Name: measuring the interaction force between a droplet and a super-hydrophobic substrate by the optical lever method
Uploaded: 2019-06-14T14:00:00
Description: Watch this Scientific Journal Video about Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method at JoVE.com

The authors thank the Tianjin Natural Science Foundation (No. 18JCQNJC04800), Tribology&#160;Science&#160;Fund&#160;of&#160;State&#160;Key&#160;Laboratory&#160;of&#160;Tribology (No. SKLTKF17B18) and National Natural Science Foundation of China (Grant No. 51805367) for their support.

1. Assembly of the SOL calibration system
<ol>
	<li>Assemble the SOL calibration system according to the schematic diagram shown in Figure 2.</li>
	<li>Fix the laser to a support, making the angle between the laser and the horizontal direction be 45&#176;.</li>
	<li>Fix the PSD to another support, making the PSD perpendicular to the laser. Connect the PSD to the data acquisition device and the data acquisition device to the computer. 
	NOTE: These angles are dete...

<ol>
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In this protocol, a measurement system based on optical lever method is assembled and calibrated, which is designed for measuring the interaction force between the droplets and super-hydrophobic substrates. Among the all steps, it is critical to calibrate SOL using electrostatic force. The results of the calibration experiment verify Eq. (8): P(1/Vp1-1/Vp2) is proportional to 2(1/Vs12-1/Vs22) and make it possi...

The contact between a droplet and a super-hydrophobic surface is very common in daily life and industrial production: water droplets sliding from the surface of lotus leaf1,2, and a water strider traveling rapidly over the water3,4,5,6. A super-hydrophobic coating on the exterior surface of a ship can help reduce the corrosion degree of the ship and reduce the resistance of the navigation7,8,9,10. There is great value for industrial production and bionics research in studying the contact process between a droplet and a super-hydrophobic surface.
To observe the spreading process of droplets on a solid surface, Biance used a high-speed camera to photograph the contact process and found that the duration of the inertial regime is mainly fixed by the drop size11. Eddi photographed the contact process between the droplet and the transparent plate from the bottom and side using a high-speed camera, which comprehensively revealed the variation of the contact radius of the viscous droplet with time12. Paulsen combined an electrical method with high-speed camera observation, thus reducing the response time to 10 ns13,14.
Atomic force microscopy (AFM) has also been used to measure the interaction force between the droplet/bubble and solid surfaces. Vakarelski used an AFM cantilever to measure the interaction forces between two small bubbles (approximately 80-140 &#956;m) in aqueous solution during controlled collisions on the scale of micrometers to nanometers15. Shi used a combination of AFM and reflection interference contrast microscopy (RICM) to simultaneously measure the interaction force and the spatiotemporal evolution of the thin water film between an air bubble and mica surfaces of different hydrophobicity16,17.
However, since commercial cantilevers used in AFM are too small, the laser spot irradiated on the cantilever would be submerged by droplets or bubbles. The AFM has difficulties in measuring the interaction force between droplets and droplets/substrates in the air.
In this paper, a measurement system based on an optical lever method is designed to measure the interaction force between droplets and super-hydrophobic substrates. The force sensitivity of the optical lever (SOL) is calibrated by electrostatic force18, and then the interaction forces between droplets and different super-hydrophobic substrates are measured by the measurement system.
The schematic diagram of the measurement system is shown in Figure 1. The laser and position sensitive detector (PSD) constitute the optical lever system. A millimetric silicon cantilever is used as a sensitive component in the system. The substrate is fixed on the nanopositioning z-stage, which can move in vertical direction. When the substrate approaches the droplet, the interaction force causes the cantilever to bend. Thus, the position of the laser spot on PSD will change, and the output voltage of PSD will change. The output voltage of PSD Vp is proportional to the interaction force Fi, as shown in Eq. (1).
<img alt="Equation 1" src="/files/ftp_upload/59539/59539eq1.jpg" /> (1)
In order to acquire the interaction force, SOL must be calibrated first. The electrostatic force is used as the standard force in the calibration of SOL. As shown in Figure 2, the cantilever and the electrode make up a parallel plate capacitor, which could generate electrostatic force in a vertical direction. The electrostatic force Fes is determined by the voltage of the DC power supply Vs, as shown in Eq. (2)19,20,21.
<img alt="Equation 2" src="/files/ftp_upload/59539/59539eq2.jpg" /> (2)
where C is the capacitance of the parallel plate capacitor, z is the displacement of the cantilever free end, and dC/dz is called capacitance gradient. The capacitance could be measured by the capacitance bridge. The mathematical relationship between C and z can be fitted by a quadratic polynomial, as shown in Eq. (3).
<img alt="Equation 3" src="/files/ftp_upload/59539/59539eq3.jpg" /> (3)
where Q, P and CT are the coefficients of the quadratic term, the primary term and the constant term respectively. Therefore, the electrostatic force Fes can be expressed as Eq. (4).
<img alt="Equation 4" src="/files/ftp_upload/59539/59539eq4.jpg" /> (4)
Since the overlap area of two plates of the capacitor is very small, the elastic force acted on the cantilever can be expressed as Eq. (5), according to Hooke&#39;s law:
<img alt="Equation 5" src="/files/ftp_upload/59539/59539eq5.jpg" /> (5)
where k is the stiffness of the cantilever.
When the elastic force and electrostatic force applied on the cantilever are equal (i.e., Fi = Fes), the cantilever is in equilibrium. Eq. (6) can be derived from Eqs. (1), (2) and (5):
<img alt="Equation 6" src="/files/ftp_upload/59539/59539eq6.jpg" /> (6)
In order to reduce the uncertainty of calibration results, a difference method is used to calculate SOL. The results of two experiments are taken as Vs1, Vp1 and Vs2, Vp2, and are substituted into Eq. (6):
<img alt="Equation 7" src="/files/ftp_upload/59539/59539eq7.jpg" /> (7)
Transforming the equations and subtracting the lower equation from the upper equation in Eq. (7), the parameters Q and k are eliminated. Then the calibration formula of SOL is obtained, as shown in Eq. (8):
<img alt="Equation 8" src="/files/ftp_upload/59539/59539eq8.jpg" /> (8)
Performing a series of experiments, the curve is drawn with P(1/Vp1-1/Vp2) as the ordinate and 2(1/Vs12-1/Vs22) as the abscissa. The slope of the curve is SOL.
After obtaining SOL, the electrode will be replaced by different super-hydrophobic substrates. The interaction forces between droplets and super-hydrophobic substrates will be measured by the system shown in Figure 1.

<table>
	<tbody>
		<tr>
			<td>Camera</td>
			<td>Shenzhen Andonstar Tech Co., Ltd</td>
			<td>digital microscope A1</td>
			<td>Frame rate: 30 frames/sec; Focal distance: 5 mm - 30 mm</td>
		</tr>
		<tr>
			<td>Capacitive bridge</td>
			<td>Andeen-Hagerling</td>
			<td>AH2550A</td>
			<td>The capacitive bridge is used to measure the capacitance between the cantilever and the plate electrode.</td>
		</tr>
		<tr>
			<td>Data acquisition device</td>
			<td>National Instruments</td>
			<td>USB-4431</td>
			<td>The data acquisition device is used to read the output voltage data.</td>
		</tr>
		<tr>
			<td>DC power supply</td>
			<td>Keithley</td>
			<td>2410</td>
			<td>Voltage range: &#177;5 &#956;V; Accuracy: 0.012%</td>
		</tr>
		<tr>
			<td>Grid</td>
			<td>Electron Microscopy China</td>
			<td>AGH100, AGH150, AGH300</td>
			<td>The grid fractions of AGH100, AGH150 and AGH300 are 46.18%, 51.39% and 58.79% respectively</td>
		</tr>
		<tr>
			<td>Laser</td>
			<td>Shenzhen Infrared Laser Technology Co., Ltd.</td>
			<td>HW650AD100-10BD</td>
			<td>Laser wavelength: 650 nm</td>
		</tr>
		<tr>
			<td>Nanoparticle</td>
			<td>Rust-Oleum</td>
			<td>274232</td>
			<td>NeverWet Multi-Surface Liquid Repelling Treatment is a revolutionary super hydrophobic coating.</td>
		</tr>
		<tr>
			<td>Nanopositioning z-stage</td>
			<td>Physik Instrumente</td>
			<td>P622.ZCD</td>
			<td>Travel ranges 50 &#181;m to 250 &#181;m (350 &#181;m open loop); Resolution to 0.1 nm; Linearity error only 0.02%</td>
		</tr>
		<tr>
			<td>Position sensitive detector</td>
			<td>Hamamatsu Photonics K.K.</td>
			<td>S1880</td>
			<td>The two-dimensional PSD is used to translate optical signals into electrical signals.</td>
		</tr>
	</tbody>
</table>

measuring the interaction force between a droplet and a super-hydrophobic substrate by the optical lever method

The goal of this paper is to investigate the interaction force between droplets and super-hydrophobic substrates in the air. A measurement system based on an optical lever method is designed. A millimetric cantilever is used as a force sensitive component in the measurement system. Firstly, the force sensitivity of the optical lever is calibrated using electrostatic force, which is the critical step in measuring interaction force. Secondly, three super-hydrophobic substrates with different grid fractions are prepared with nanoparticles and copper grids. Finally, the interaction forces between droplets and super-hydrophobic substrates with different grid fractions are measured by the system. This method can be used to measure the force on the scale of sub-micronewton with a resolution on the scale of nanonewton. The in-depth study of the contact process of droplets and super-hydrophobic structures can help to improve the production efficiency in coating, film and printing. The force measurement system designed in this paper can also be used in other fields of microforce measurement.

The displacement of the plate electrode and the corresponding capacitance between the cantilever and the electrode measured in one experiment are shown in Table 1. The relationship between capacitance C and displacement z is fitted by quadratic polynomial using the polyfit function in MATLAB, as shown in Figure 4. The first order coefficient P can be obtained by the fitting function. The final value of P is 0.2799 pF/mm, which is the average calculated from...

Watch this Scientific Journal Video about Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method at JoVE.com

Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method

The protocol aims to investigate the interaction between droplets and super-hydrophobic substrates in the air. This includes calibrating the measurement system and measuring the interaction force at super-hydrophobic substrates with different grid fractions.

The goal of this paper is to investigate the interaction force between droplets and super-hydrophobic substrates in the air. A measurement system based on ...

This method can help answer key questions in the field of bionics and fluid mechanics, such as superhydrophobic structures of lotus leaves and the droplet coalescence processes. The main advantage of this technique is that a force on the scale of sub micro-newtons can be measured with a resolution of scale of nanonewtons. This method could provide insight into the contact process of droplet and superhydrophobic structures.And it can also be applied to other fields of micro force measurement. Individuals who have never performed this technique will struggle because the distance between droplets and the superhydrophobic substrates is difficult to control accurately. Prepare the measurement system on an appropriate lab bench.At the center of the system is the silicon cantilever, which is suspended over a nanopositioning Z stage. The five millimeter long cantilever is mounted at the end of the holder. A high speed camera is in place with the line of sight perpendicular to the cantilever.The nanopositioning Z stage has a support that holds an electrode that at this point. Finally, a laser and a position sensitive detector are arranged to measure the cantilever deflection. After measuring the capacitance gradient, use a computer controlled DC power supply to calibrate the optical lever.This schematic provides andoverview of the setup for calibration. A plate electrode is on the nanopositioning Z stage. It is 100 micrometers below the cantilever with an overlap length of one half millimeter.The cantilever and the electrode form a capacitor, with the positive pull of the DC power supply connected with the cantilever and the negative pull with the plate electrode. Next, adjust the relative positions of the laser, the position sensitive detector, and the cantilever. Arrange them so the laser beam is reflected by the cantilever to the detector.At the computer, set the data acquisition rate of the detector output voltage to one kilohertz. In the DC power supply control software, set the start voltage to zero volts. Set the end voltage to 125 volts.Have the voltage increase in 25 volt increments. Hold each voltage value for five seconds. As the voltage is varied, monitor the voltage output of the position sensitive detector.After this sequence of measurements, perform an analogous sequence starting with the voltage at 125 volts and decreasing to zero volts in increments of 25 volts. Use the data from five complete measurements to create a plot in which the slope is the constant of proportionality between the interaction force and the position sensitive detector output voltage. To prepare for the measurements, disconnect the DC power supply from the plate and cantilever.Next, work with the nanopositioning Z stage. Identify the electrode on its plate support and remove both by unscrewing the support from the stage. In their place, screw a new plate support to the z stage before continuing.Ensure the high speed camera's line of sight is perpendicular to the cantilever. Next, get a superhydrophobic structure for the plate support. Use the structure with a contact angle of almost 180 degrees to suspend the water droplet from the cantilever.For the experiment, affix this structure to the plate support on the Z stage. With a micro pipette, place a two microliter droplet of water on the superhydrophobic structure. Now begin working with the nanopositioning stage software.In this software, go to the speed dialogue box and set the speed to 10 micrometers per second. Click the forward button to start the droplet moving upward. Click stop when the droplet contacts the free end of the cantilever.After one or two seconds, manually move the Z stage away from the cantilever. A hemispherical droplet of water should remain suspended from the lower surface of the cantilever. To continue, remove the superhydrophobic structure from the plate support and get a superhydrophobic substrate to replace it.This substrate consists of a copper grit with sprayed on nanoparticles. The substrate is glued onto a cylinder. This substrate has a grid fraction of 46.18%Place the substrate on the plate support.Adjust the position of the superhydrophobic substrate so it is 100 micrometers from the hemispherical droplet on the cantilever. With the detector, laser, and camera on, return to work with the nanopositioning control software. In the speed dialogue box, set the speed to 10 micrometers per second.Click the forward button to start the substrate moving upward. Click stop when the substrate and droplet make contact. Click the back button to move the superhydrophobic substrate downward.Click the stop button when the substrate and droplet are separated. There are different scenarios represented in these plots of Interaction Force verses Time. First focus on the data in the black curve which is for the substrate with grid fraction 46.18%Initially, the substrate and the droplet are far from contact.At this point, the force is zero. As the distance between the substrate and the droplet decreases, a repulsive force arises. This is reflected by the increase in force.Once the substrate and droplet come into contact, the force between the two becomes attractive, leading to a decrease in the curve as the droplet gradually wets the substrate through capillary action. Eventually, the cantilever oscillates around an equilibrium position. When other higher grid fractions are used, the magnitude of the force between the droplet and the substrate decreases.While attempting this procedure, it is important to remember that the relevant position between laser, PSD, and the cantilever can't be changed. Which can ensure the accuracy of measurement results. After it's development, this technique paves a way for researches in the field of tension-force measurement to explore the force during droplets in contact with substrate in air.

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