ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Regular Article
Effect of Viscosity and Surface Roughness on Improvement of Solid-liquid Wettability by Ultrasonic Vibration
Keiji Okumura Yuya TanakaKazuhiko Iwai
Author information
JOURNAL OPEN ACCESS FULL-TEXT HTML

2022 Volume 62 Issue 11 Pages 2217-2224

Details
Abstract

In order to investigate the influence of liquid viscosity and surface roughness of the substrate on the improvement of wettability by ultrasonic vibration, a liquid droplet was put on a Langevin type vibrator, and ultrasonic vibration was applied to observe the change of the droplet shape. The droplets were deformed by the application of ultrasonic vibration, and the contact angle between solid and liquid was reduced, so that the wettability was improved. It was considered that the ultrasonic radiation pressure acting inside the droplet had an effect on the deformation of the droplet, and the value of the radiation pressure was estimated based on Laplace’s equation. It was confirmed that when the viscosity of the liquid was high, the change in the shape of the droplet was prevented by an increase in the shear stress for deformation. Regarding the surface roughness, it was found that the pinning effect made it difficult to reduce the contact angle. When the ultrasonic vibration was stopped, the shape of the droplet recovered to some extent before the ultrasonic vibration, but did not completely return to the original shape.

1. Introduction

In the steel making process, a high-temperature metal melt is charged into a refractory container and refined. In general, the molten metal has poor wettability with refractories, which is different from the wet model system using water and refractories at room temperature. Therefore, in order to apply the model experimental system at room temperature to a high temperature system using molten metal, it is necessary to carry out the experiment in consideration of wettability. For example, in the smelting process, a gas injection process is performed to promote the refining reaction, but injection nozzles, blowing lances and porous plugs used are made of refractories and have poor wettability with molten metal. It is known that when gas is injected under poor wettability conditions, the generated bubble size becomes larger than under good wettability conditions.1,2,3) This is due to the difference in the behavior of bubble formation behavior at the gas inlet. In the case of a nozzle, if the wettability is good, bubbles specified by the nozzle inner diameter are generated at the nozzle outlet. On the other hand, if the wettability is poor, bubbles specified by the outer diameter of the nozzle are formed. In a porous plug with a structure that has multiple fine inlets, the generated bubbles at the porous plug coalesce each other, and the bubbles become very large.4,5)

J. Park et al.6) investigated initial wetting phenomena and spreading property of CaO–SiO2 slag on MgO substrate using sessile drop technique. They found that the initial wetting is controlled by viscous friction. S. Ogyu et al.7) measured the sliding angle of water droplet and the advancing and receding contact angles on the coke surface. They found that the fine irregularity and the large pores on the coke surface have different influences on the sliding angle of the droplet. T. Furukawa et al.8) measured the contact angle and interfacial energy between molten Fe and Fe–Cr–Ni alloy, and non-metallic inclusion-type oxide substrates at 1873 K. They found that the interfacial tension and energy between molten Fe–Cr–Ni alloy and the substrates were lower than those between molten Fe and the substrates. N. Saito et al.9) investigated the apparent viscosity of suspensions of polyethylene beads in a matrix of silicone oil or aqueous glycerol at room temperature. They proposed the viscosity models and found that the trend of increasing viscosity of the molten slag suspensions with dispersed CaO and MgO particles was similar to that of the room-temperature suspensions.

Other studies have been conducted on the application of ultrasound to the production of metal-based composite materials. It is known that the wettability of molten metal matrix materials and reinforcing materials can be improved by applying ultrasonic vibration.10,11,12,13,14) In addition, R. Galleguillos-Silva et al.15) investigated the change in wettability when ultrasonic vibration was applied to water droplets on a smooth titanium substrate. As a result, it was clarified that the wettability depends on the vibration velocity and not on the frequency. However, their experiments were conducted under wetting conditions. Therefore, the improvement of wettability by ultrasonic wave vibration under non-wetting conditions has not been clarified.

The viscosity and surface tension of molten metal are higher than those of water. Hence it is considered that the difference in their physical properties may affect the improvement of wettability by ultrasonic vibration. In conventional studies, the droplets have usually been placed on the smooth surface of the substrate. It is also necessary to investigate the effect of surface roughness on the improving wettability. Consequently, in this study, we used water and glycerin as liquids to clarify the effect of viscosity and abrasive paper to find the effect of surface roughness. The effects of viscosity and surface roughness on the improvement of wettability under poor wettability conditions were investigated.

2. Experiment

2.1. Effect of Liquid Viscosity

Figure 1 shows the schematic illustration of the experimental equipment. In this experiment, a wettability improvement experiment was conducted by ultrasonic vibration using the sessile drop method. The sine wave signal generated by the function generator was amplified by a high-speed power amplifier and then applied to the ultrasonic transducer. The ultrasonic transducer used was a Langevin type with a nominal resonance frequency of 20 kHz. In addition, the vibration amplitude of the ultrasound transducer was measured using a laser displacement meter. Water and glycerin were used as liquids. The viscosity of each liquid is about 1.0 mPa·s for water and about 1500 mPa·s for glycerin. The volume of the droplet was 0.01 ml for all liquids. The surface of the vibrator made of aluminum was coated with a silica water repellent in advance. The vibration amplitude of the vibrator was changed by changing the applied voltage to the vibrator. If the applied voltage is too high, the droplets will be atomized, so the measurement was performed within the range where atomization was not performed. First, a droplet with a volume of 0.01 ml was dropped onto the vibrator with a syringe. The shape of the droplets before and during the vibration was recorded with a video camera. Since the shape of the droplet changed immediately after the start of vibration, the contact angle was measured from the image 10 s after the start of vibration. The measurement was performed 3 times under the same conditions, and the reproducibility was confirmed.

Fig. 1.

Schematic diagram of experimental equipment. (Online version in color.)

2.2. Effect of Vibrating Surface Roughness

The vibrating surface roughness was changed by attaching polishing paper to the vibrator. The smooth surface was the vibrator surface to which polishing paper was not attached. The polishing paper, P120, P320, and P1500 were used. The surface roughness decreases in the order of P120, P320 and P1500. The average particle size of the abrasive on each polishing paper is 90 μm, 46.2 μm, and 12.6 μm, respectively. The polishing paper is coated with a silica water repellent in advance. The vibration amplitude of the vibrator was changed by changing the applied voltage to the vibrator. The liquid used was 0.01 ml each of water and glycerin. The shape of the droplets before and during the vibration was recorded with a video camera. Since the shape of the droplet changed immediately after the start of vibration, the contact angle was measured from the image 10 s after the start of vibration. The measurement was performed 3 times under the same conditions, and the reproducibility was confirmed.

2.3. Droplet Shape after Ultrasonic Vibration

The liquid used was 0.01 ml each of water and glycerin. The vibration amplitude of the vibrator was changed by changing the applied voltage to the vibrator. Since the silica water repellent is peeled off when ultrasonic vibration is applied for a long time, a Teflon tape is used instead. A Teflon tape was attached to the vibrator surface and a droplet with a volume of 0.01 ml was dropped onto the vibrator with a syringe. The experimental procedure is the same as in 2.1 and 2.2, but after applying ultrasonic vibration for about 30 s, the state of the droplets after the vibration was stopped was photographed.

3. Results and Discussions

3.1. Effect of Liquid Viscosity

Figure 2 shows droplets whose shape has changed by applying ultrasonic vibration. The droplets in the left images are water and the images on the right are glycerin. The upper images are droplets before ultrasonic vibration, and the lower images are those during ultrasonic vibration. Both vibration amplitudes were 5.63 μm. From Fig. 2, it was found that the shape of the droplet was changed by the ultrasonic vibration, and it was confirmed that the ultrasonic vibration has the effect of improving the wettability. In the case of water, the inside of the droplet became cloudy.

Fig. 2.

Change of droplet shape under ultrasonic vibration ((a), (c): before US, (b), (d): during US). (Online version in color.)

In this paper, the contact angle was used to evaluate the wettability. If the contact angle is smaller than 90°, it indicates that the wettability is good, and if the contact angle is 90° or more, it indicates that the wettability is poor. The analysis software of Image J was used to measure the contact angle of the droplet images.

The contact angles of all experiments are shown in Fig. 3. When the amplitude due to ultrasonic vibration was small, there was not much difference in the results due to viscosity, but as the amplitude increased, the difference due to viscosity appeared. It was found that the contact angle of the high-viscosity liquid is less likely to decrease than that of the low-viscosity liquid. K. Brabec and V. Mornstein16) showed that the higher the kinematic viscosity of the liquid, the higher the cavitation threshold. In addition, it was confirmed that the inside of the droplet became cloudy when the amplitude was large in the low-viscosity liquid, but not in the high-viscosity liquid.

Fig. 3.

Relationship between contact angle and vibration amplitude.

When the amplitude is large, the contact angle of the high-viscosity liquid is less likely to decrease than that of the low-viscosity liquid. This may be due to the relationship between the shear stress and the viscosity. Shear stress is expressed by Newton’s law, and since a high-viscosity liquid has a large viscosity coefficient, the magnitude of shear stress also increases. Therefore, it can be said that the high-viscosity liquid has a large shear stress required to change the shape of the droplet. The shape of the high-viscosity droplet is unlikely to change even when ultrasonic vibration is applied.

It is also considered that the generation of cavitation bubbles in the droplet by ultrasonic vibration also affects the shape of the droplets. This is because the microjet generated when the cavitation bubble is destroyed and the flow inside the droplet due to the movement of the cavitation bubble are related to the change in the shape of the droplet. Generally, cavitation bubbles are more likely to be generated as the saturated vapor pressure of a liquid is higher, but cavitation bubbles are less likely to be generated in a highly viscous liquid because the saturated vapor pressure is lower. The white turbidity generated inside the droplet during ultrasonic vibration during the experiment with water is thought to be due to cavitation bubbles. In this way, it is considered that the presence or absence of cavitation bubble generation also affects the shape change of the droplet. In the present study, the acoustic radiation pressure17) was examined to quantify the intensity of ultrasonic vibration.

Figure 4 shows a droplet on a flat plate placed perpendicular to gravity in the gravitational field. The pressure difference ∆P (Pa) acting on the liquid surface of a liquid having a curved surface represented by the following Laplace’s equation.   

ΔP=σ( 1 R 1 + 1 R 2 ) (1)
Where, σ (N/m) is the surface tension of liquid, R1 (m) and R2 (m) are two principal curvature radii.
Fig. 4.

Illustration of calculation of radiation pressure.

In the (x, z) coordinate system, Laplace’s equation is as follows depending on the balance between gravity and pressure.   

σ( 1 R 1 + 1 R 2 ) =ρg( h-z ) +ΔP (2)
Where, ρ (kg/m3) is the density of liquid, g (m/s) is the gravitational acceleration, and h (m) is the height of the droplet.

P is the pressure difference between the inside and outside of the liquid at the apex of the droplet. It is expressed by the following equation using the principal curvature radius b (m) of the apex.   

ΔP= 2σ b (3)

φ in Fig. 4 is the angle at which the normal passing through an arbitrary point (x, z) of the droplet contour and the central axis of the coordinate axis intersect. It has the following relationship with R2.   

R 2 = x sinφ (4)
Substituting Eqs. (3) and (4) into Eq. (2) and solving for R1 gives the following equation.18)   
R 1 = 1 ρg σ ( h-z ) + 2 b - sinφ x (5)

On the other hand, for a droplet deformed by applying ultrasonic vibration, the pressure difference between the inside and outside of the droplet, ∆P’(Pa), is expressed by the following equation.   

Δ P = 2σ b =ΔP- P s (6)
Where, b′ (m) is the principal curvature radius of the apex and Ps (Pa) is the static pressure due to the radiation pressure. It is assumed that the surface tension σ, which is the physical property value of the liquid, does not change due to ultrasonic vibration. Since the principal curvature radius at the apex of the droplet during ultrasonic application is larger than that before application, the relationship of ∆P′<∆P can be obtained. Therefore, it can be said that the addition of Ps (Ps>0) increases the principal curvature radius of the droplet.

Substituting Eqs. (4) and (6) into Eq. (2) and solving for R1 gives the following equation.   

R 1 = 1 ρg σ ( h-z ) + 2 b - sinφ x + P s σ (7)

The height h of the droplet was measured using the analysis software of Image J for the droplet. The radius of curvature b′ and the static pressure Ps were determined as the values when the shape of the droplet in the experimental result can be reproduced by calculation.

Figure 5 shows an example of the result of reproducing the droplet shape by calculation. From the figure, it can be said that the calculation result of the droplet shape using Eq. (7) can reproduce the experimental result well. Figure 6 shows the relationship between the calculated static pressure Ps by radiation pressure and the vibration amplitude. When the amplitude was 3.0 μm or more, Ps was larger in water than in glycerin. Since Ps increases when the amount of deformation of the droplet is large, it can be said that water is more easily deformed by ultrasonic vibration. This can be seen from the fact that water is more easily deformed because the viscosity of water is smaller than the viscosity of glycerin.

Fig. 5.

Calculation result of droplet shape (water, amplitude: 3.32 μm, Ps=5.28 Pa, droplet bottom width: 2.09 mm, droplet height: 1.52 mm). (Online version in color.)

Fig. 6.

Relationship between radiation pressure and vibration amplitude.

3.2. Effect of Surface Coarseness

Figure 7 shows the photographs of the water and glycerin droplets before and during ultrasonic vibration. The left side shows the water droplet, whereas the right side shows the glycerin droplet. Both are present on a P320 abrasive surface. The amplitude of the ultrasonic vibration was 6.67 μm. The photographs show that the shape of the water and glycerin droplets changed because of the ultrasonic vibration. This confirms that ultrasonic vibration is effective in improving wettability even when the vibration surface is uneven.

Fig. 7.

Change of droplet shape (P320). (a), (c): before US, (b), (d): during US. (Online version in color.)

The contact angles of the droplets are shown in Figs. 8 and 9. The results for water and glycerin are shown in Figs. 8 and 9. It can be seen that the contact angle of the water droplet is less likely to change on the abrasive paper (P320) than on the smooth surface. When observing the roughness of the abrasive paper, the contact angle with P120 barely changed. However, with P320, the contact angle reduced sharply at vibration amplitude of approximately 4.0 μm and tended to be smaller when compared to the droplet on the smooth surface. The contact angle at this amplitude was approximately 90°. With P1500, the contact angle decreased linearly to the right; however, these contact angle values are slightly larger than those for the droplets on the smooth surface are. Similar to water, it can be seen that the contact angles of the glycerin droplets on abrasive paper are less likely to be affected than the droplets on the smooth surface. In other words, the contact angle of the glycerin droplet is less likely to be lower than that for the water droplet. For the glycerin droplet, the contact angle with the smooth surface was the smallest regardless of the vibration amplitude. However, the contact angle with the coarsest surface (P120) sharply decreased at amplitude of approximately 6.0 μm. The contact angle with P320 decreased sharply when the vibration amplitude was between 6.0 and 7.0 μm. Likewise, the contact angle with P1500 decreased sharply between the vibration amplitudes of 4.0 and 5.0 μm. Droplets on high-coarse surfaces tended to have larger contact angles than the droplets on smooth surfaces. One possible reason for this result is the generation of a “pinning,” (i.e., holding) effect at places where surface irregularities act as a barrier to the edge of the droplets spreading in a lateral direction.

Fig. 8.

Relationship between contact angle and vibration amplitude (water).

Fig. 9.

Relationship between contact angle and vibration amplitude (glycerin).

Figure 10 shows a schematic of a droplet on a substrate with high surface roughness. This state is called the Cassie–Baxter state.19,20) In this state, the convex part of the substrate acts as a barrier for the droplet to spread laterally. However, on a substrate with low surface roughness, the convex part does not offer a sufficient barrier to prevent the droplet edge from spreading laterally.

Fig. 10.

Droplet on substrate with high surface roughness before applying ultrasonic vibration (Cassie-Baxter model).

In an experiment conducted on abrasive paper with a large average grain size, the contact angle of the droplets decreased rapidly when the ultrasonic wave vibration amplitude surpassed a certain value. Figure 11 shows that when the ultrasonic vibration amplitude was decreased slightly, the droplet contact angle was smaller than that when the ultrasonic vibration amplitude was decreased rapidly. Further, bubbles were observed at the bottom of the droplet with rapid change in vibration amplitude. This phenomenon is explained in the following.

Fig. 11.

Bubble formation at glycerin droplet bottom under ultrasonic vibration (P320). (Online version in color.)

Figure 10 shows the droplet in a state prior to the application of ultrasonic vibration. The droplet does not completely penetrate the surface irregularities, as it is supported by convex areas. The concave area does not come into contact with the droplet due to the trapping of air in this area. In cases where ultrasonic vibration is not applied, this Cassie–Baxter state of the droplet is in a stable state. Here, when an external force is applied to the system–in this case, an ultrasonic vibration with amplitude of 6.0–7.0 μm–the system shifts to the state shown in Fig. 12. This state is referred to as the Wenzel state.19,20,21) In the Wenzel state, the droplets completely penetrate the surface irregularities. As seen in the experimental results, the air bubbles at the bottom of the droplet are thought have resulted from expelling of the air trapped in the recesses during the Cassie–Baxter state by the liquid. In this state, the substrate and droplet are thought to be wet, and it is considered that when applying the force necessary for the droplet edge to spread laterally over the surface irregularity, the droplet contact angle reduces sharply and the droplet spreads laterally.

Fig. 12.

Droplet on substrate with high surface roughness under ultrasonic vibration.

The contact angle of the water and glycerin droplets decreased sharply when the vibration amplitude was 4.0 and 6.0 μm, respectively. We can explain this result from the change in the apparent contact angle based on Wenzel’s equation,21) which is explained as follows:   

cosφ=rcosθ (8)
Here, φ is the apparent contact angle, θ is the accurate contact angle, and r is the surface area ratio (actual surface area/apparent surface area).

When the accurate contact angle is less than 90°, the droplet resembles the state shown in Fig. 13(a) and the apparent contact angle is larger than the accurate contact angle. If ultrasonic wave vibration is applied, a state similar to that shown in Fig. 13(b) is obtained. In other words, if the contact angle is 90° or less, the apparent contact angle is smaller than the true contact angle, resulting in more wettability. During the experiment, the contact angle showed a rapid decrease, tended to be less than 90°, and became less than that of a droplet on a smooth surface. Based on the above result, when wettability is improved by ultrasonic vibration, the apparent contact angle (θ < 90°) decreased based on Wenzel’s equation.

Fig. 13.

True and apparent contact angles on rough surfaces according to the Wenzel model. (a) θ>90°, (b) θ<90°.

3.3. Droplet Shape after Ultrasonic Wave Vibration

Thus far, reports on wettability improvements by ultrasonic vibration have focused on the droplet shape before and while applying ultrasonic vibration on a smooth surface and have rarely investigated the droplet’s state after ultrasonic vibration. If information regarding the wettability of the liquid after applying ultrasonic vibration can be obtained, there may be potential industrial uses.

Figures 14(a), 14(b), and 14(c) show photographs of droplets taken in an experiment using water. Figures 14(a) and 14(b) show photographs of a droplet before, and during ultrasonic vibration application. Figure 14(c) shows the photograph of a droplet 30 s after the vibration stopped. The amplitude at the time of stopping was 4.96 μm. The photos reveal the changes in the shape of the droplet due to ultrasonic vibration and when the vibration is stopped, the shape of the droplet returns to a near approximation of the original shape prior to ultrasonic vibration application. Before the application of ultrasonic vibration, the contact angle is 105.2°, with a high droplet height and narrow droplet base width. During the application of ultrasonic vibration, the contact angle is reduced to 62.1°, with small droplet height and a wide droplet base. After the application of ultrasonic vibration, the contact angle is 88.3° and the droplet height and base width are closer to the original previbration state. In the sessile drop method, the bottom surface of the droplet spreads on the substrate when the droplet is dropped on the substrate. The contact angle before the ultrasonic vibration application is referred to as the forward contact angle and the contact angle after ultrasonic vibration application is referred to as the backward contact angle.22) It is important to note that the droplet did not completely return to its previbration state even when the ultrasonic vibration was stopped.

Fig. 14.

Change of droplet shape due to ultrasonic vibration. (a) before US, (b) during US, (c) after US (water, vibration amplitude: 4.96 μm). (Online version in color.)

All contact angles observed in the experiments are shown in Figs. 15 and 16. Figure 15 shows the results for water, and Fig. 16 shows the results for glycerin. These photographs show that, in water, the contact angle reduced by ultrasonic vibration does not completely return to the original contact angle value when ultrasonic vibration is stopped, but instead becomes 90°. This tendency was confirmed regardless of the strength of the ultrasonic output. The contact angle of glycerin was also observed to decrease with ultrasonic vibration but remained virtually unchanged even after stopping ultrasonic vibration.

Fig. 15.

Change of contact angle due to ultrasonic vibration (water).

Fig. 16.

Change of contact angle due to ultrasonic vibration (glycerin).

For all experiments, the diameter of the base of the droplet and the rate of change of the droplet height were also calculated. The diameter of the droplet base is shown in Figs. 17 and 18, and Figs. 19 and 20 show the droplet height. For water and glycerin, it can be seen that the base diameter as well as the height of the droplets increases with ultrasonic vibration. When ultrasonic vibration is stopped, the droplet partially returns to the original droplet shape. If water and glycerin are compared, the base diameter and height of the droplets are closer to the previbration state for water. This result is possibly associated with the surface tension and liquid viscosity. The droplet returns to its original shape after ultrasonic vibration is stopped, as the surface tension works to reduce the surface size. The surface tension values of water and glycerin are 72.75 and 63.40 mN/m; thus, water is much more likely to return to its original state. The degree of resistance to shape change is also affected by viscosity and, even after the ultrasonic vibration is stopped, the droplet tries to maintain the shape it had during ultrasonic vibration. The viscosity value of water is approximately 1 mPa·s, whereas that for glycerin is approximately 1500 mPa·s, indicating that glycerin is significantly more viscous. Therefore, during the application of ultrasonic vibration, we can say that glycerin tries harder to maintain its shape than water. From the above, the relationship between surface tension and viscosity is considered to cause a difference in the way the shape of water and glycerin droplets change.

Fig. 17.

Change of droplet bottom width due to ultrasonic vibration (water).

Fig. 18.

Change of droplet bottom width due to ultrasonic vibration (glycerin).

Fig. 19.

Change of droplet height due to ultrasonic vibration (water).

Fig. 20.

Change of droplet height due to ultrasonic vibration (glycerin).

4. Conclusions

Experiments on the improvement of wettability by ultrasonic vibration under various conditions were conducted to propose a process using ultrasonic vibration as a means of improving the wettability between molten metal and refractory materials. The following conclusions were reached using water and glycerin, which have similar surface tensions but significantly different viscosities.

(1) Based on Newton’s equation, high-viscosity liquids are less likely to improve wettability by ultrasonic vibration than low-viscosity liquids because of the high shear stress and less occurrence of cavitation bubbles. The static pressure due to radiation pressure in the droplets was also smaller in the case of high-viscosity liquids than in low-viscosity liquids.

(2) It was found that droplets on surfaces with high surface roughness tended not to improve wettability. However, when high output ultrasonic wave vibration was applied, wettability improved drastically. This is considered to be related to the shift from the Cassie–Baxter state to the Wenzel state.

(3) The droplets of water and glycerin did not completely return to their original state after the application of ultrasonic vibration was stopped. Furthermore, when comparing water and glycerin, water returned more closely to its original shape because water has higher surface tension and lower viscosity.

References
 
© 2022 The Iron and Steel Institute of Japan.

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
feedback
Top