Observation of Wetting Behavior with Ultralow Contact Angle by a Total Reflection and Interference Fringe Method

In order to study the wetting behavior of a liquid film on a surface with ultra-low contact angle, the interference fringe method with oblique upward laser is developed. This method allows to detect the position of contact line precisely and observe the surface profile of very thin film. The contact angle measurement is verified within from 0.007 ° to 3 ° . The wetting behavior of silicone oil droplet on a glass substrate is observed. The wetting process can be distinguished with three stages, such as advancing, stable and receding stage. In the stable stage, there are two angles near the contact line. And the two angles have opposite variations in trend. It can be seen that there are some reciprocating changes in the two angles and the thickness of the liquid film near the contact line during the stable stage, like the edge of the surf.


INTRODUCTION
When a droplet is placed on a substrate, wetting behavior will occur.No matter in natural systems or man-made systems, wetting behavior is important in large scale and small scale.For example, in oil recovery, 1 coating, 2 friction, 3 , 4 printed electronics 5 and printing, 6 , 7 hydrophobicity/oleophobicity and hydrophilicity/oleophilicity play significant roles.The superhydrophilicity is desirable for self-cleaning and antireflective coatings applied in glasses, flexible electronics, and solar cells protective panels. 8,9In particular, in the printed electronics technology, high-definition thin film patterns such as semiconductors and metals are formed using printing technology for drawing characters and photographs, and these are combined to manufacture electronic devices, and in the process it requires ink droplets mixed with other materials.But there are some unclear problems on the thin film growth occurs near the surface of the ink droplet.And it is also a subject to be solved that whether such thin film growth is possible for various ink combinations.So that, measurement and observation for the wettability and wetting behavior of the inks which have super-hydrophilicity/super-oleophilicity is necessary.Since the tendency for the liquid to spread has relation to contact angle.Hence, the contact angle is a useful measure of wettability. 10The contact angle located at contact line (C.L.), is the angle formed by the liquid-gas interface and the solid or immiscible liquid surface. 11The C.L., defined to be the locus of points that are simultaneously in contact with the gas, liquid and solid phases. 12ere are some methods applied to measure the contact angle.One of the most common methods is the side view method. 13 -16This method can be used to measure the contact angle with an accuracy ±1°~2°, 17 however, it is difficult to determine the position of the C.L. precisely, especially in super-hydrophilic/super-oleophilic surface with very small contact angle.For measuring small contact angles, the reflection of a laser beam method can be used for measuring contact angle θ>4° with an accuracy of ±0.5°, 18 and the interferential reflection contrast microscopy (IRCM) method can be used for measuring contact angle 1°<θ<4° with an accuracy of ±0.01°. 19IRCM is known as a fringe method.With the fringe method, the contact angle and surface profiles of alcohol droplets 20,21 , silicone oil droplets 22 and water droplets 23 can be measured.
When the thickness of the film is tens micrometer or even nanometer, the Brewster angle microscope can be used to observe it. 24,25Contact angle and the C.L. can also be observed simultaneously.But there is a problem when the liquid is located between two planes that have a narrow gap or when an object on the liquid, 15,25 observation cannot be performed because the light for interfering is blocked.Although the film trapping technique (FTT) can be used to measure the contact angle when micrometer particles on the liquid, the measurement accuracy of FTT is ±2°~5°, 26 which is obviously difficult to measure the small contact angle on superhydrophilic/super-oleophilic surfaces.In our experiment, the fringe method with oblique upward laser is developed.The contact angle and surface profile could be evaluated by observing interference fringes.At the same time, the C.L. can also be determined.

EXPERIMENTAL SECTION
Experimental principle.In this experiment, the laser enters from bottom to the observation plane.By setting the incident angle that yields total reflection at solid-gas interface and partial refection at solid-liquid interface, the wetting and non-wetting area can be distinguished clearly.
So that, the C.L. can be determined.And incident laser which reflected at liquid-air interface generates an interference fringe pattern which corresponds to the surface profile of the liquid.When a droplet is placed on a glass substrate and forms a liquid film, if only the surface profile of the liquid film near the C.L. is concerned, the curve at the air-liquid interface can be approximated as a straight line.Figure 1 schematically shows the profile of liquid film near the C.L. on the glass substrate, for which the contact angle is .Light  1 enters and refracts at point  1 on the liquid-glass interface with incident angle   and penetrates into the liquid, and then reflects at point  1 on the air-liquid interface, finally, refracts at point  1 on the liquid-glass interface.Coherent light  3 intersects light  1 at point  1 .The point  on light  1 and point  1 on light  3 have same phase. 1 +  1  1 =  1 is the optical path difference between reflected light of  1 and light  3 at point  1 .When the phase difference between the lights is an even multiple of π, constructive interference occurs, and the intensity of the interferogram is strong (light fringe).
Similarly, when the phase difference is an odd multiple of π, destructive interference occurs, and the intensity of the interferogram is weak (dark fringe). 27The optical path difference of one wavelength corresponds to one phase difference of 2π.
The condition of first dark fringe is: phase difference = π,  1 = .Where  is the wavelength of light in liquid.Similarly,  2 is the optical path difference corresponding to the second dark fringe, then the difference between  1 and  2 is . is the distance between the two adjacent dark fringes.
(the distance between two adjacent light fringes also equals to , and here we just use dark fringes.)An equation about contact angle  and  can be derived: With eq (1), the contact angle  can be calculated.When calculating the contact angle at left side of the droplet (as shown in Figure 2), the upper "+" of plus-minus sign in eq (1) is used.Images including interference fringes were taken by the camera.
Facilities and materials.The schematic diagram of experiment apparatus is shown in Figure 2.
According to the technical data, the refractive index of silicone oil is 1.382 (25℃) 28 .The silicone oil droplet has a volume of 1μL, a density of  = 818kg m −3 , a surface tension of  = 16.9mNm −1 and a kinematic viscosity of  = 1mm 2 s −1 (25℃) 28 .The silicone oil droplet is placed on a glass substrate (MATSUNAMI MAS-GP S9902) with surface roughness  = 0.006μm by a micropipette (NICHIRYO Nichipet EX 0.5-10μL).The glass substrate is set on the dove prism (Thorlabs PS995 N-BK7).To eliminate the effect of the gap between the glass substrate and the dove prism, the gap is filled with cedar oil (FUJIFILM Wako chemicals 8000-27-9), which has an almost same refractive index with glass. 29mera (Nikon Nikon1V3 18.39million pixels, CMOS captures images in 24-bit RGB format with resolution 2.5μm/pixel) observes the interference fringes from one side of the dove prism.
The laser (Thorlabs HNL100L-JP, wavelength: 632.8nm) is set on the other side.Verification experiment.In order to verify the correctness of eq (1), a verification experiment was performed.The schematic diagram of verification experiment apparatus is shown in Figure 3.
In this experiment, contact angle  equals the angle of inclination of the glass plate.The length of horizontal side of contact angle  is L and the length of vertical side which opposites to contact angle  is H. Contact angle  can be calculated with L and H, easily.The glass plate is used as the hypotenuse of a triangle, and metal alloy cantilever is used to up and down along the vertical line to tilt the glass plate.Water is injected between the glass plate and the glass substrate.The glass substrate was placed on the dove prism so that the angle could be changed from 0 °.
In order to control the contact angle , a micro-movement stage (Sigmakoki TSD-603) with an adjustment knob is used.When the knob rotates one turn, it moves up or down by 0.5 mm.There are 50 marks on one turn of the knob, and two rounds are 1 mm, hence, the adjustment accuracy of the stage is under 0.01 mm.When the contact angle is bigger than 3 °, the interference fringe becomes blurred and cannot be distinguished.
Turn the knob to make the metal alloy cantilever rise at 0.05mm every time.During this process, images of fringes are taken by the camera.When the contact angle was located on the left side and right side, the experiment was performed 4 times respectively.The experimental result is shown in Figure 4.The measured angle from the interference method is in good agreement with the set angle.An obvious trend can be seen: as the contact angle becomes larger, the error becomes larger.
According the results of eight times' experiments, the minimum measurable angle is 0.007°.When the contact angle is between 0.5° and 3°, the error percentage is ±6%.From 0.5° to 0.2°, there is a linear increase in the error percentage from ±6% to ±10%.And the error percentage from 0.2° to 0.007° is ±10%.Thus, it is confirmed that the equation and observation method of this experiment can be used to measure the contact angle when the contact angle is smaller than 3°.

Calculation of the surface profile.
There are some reflection points which are corresponding to interference fringes, on the air-liquid interface.Before calculating the surface profile of a liquid, the horizontal and vertical positions of the reflection points need to be calculated first.Then connect these reflection points with curves to get the surface profile of the liquid.In the verification experiment, because the surface of the inclined glass plate is a plane, the angles corresponding to all interference fringes are the same.It is easy to calculate all the horizontal and vertical positions of the reflection points without a large cumulative error.However, the surface profile of the liquid film is not a plane, as shown in Figure 5.The tangent line at point  1 is  1  1 and the tangent line at point  2 is  2  2 , and the inclination angles are  1 and  2 , respectively.The angle between the reflected light  2  2 and substrate  2 is  2 =  − 2 2 .At this moment, if the angle  1 and the height ℎ 1 of the point  1 are used to calculate the height ℎ 2 of point  2 , the calculated height will be the height of  2 ′ .As shown in Figure 5, the point  2 ′ is higher than point  2 .If the subsequent points are also calculated accordingly, the final calculated result is bound to a large error.To reduce this cumulative error, we connect points  1 and  2 to form a line segment  1  2 . 1  is its extension line, and angle  12 is its inclination angle.
If it is assumed that the curve between point  1 and point  2 is part of a circle, then  12 = ( 1 +  2 ) 2 ⁄ .Similarly, the inclination angles of the next segments can be obtained by the same method.With these corrected inclination angles, the horizontal and vertical positions of the reflection points at the air-liquid interface can be calculated.
is the distance between the two adjacent dark fringes, and  is the wavelength of laser in the liquid.From With eq (2) and ( 3), an equation about  12 and  can be derived: In eq (4) and ( 5), when calculating the angles at left side of the liquid film,  1 =  − 2 1 ,  2 =  − 2 2 , and the upper "+" before cot  2 and ℎ 1 cot  1 are used.Convergence calculation is performed by using eq (5) with a calculation accuracy of 1 1000 ⁄ of , and  12 can be obtained.
And the angles for next segments can be obtained in the same manner.Then we can calculate all the horizontal and vertical positions of the reflection points.
Since the interference of light requires at least one wavelength in optical path difference, there is a minimum film thickness that can be measurable.The minimum measurable thickness changes in the range of 200 nm to 600 nm according to the incident angle   (as shown in Figure 1).

Experiment procedures.
The silicone oil is deposited on the horizontal surface of glass substrate by the micropipette through a needle and then forms a liquid film immediately.To reduce the impact of the droplet from the tip of the micropipette to the glass substrate, the tip of the micropipette is in contact with the glass substrate when the droplet is placed.Experiments were performed under 18±0.5℃room temperature and 46%±2% of relative humidity.The capillary length under this condition is   = 1.45mm.
The material of dove prism and glass substrate is BK7, and the refractive index of BK7 is 1.517.
From Snell's law, we can know that the ratio of phase velocities in two media is equal to ratio of sine of incident angle   in one media and sine of refraction angle   in the other media. 30So the critical angle of total reflection between glass substrate and air is 41.2° and the critical angle of total reflection between glass substrate and silicone oil is 65.6°.The middle value of the two critical angles is 53.5°.Taking liquids with higher refractive index into account, the incident angle   is set between 48.3° and 53.5°, in which the reflection of non-wetting area is total reflection, and the reflection of wetting area is partial reflection.In this experiment, the incident angle   is 50.3°.
Before each new experiment, the glass substrate is replaced with a new one.Under the same conditions, the experiment was performed five times.The results of these five experiments showed the similar trend.In addition, we also used acetone-cleaned glass plates for experiments, and the experimental results are in good agreement with the results of using new glass plates.The treatment of the acetone-cleaned glass plate is as follows: the glass substrate is put inside an ultrasonic washing machine in purified water to eliminate dusts and fats on the surface of the glass substrate for 10min, then, the glass substrate is put in acetone and washed by the ultrasonic washing machine for 10min to eliminate tiny contamination.Then the glass substrate is washed by using distilled water to eliminate acetone that is remained on the surface.Finally, the clean glass substrate is subsequently dried in a vacuum over at 70℃ for 30min, at the end of which the glass substrate is allowed to cool under vacuum.
During the wetting process, the C.L. and the interference fringes formed by the surface shape of the liquid film are recorded by the camera with a frame rate of 30 f.p.s..When observing the wetting behavior of silicone oil, the observed spreading time of the liquid is greater than 100 s.The blue curve indicates the brightness of the reflected light with the droplet.In Figure 6 (c), the black curve indicates the calculated surface profile of the droplet, and the red dotted rectangular part is an illustration of CA a and CA n .

RESULTS AND DISCUSSION
The wetting experiment of silicone oil droplet is observed by our interference fringe method.
Figure 6 shows the typical interference fringe, brightness curve and calculated surface profile of the liquid film.(a), when reading the brightness along the green line, if the reading width is only 1 pixel, there will be a lot of noise on the peak value of the read brightness.Adjust the reading width to get the spatial average with 20 pixels (50 μm), in which condition, there will be much less noise while the brightness value can also be read clearly.However, it is still impossible to easily determine the specific location of the brightness peak.Since the distance between adjacent dark fringes is longer than 40 μm, to reduce noise, we choose a low-pass filter to filter the wavelength which is shorter than 40 μm.According to the processed graphics, the brightness peak values can be found quickly, thereby the  can be measured.With , the surface profile of the liquid film can be calculated by using eq (5) (as shown in Figure 6 (c)).Figure 7 shows the surface profiles which are calculated by this method at four moments during the wetting process.According to the surface tension, the curvature of a part of the surface profile can be approximated as an arc.Take two points which are closest to the center on the calculated profiles of left and right side and take another point which is near one of the two points to determine a circle.The same operation is repeated ten times to obtain ten circles, and the radii of these ten circles are averaged to obtain the radius of the fitted circle.In Figure 7, the dashed lines represent parts of the fitted circles.The thickest part of the liquid film is around 20μm.With the passage of time, the wetting diameter is constantly changing.
At the same time, the thickness of the liquid film is getting thinner and the total volume continues decreasing due to evaporation.The volume of the liquid film through the obtained surface profile can be calculated, thereby the average evaporation rate can be obtained.In this experiment, the calculated average evaporation rate of the silicone oil is 1.44 × 10 −5 μL/(s • mm 2 ).By observing the wetting process, around the C.L., different area has different trend that is found.
The angle between the first fringe and C.L. has some relatively large reciprocating changes, while the angle between the first fringe and the third fringe has some relatively small reciprocating changes.The third fringe to the forth fringe or to the further fringe that approach to the center of the film, the angle hardly has reciprocating changes.In the experiment, when measuring the contact angle, there are two angles around the C.L. can be used to characterize the process of wetting.In this study, CA a represents the angle between the first fringe and C.L., and CA n represents the angle between the first fringe and the third fringe.As shown in Figure 6 (c), in the same cross section, connect the point of the C.L. and the reflection point of the first fringe to form a line segment.The CA a is the inclination angle of this line segment.From the geometric relationship about the spacing between the C.L. and the first fringe (  ) and CA a in Figure 6 (c), we can know that   and CA a are negatively correlated.Figure 8 indicates the relationship about position of the C.L. and the first fringe, the CA a and the CA n in the wetting process.However, as For the reciprocating changes of contact angles, evaporation is an important factor that has to be considered.From the profiles shown in Figure 7, the liquid has been evaporating.Since the liquid film near the C.L. is very thin, a small amount of evaporation will affect the contact angle.
As the liquid film becomes thinner, the CA a also becomes smaller.According to Young's equation, when the contact angle of a liquid initially in equilibrium becomes smaller, the combined force of the liquid surface tension and the solid-liquid interfacial tension will be greater than the solid-gas interfacial tension.However, since the CA n becomes bigger, the Laplace pressure at the reflective surface of the first fringe gets bigger.When the C.L. tends to move to return to the equilibrium state, the liquid at the reflective surface of the first fringe will also tend to flow to return to the equilibrium state.But due to the difference in liquidity, the liquid at the reflective surface of the first fringe completed the flow faster.The repetition of this process forms the phenomenon of reciprocating changes in the contact angles.to 7 in the stable stage (as shown in Figure 8 and Figure 9).It can be seen that the reciprocating changes in the two contact angles and the thickness of the liquid film near the C.L., like the edge of the surf.The moment of 8 is the end of the stable stage, as shown in Figure 9 (a), and it is also the end of the reciprocating changes.
According to the experiments we have done, under the same experimental conditions and using the glass substrate of the same product, decane and octane also show similar fluctuations to the silicone oil in contact angles.
In addition, the presence of the very thin liquid film near the C.L. reminds us of the precursor film.2][33] And the inflection point can be found at the junction of the precursor film region and the outer macroscopic region to determine the small apparent contact angles. 34In this experiment, the thickness of the liquid film on the μm scale was observed, and the length of the part whose thickness was less than a few μm was not related to time.Because the thickness of the liquid film is within about 20 μm, the liquid film does not show an obvious inflection point to determine the apparent contact angle.The information

CONCLUSIONS
In order to measure the contact angle and the position of the contact line of the liquid film simultaneously, an interference fringe method with oblique upward laser is developed.In the wetting experiment, by setting the incident angle of laser, so that the non-wetting part has total reflection and wetting part has partial reflection.As a result, the position of the contact line can be determined.The contact angles and profile of liquid film can be calculated by the derived equations with the spacing of the fringes.The equation is confirmed by verification experiment.And the verified minimum measurable angle is 0.007°.When the contact angle is between 0.007° and 3°, this method can be accurately used for measurement.
The wetting behavior of a liquid film on a surface with ultra-low contact angle is observed by this interference fringe method.According to the results of the wetting experiment, position of the contact line, the surface profile of the liquid film and the contact angles can be observed simultaneously.While, when measuring the contact angle, two contact angles are measured.And the two contact angles have opposite trends.In addition, there are three stages occurred in the wetting process.They are advancing, stable and receding stage.In the first stage, the position of the contact line continues advancing.And both contact angles have a monotonous change.In the second stage, the position of the contact line does not change significantly, while there are some fluctuations in the   .That is caused by reciprocating changes in the CA a .In the third stage, the position of the contact line is receding and the contact angles have no reciprocating changes.The advancing contact angle is often larger than the receding contact angle in the wetting process. 11,35 this experiment, the CA a is constantly increasing in the advancing stage, however remains unchanged in the receding stage, and the CA a in the advancing stage is larger than it in the receding stage.For the CA n , in the first half of the receding stage, the CA n keeps unchanged, and in the latter half of the stage, the CA n rapidly decreases.And the CA n in the advancing stage is smaller than it in the receding stage.

Figure 1 .
Figure 1.Schematic diagram of relationship between spacing of interference fringe and contact

Figure 2 .
Figure 2. Schematic diagram of experimental apparatus.The experimental device is located on

Figure 3 .
Figure 3. Schematic diagram of experimental apparatus of verification.The micro-movement

Figure 4 .
Figure 4. Result of verification experiment.In this figure, the red dots indicate the measured value

Figure 5 .
Figure 5. Image of the surface profile of a liquid film.Line  1  1 is a tangent line passing through point  1 , line  2  2 is a tangent line passing through point  2 , and the corresponding inclination angles of these two lines are  1 and  2 .And  12 is the inclination angle of line  1  2 .The surface profile of the liquid is composed of line segments such as  1  2 and  2  3 .

Figure 6 .
Figure 6.A snapshot of interference fringes of the liquid film formed by silicone oil droplet in the

Figure 6 (
b) shows the brightness-position curve.Due to the total reflection area and partial reflection area, it is easy to determine the position of the C.L. from the brightnessposition curve.The first fringe is the first dark fringe adjacent to the C.L..As shown in Figure6

Figure 7 .
Figure 7. Surface profiles of the liquid film at four moments.In this figure, the solid line parts are

Figure 8 (
Figure 8 (b) and (c) indicate, the CA a and the CA n show opposite trends.As Figure 8 (a) shows,

Figure 8 .
Figure 8. Relationship about position of the C.L. and the first fringe, the CA a and the CA n .In

Figure 10 .
Figure 10.Partial enlarged drawing of the profiles at the moments of 4 to 6 near the C.L.. Profile