequencies is seen. Assuming a linear correlation between data, the slopes of the lines are similar to one another. It is important to note that the 6 kHz line behavior does not follow the general trend, with this line having a lower slope. This behavior is shown in Fig. 9, where the slope of the contact angle versus the peak vibration velocity is plotted for different frequencies. The slopes for all the frequencies are almost the same, except for the 6 kHz slope, for which it is lower than those for the other frequencies studied. A possible reason for this difference
-0,02 -0,04 -0,06 -0,08 -0,10 -0,12 -0,14 -0,16 -0,18 5
10
15
20
25
30
35
40
Frequency (kHz)
Fig. 7. Ratio of contact angle and peak vibration amplitude vs. frequency.
1,3
6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
1,2 1,1
Contact angle (rad)
1,3
Contact angle / Peak amplitude (rad/microns)
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1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
Peak speed (m/s) Fig. 8. Contact angle vs. peak speed for different frequencies.
would be the presence of capillary waves, hindering the measurement of the contact angle. Fig. 10 shows capillary waves with a wavelength of 250 lm for this frequency. It should be noted that the length of a capillarity wave is about one-tenth the drop diameter at this frequency, affecting the measurement processes. As frequency increases, the impact of these capillarity surface waves decreases. Despite the behavior at 6 kHz, the general trend of the curves shows that the apparent wettability is proportional to the peak vibration velocity, at least for a frequency range from 11 kHz to
Fig. 6. Pictures showing the effect of vibrations on the apparent contact angle of a water drop on titanium surface: a) Vibration-free. b) Subject to vibration.
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Contact Angle / speed amplitude (rad/(m/s))
6
0,0 -0,1 -0,2 -0,3 -0,4 -0,5 -0,6 -0,7 -0,8 -0,9 -1,0 -1,1 -1,2 5
10
15
20
25
30
35
40
Frequency (kHz) Fig. 9. Ratio of contact angle and peak vibration speed vs. frequency.
Fig. 10. Drop of water on a solid surface vibrating at a frequency of 6 kHz below the atomization threshold, showing the presence of capillary waves on the liquid surface.
38 kHz, with an average proportionality constant of 0.707 rad/ (m/s). The intercept value represents the contact angle without vibrations, i.e. at rest, and has an average value of 1.189 rad. With a correlation coefficient of R = 0.84. From this, an empirical relationship between these two variables can be written as:
happarent ¼ 1:189 0:707m
ð2Þ
where happarent is the apparent contact angle, measured in radians, and m is the peak vibration velocity measured in m/s. This expression is independent of the vibration frequency at least in the range from 11 kHz to 38 kHz and corresponds only to the variation of the wettability for the Water/Ti-6Al-4V/Air interface under the specified laboratory conditions. The behavior during testing shows a dramatic increase of the apparent wettability with increasing vibration velocity. Expression (2) allows the determination of the upper wettability limit; the velocity can be increased until the value of h became zero, and beyond this value expression (2) loses its meaning. This expression facilitates the application of the technique, but does not imply that they can consider other more general relations. 4. Discussion The onset of atomization was selected as the control parameter; the threshold of atomization decreases as the frequency increases, and this has been experimentally demonstrated and reported elsewhere [22]. The atomization displacement amplitude threshold
was found to be inversely and monotonically dependent on frequency. This relationship may be quite different if the velocity amplitude or the kinetic energy threshold were considered. We have conducted experiments to test the hypothesis that it is possible to produce atomization without cavitation. Preliminary results seem to confirm this hypothesis, although the final results have been delayed due to the experimental complexity of the problem. At present there are two theories about atomization: one of them is the capillary theory, explaining that atomization appears because with increasing vibration amplitude capillary waves produced on a vibrating surface become unstable and the wave crests become separated, producing droplets [23–26]. The other hypothesis proposes that the atomization is produced because the supersonic jets generated in a cavitation regime cut the crests of capillary waves, thus producing atomization [25]. The contact angle versus peak vibration amplitude, in Fig. 5, shows a linear trend with a small dispersion for each frequency studied. As frequency increases, the slope of each wettability curve obtained experimentally decreases. This shows that the wettability predictably increases with increasing vibration amplitude for the studied system. It is also possible to obtain maximum limits of contact angle for each frequency. The results found in this research for the wettability angle dependence on the vibration velocity are similar to those reported by Tammar S. Meiron, et al. [17] using frequencies (between 30 and 80 Hz), well below those used in this study. A variation is seen for the curves drawn for each frequency in the value of the intercept with the ordinate axis. This value corresponds to the contact angle when the vibration amplitude is zero, and in theory it should have the same value for all experiments. However, the intercept depends not only on the materials involved, but also on the system’s temperature, wet history, surface finish, and the properties of the gas in contact with the drop. These facts may explain why, in spite of the care in the preparation of the surfaces, it was difficult to maintain exactly the same conditions for all experiments. These variations in the experimental conditions were considered as the explanation of the dispersion of the obtained data. It should be pointed out that in our data the 6 kHz curve appear to have a behavior different from that of the other explored frequencies, a discrepancy that was interpreted as probably caused by the early onset of capillary waves, as shown in the image of Fig. 10. A somewhat surprising result is the non-dependence of the wettability increase on frequency, which shows that the problem of wettability, as had been assumed, is an energy problem, since energy can be obtained using the vibration velocity amplitude. For instance, effects on wettability were reported in Ref. [17] for millimeter vibration amplitudes and frequencies between 30 and 80 Hz. In contrast, in this research the vibration amplitudes used are micrometric and the frequencies are in the kHz range. This could be an important factor to consider, because the velocity depends linearly on the frequency, and the acceleration depends on the square of this magnitude. For instance, in Ref. [17] the maximum velocity reported is 0.43 m/s at 30 Hz, while in the data of the present paper, for a frequency of 30 kHz the maximum velocity was almost the same (0.49 m/s). However, the accelerations are quite different; 81.7 m/s2 for 30 Hz, and 9571 m/s2 for 30 kHz. As frequency increases, the slope of each curve decreases, showing the relationship between the contact angle and the vibration amplitude. This shows that, predictably, the wettability increases with increasing amplitude of vibration for the system studied. This does not allow making a theoretical model of the phenomena because, besides the usefulness of such a curves, the slope of the vibration amplitude curves has not meaning from dynamic or energy theories.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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cSL ¼ jcLG cSG j
ð3Þ
and Young’s equation (1) it is easy to obtain the relationship
cos h ¼ 1 þ 2
cSG cLG
ð4Þ
replacing the value of liquid surface free energy, cLG ¼ 0; 0720½J=m2 and the contact angle for the system at rest, hSessile drop ¼ 1:18297½rad, Eq. (4) gives for cSG the value:
cSG ¼ 0; 0496½J=m2 Then, if we assume that the mechanical vibrations produces an ‘‘apparent” effect on the surface tension cLG only, it is possible to calculate the new value (cLG ) for each contact angle measured and plot the evolution of this parameter as a function of the vibration speed. Then cLG has the form
cLG ¼
2 0; 0496 ½J=m2 cos h þ 1
ð5Þ
Fig. 11 shows, for the experimental system described and for all vibration frequencies measured in this research, the evolution of the apparent surface tension with peak speed. The behavior of this curve, in Fig. 11, shows a clear trend, independent of the vibration frequency. Due to the large data dispersion it is difficult to define a functional relationship between the variables, although from Fig. 11 a decreasing dependence of the surface tension of this liquid on the velocity amplitude of ultrasonic vibration can be established. Finally, a simple calculation considering the energy present in the waveguide and the transmission coefficient of acoustic energy from the titanium to the water shows that the energy available for the process is thousands times higher than necessary to produce the wettability effects reported in this paper.
80 75
Liquid Surface Tension (mJ/m^2)
The wettability behavior is represented by the slope and intercept of a straight line plotted with the acquired data. The intercept is the contact angle for a drop at rest and the slope shows the change under different vibration velocities. To avoid hysteresis problems in the measurements, the amplitude increase during the experiments was monotonic. The obtained relationships show that the wettability can be described as an energy problem, because the data related to this magnitude can be interpreted more easily and straightforwardly than the data related to acceleration. If the more important mechanism of wettability is dynamic, the behavior can change abruptly when the g value is overcome. However, we reached several thousand g without a detectable effect. This proposes a fascinating problem to study the balance of energy supplied to the drop by the vibrations; of course the problem has a complex dynamics because in a first stage the energy was communicated to the liquid and then, after this transient time interval that can be estimated at about 0.7 ls, the energy from the surface is radiated by the drop. In this problem the energy balance can be calculated by determining the exact shape of the drop, calculating the potential energy content, and comparing with the initial energy. Afterwards the differences in energy can be compared with the values obtained from the Young and Wenzel equation, producing an advance in the vibratory wettability theory. Our present experimental sept-up does not allow making such a determination, and the problem will be tackled in coming research. On the other hand, if we consider some approximations, it is possible to calculate the surface free energy in the liquid for each vibrational state. Considering the Antonow relationship [27]:
70 65 60 55
6[kHz] 11[kHz] 17[kHz] 22[kHz] 25[kHz] 30[kHz] 38[kHz]
50 45 40 35 30 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Peak Speed (m/s) Fig. 11. Surface tension of the water vs. peak speed for different frequencies.
5. Conclusions It was confirmed that an increase in the wettability of a surface occurs when it is activated by mechanical vibrations at low ultrasonic frequencies. Interestingly, the improvement in the wettability seems to be independent of the exciting frequency. An empirical relationship is obtained between the growth of the wettability for a vibrating surface and the velocity amplitude of the vibration (Eq. (2)). The results reported in this paper may lead to the improvement of important industrial methods like those reported in [1], because the curves obtained can be used to choose the working frequencies for industrial process in which one can avoid some negative effects of large vibration amplitudes, for instance. Acknowledgements This research was financially supported by CONICYT – Chile under FONDEF Project D09I1235. References [1] L. Liu, Y.D. Huang, Z.Q. Zhang, X.B. Yang, Effect of Ultrasound on Wettability Between Aramid Fibers and Epoxy Resin, Wiley InterScience, 2005, http://dx. doi.org/10.1002/app.22859. [2] George B. Sigal, Milan Mrksich, George M. Whitesides, Effects of surface wettability on the adsorption of proteins and detergents, J. Am. Chem. Soc. 120 (1998) 3464–3473. [3] Yuan Li, Zhaozhu Zhang, Xiaotao Zhu, Xuehu Men, Bo Ge, Xiaoyan Zhou, Fabrication of a superhydrophobic coating with high adhesive effect to substrates and tunable wettability, Appl. Surf. Sci. 328 (2015) 475–481. [4] Xiaming Luo, Limin He, Hongping Wang, Haipeng Yan, Yahua Qin, An experimental study on the motion of water droplets in oil under ultrasonic irradiation, Ultrason. Sonochem. 28 (2016) 110–117. [5] C.W. Extrand, Contact angles and hysteresis on surfaces with chemically heterogeneous islands, Langmuir 19 (2003) 3793–3796. [6] Lichao Gao, Thomas J. McCarthy, How Wenzel and Cassie were wrong, Langmuir 23 (7) (2007) 3762–3765. [7] R.N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28 (1936) 988. [8] A.B.D. Cassie, S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40 (1944) 546–551. [9] Elias I. Franses, Osman A. Basaran, Chien-Hsiang Chang, Techniques to measure dynamic surface tension, in: Colloid Interface Sci. 1 (1996) 296–303. [10] A.B.D. Cassie, Contact angles, Discuss. Faraday Soc. 3 (1948). [11] Thomas. Young, An essay on the cohesion of fluids, Phil. Trans. R. Soc. Lond. 95 (1805) 65–87. [12] H. Erbil Yildrim, The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: a review, Surf. Sci. Rep. 69 (2014) 325–365.
Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011
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Please cite this article in press as: R. Galleguillos-Silva et al., Wettability of a surface subjected to high frequency mechanical vibrations, Ultrason. Sonochem. (2016), http://dx.doi.org/10.1016/j.ultsonch.2016.09.011