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...

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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 ...

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6.6K visualizações.  Tianjin University. Este método pode ajudar a responder a perguntas-chave no campo da biônica e da mecânica de fluidos, como estruturas superhidrofóbicas de folhas de lótus e os processos de coalescência de gotículas. A principal vantagem desta técnica é que uma força na escala de sub-micro-newtons pode ser medida com uma resolução de escala de nanonovos. Este método poderia fornecer insights sobre o processo de contato de gotículas e estruturas superhidrofóbicas.E também pode ser aplicado...