Multimodal Sensing Transparent Droplet Probe for Characterization of Superhydrophobic Surfaces

—Natural and artificial superhydrophobic surfaces are a rapidly growing topic in both academia and industry due to their unique properties and applications. Numerous techniques have been developed to characterize the wetting properties of such surfaces, such as the optical contact angle goniometer, force-based methods, and microscopic techniques for visualizing the wetting interface. However, a method that combines nN resolution force measurement with direct observation of the wetting interface on opaque superhydrophobic surfaces is missing. Here, we report a high-sensitivity multimodal force-sensing transparent droplet probe for the characterization of superhydrophobic surfaces that allows simultaneous visualization of the wetting interface and measurement of interaction forces. The probe is composed of a transparent glass cantilever with a droplet probe attached to its end. During the interaction with the sample, the wetting interface is directly imaged through the probe, illuminated with coaxial lighting. The interaction force is simultaneously measured as the deflection of the cantilever-shaped probe. By combining top view, side view, and high-resolution force sensing, the probe can reveal force contributions from both surface tension and Laplace pressure and measure super-repellent surfaces with contact angles near 180 ◦ with a low experimental uncertainty of 0.5 ◦ .


I. INTRODUCTION
W ATER-REPELLENT surfaces are ubiquitous in nature, such as lotus leaves [1], rose petals [2], and insect wings [3]. A wide variety of artificial surfaces have also been created for applications such as self-cleaning [4], antifogging [5], anti-icing [6], and energy harvesting [7]. These surfaces often contain chemical or topographical inhomogeneities, such as irregular roughness or surface coating. The resulting wetting interface is often complex, with trapped air pockets and irregular contact lines [8], where the state of the interface is also dependent on the history of the interaction [9]. Many surface-wetting characterization techniques have been developed, from the classical contact angle goniometer to different force-based instruments. Contact angle goniometry (CAG) is a gold standard given its ease of use but cannot visualize the interface. Moreover, when the surface is super-repellent or not flat, CAG becomes increasingly unreliable [10]. Force-based methods are also commonly used in wetting characterization for measuring either lateral friction forces during motion [11] or oscillation [12], or vertical adhesion forces [13], [14]. These techniques are easy to apply and provide a direct quantitative measure from which important wetting quantities can be derived, e.g., work of adhesion [13], [15] or wetting maps of the surfaces [14]. The force-based methods can also be highly sensitive, e.g., techniques based on atomic force microscopy (AFM) can achieve 20 pN force sensitivity and ∼1 µm lateral resolution in wetting characterization [16]. However, despite impressive advances in resolution, those force-based methods cannot accurately relate the force to advancing and receding contact angles of the surface and the exact contact line interactions associated with force events, except in very special cases such as on model pillar surfaces.
On the other hand, many methods have been used to image the wetting interface, such as environmental scanning electron microscopy (ESEM) [17], X-ray tomography [18], and AFM in imaging mode [19]. Nonetheless, only a few techniques are suitable for imaging the advancing and receding contact line. Bottom-view methods, such as laser scanning confocal microscopy [20] and reflective interference contrast microscopy [21], are probably the most fruitful techniques, but those methods require the sample to be transparent and cannot be applied when the sample is opaque, which is the property of the majority of water-repellent surfaces. Top-view methods have also been proposed for wetting characterization, especially in the hydrophilic regime, to measure contact line roundness and calculate contact angle from interface diameter and volume [22], [23]. On the other hand, those techniques are not reliable in the phobic regime due to contact line occlusion [24]. Through-droplet imaging techniques in the superhydrophobic regime have also been proposed for imaging the interface [25], [26]. Recently, promising results of through-droplet imaging using a transparent droplet probe have been reported [27] to directly image the contact interface and measure the advancing and receding contact angles on superhydrophobic surfaces. The method accurately estimates contact angles using the Young-Laplace relation during the measurement by precisely measuring the droplet's shape. However, a method that directly relates force measurement and advancing and receding contact angles is still missing.
Here, we present a force-sensing transparent droplet probe for multimodal characterization of super-repellent surfaces. The technique combines through-droplet imaging, side-view imaging, and high-resolution force-sensing to characterize super-repellent surfaces that can precisely distinguish the contributions of the contact line tension and Laplace forces, determine the phases of the wetting, and link forces and contact angles.
This article is organized as follows. Section II introduces the structure and working mechanism of the sensing system. Section III describes the design of the transparent droplet probe and Section IV explains the design of the optical system. Section V discusses the force-sensing mechanism and measurement procedure. Section VI describes the multimodal measurements combining vision and force. Section VII concludes this article.

II. SYSTEM OVERVIEW
The force-sensing transparent droplet probe is a two-modal system, using both optical observation and force measurement.
The key components of the system are shown in Fig. 1(a). The top-view optical observation is achieved with a transparent droplet probe, which can hold a spatially well-confined millimeter-sized droplet as the probing end-effector interacting with the sample surface. The interaction of the droplet and the sample surfaces, e.g., the state of the contact line and contact area, is observed using a top-view microscope and camera. A beam splitter is placed between the objective of the microscope and the transparent probe, allowing a white light source to illuminate the droplet-sample interface coaxially with the camera. To measure the deflection of the cantilever probe, a laser interferometer measures the displacement of the droplet-holding cantilever through a fixed reflection mirror. The droplet-sample interaction forces are then calculated from the deflection of the cantilever. The sample is mounted on an XYZ precision motorized stage, allowing precise and repeatable droplet-sample interaction. A noncontact droplet dispenser is mounted on the side of the XYZ sample stage and supplies liquid to form and maintain the droplet probe.

III. TRANSPARENT DROPLET PROBE
The transparent droplet probe is a key element of the system. The design of the probe aims to achieve two objectives: 1) to allow a stable and repeatable observation of the wetting interface and 2) to provide the measurement of the interaction force. To perform precise and repeatable measurements, wetting characterization devices need to have some form of liquid stabilization, such as holding the droplet at the end of a dispensing needle. Stabilizing the droplet is especially important for superhydrophobic samples where droplets readily roll off [4]. To hold and accurately manipulate the liquid droplet and allow optical observation, we employ a transparent disk with a 1 mm diameter. The disk has an undercut edge that confines the droplet-wetting surface to the perimeter of the disk [28], forming a well-defined boundary. The disk is in turn attached to the end of a transparent glass cantilever, shown in Fig. 1(b), providing a stable optical interface for the top-view camera to image through (see Appendix I for detailed probe fabrication steps).
To form the droplet probe, we use a noncontact dispenser (PipeJet, BioFluidix GmbH, Germany) to dispense purified water (Direct-Q 3UV-R water purification system, Millipore SAS, France) from beneath onto the underside of the disk. The dispenser is attached to the side of the motorized sample stage, allowing precise alignment beneath the disk and automatic refilling. To form the droplet probe, smaller droplets of approximately 5-nL volume are dispensed sequentially. Before each measurement, the volume of the droplet probe is set to 1.5 µL, in line with our previous works [14], [27]. This volume is a compromise between the effects of gravity and evaporation. The diameter of the droplet corresponding to this volume is 1.44 mm, well below the capillary length of water of 2.7 mm, such that the effects of gravity over its shape are insignificant. The droplet should also be sufficiently large that evaporation effects are insignificant throughout a measurement. An evaporation rate of around 1.8 nL/s has been observed under normal ambient conditions or 3% volume reduction during a typical 25 s measurement.

IV. OPTICAL SYSTEM
The optical system is designed as a compromise between four main criteria: 1) an objective with a sufficiently small acceptance angle to resolve the contact line; 2) a sufficiently large field-of-view to image the whole contact interface; 3) a sufficiently high resolution that can observe small changes on the interfacial contact line and area; and 4) a sufficiently large working distance to accommodate the instrument components.
The illumination strategy exploits the reflective nature of the interface to achieve contrast between the droplet-sample interface and the droplet sidewalls. Most superhydrophobic surfaces exhibit an air layer or pockets of air at the interface between the droplet and the rough surface, also known as plastron. The ability of the surface to retain this air layer is key to the water-repelling properties of the surface [8].
The maximum slope angle of the plastron at which light will reflect into the camera is defined by the combination of the illumination angle of the light source, ϕ L , and acceptance angle of the objective, ϕ o [see Fig. 2(a)]. A collimated white light source (OSL2 with collimating lens OSL2COL, Thorlabs Inc., USA) is reflected through a beam splitter (15 mm 50R/50T, Edmund Optics Inc., USA) mounted between the cantilever and the probe, which illuminates the droplet-sample interface coaxially to the camera. The light source is placed approximately 150 mm away and has an 11 mm radius aperture, resulting in an illumination angle of ϕ L ≃ 2.1 • . A microscope with a magnification of 6× is used to provide a full view of the wetting interface (VZM 600i, Edmund Optics Inc., USA, and a color camera BFS-U3-28S5C C or grayscale camera BFS-U3-28S5M C, Flir LLC). The field-ofview is approximately 1.1 × 1.1 mm 2 at a working distance of 60 mm and a pixel resolution of ∼750 nm/px. A large working distance is preferred as it minimizes the angular aperture, ϕ o ≃ 7.0 • , while also providing the space between the camera and the probe for other components.
The maximum slope angle of the plastron at which light will partially reflect into the camera is (ϕ o + ϕ L )/2 ≃ ±4.6 • and fully reflected into the camera is (ϕ o − ϕ L )/2 ≃ ±2.5 • . This slope angle is small enough to image the plastron while providing a margin to account for the sample mounting angle and variations in the flatness of the plastron. To prevent direct reflection from optical components, in particular the walls of the beam splitter, we tilt the light source by 10 • and the beam splitter by 5 • .
The performance of the illumination and vision system was evaluated on four different samples: fluoropolymer-coated silicon nanograss [ Fig. 2 In general, if the dry surface is light-absorbing or reflective, the plastron will show high contrast. However, if the surface scatters light, the light reflected from the plastron may provide less contrast against the scattered light. For such samples, the probe may be tilted, e.g., by 5.5 • to improve the contrast. Fig. 2 shows the examples of the sample images. Dry silicon nanograss [ Fig. 2(b)] is black under the naked eye and the plastron appears with great contrast. On the Glaco sample, Fig. 2(c), the wetting interface also shows high contrast despite the reflective nature of the dry Glaco surface. Light reflected outside the interface does not reach the objective. On the other hand, on the Maranta leaf, Fig. 2(d), the plastron shows bright discontinuous regions, attributed to heterogeneous surface composition and roughness of the surface. The rest of the surface appears green due to scattered light. On the silicon micropillars, Fig. 2(e), the droplet is in contact with the top of 21 pillars but does not touch the bottom of the pillars, also known as the Cassie state [29]. In this case, the wetted pillar tops appear bright relative to other pillars. The trapped air layer accounts for only a limited amount of brightness in the image, with some light also scattering from the rough surface at the bottom of the pillars.

V. FORCE MEASUREMENT SYSTEM
The droplet probe is also designed to measure the wetting forces, where the design is centered around a compromise between force resolution and time response. During interaction with a water-repellent sample, a millimeter-sized droplet experiences wetting forces that range from tens of µN down to and below 1 nN, and wetting events occur at the millisecond scale [14]. The interaction forces bend the cantilever-shaped glass probe, where the deflection is measured by a nanometer resolution laser interferometer (model IDS3010 with fiberoptic sensor head D4/F17, Attocube Systems AG, Germany) shining through a 45 • mirror, as shown in Fig. 1(a). The laser head and mirror are assembled on a custom tilt stage, as shown in Fig. 1(c). The alignment between the laser and the cantilever is achieved by maximizing the laser signal intensity while adjusting the three screws on the tilt stage. Fig. 3(a) shows a typical force curve acquired at 50 kHz, used to characterize the performance of the force sensor. During the approach, the sample is raised toward the droplet. The sample contacts the droplet at approximately 0.7 s, from which the force gradually increases up to ∼18.9 µN. At around 11 s, the sample stage reverses and the force decreases. From ∼18.4 s, the droplet experiences negative forces due to adhesion to the surface. Finally, the droplet detaches in an abrupt event at ∼23.9 s.
The deflection profile of the cantilever under the droplet-sample interaction forces, D(x), can be derived from the Euler-Bernoulli beam theory (1). The cantilever's elastic constant k relates a force acting at the center of the dropletholding disk, x = l, to the vertical displacement at the same location, see (2). We measure l as the distance from the base of the cantilever to the center of the droplet-holding disk where E is Young's modulus of the glass and w and t are the width and thickness of the cantilever, respectively. The force signal calibration k t relates the displacement, D(x 1 ), to the force, F, acting on the droplet, where x 1 is the distance from the base of the cantilever to the laser measurement site, as shown in Fig. 1 For the camera to have a clear view over the disk, the laser interferometer needs to be aligned further back in the cantilever, as shown in Fig. 1(a). The difference in vertical displacement at the disk and the measurement site is accounted for by α, which can be estimated as α = D(l)/D(x 1 ).
The hydrolytic class 1 glass cantilever has an average E ≃ 70 GPa with dimensions of l ≃ 18.45 mm, w ≃ 2.8 mm, and t ≃ 110 µm. In our setup, α ≃ 1.81 leading to an expected calibration constant of k t = 18.8 N/m, for a force acting at the center of the droplet-holding disk. The force measurement range is limited by the alignment tolerance angle of the interferometer laser head on a perpendicular surface, specified as ±0.3 • . The deflection angle along the cantilever, ϕ(x), is derived from (1) Using the same parameters, the expected maximum measurable force range is ±700 µN under the assumption that the laser is perfectly aligned. It is worth noting that the maximum working range of the cantilever is ∼1.3 mN when the cantilever touches the protective cover.
To calibrate the force sensor, we increase the volume of the droplet on the probe leading to a measurable displacement due to the known change in weight. An example calibration force curve is shown in Fig. 3(c). The volumes are estimated based on side-view image analysis of pictures taken before and after refilling, Fig. 3(d). The change in weight of the droplet is used to calibrate the effective elastic constant of the cantilever. For the example case of Fig. 3(c), the resulting calibration value is 20.9 N/m. This constant depends on the cantilever and installation and is calibrated per experiment, where typical values range from 15 to 25 N/m.
To estimate the resolution of the force measurement, we analyzed the force signal over 30 independent 1-s periods, while the probe was not touching the sample and the setup is idle. The mean of the standard deviations of the displacement is 0.19 nm, leading to a force resolution of ∼3.9 nN, at 100-Hz acquisition speed.
To estimate the settling time t s and the frequency of resonance f , we model the cantilever with the disk and 1.5-µL droplet as a second-order system. Upon the droplet detaching from the sample, the probe experiences an abrupt transition from approximately −6 to 0 µN, shown in Fig. 3(b), i.e., a step stimulus in force. The subsequent oscillation shows that the system is underdamped, for which the step response can be approximated as a decaying sinusoid where a is the initial amplitude, τ is the decaying time constant, f is the damped frequency of resonance, and ϕ is the phase of the oscillation. By fitting the oscillation with (5), we determine f ≃ 128 Hz and t s = 4τ ≃ 0.49 s (2% tolerance band). During the wetting experiments, the droplet probe is mostly quasi-static while in contact with the sample surface. The half-second settling time after the droplet detaches from the surface is acceptable.
VI. MULTIMODE MEASUREMENT In multimode measurements, the optical measurements and force measurements provide different perspectives of the experiments. The top-view images provide detailed information on how the contact line advances and recedes, such as pinning/depinning at surface imperfections, which might not be resolved in the force signal. Top-view images can also provide visual evidence of any changes to the interior of the interface, such as the Cassie-Wenzel transition [29], which is marked by the loss of reflectivity of the interface due to the collapse of the plastron. On the other hand, the force measurement provides a quantitative measure of important wetting quantities such as snap-in and pull-off forces (the moment when the droplet touches and detaches from the sample) or other wetting events that can be associated with visual changes in the interface.
A typical measurement consists of pressing and depressing the sample against the droplet [see Fig. 4(a)]. First, the droplet is aligned above the measurement site. During the approach phase, the sample stage is raised toward the droplet with a velocity of 10 µm/s until the droplet is pressed by approximately 100 µm. Then, the sample stage reverses its motion Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
direction and retracts at the same speed until the droplet detaches from the surface. Before each measurement, the droplet is brought into contact with an electrically grounded piece of nanograss to remove electrostatic charges, which may otherwise affect the measurement.
The simplified wiring schematic for the setup is shown in Fig. 4(b). In multimode acquisition, the top-and side-view cameras operate at 100 fps, triggered by a DAQ board (NI USB 6363, National Instruments Inc., USA). The laser interferometer is used to measure the force signals as well as the Z displacement of the sample stage, also acquired at 100 Hz. The same DAQ board acquires the laser interferometer force signal as well as sample stage displacement during measurement to ensure signal synchronization. Timestamps are used to synchronize the images from the cameras to the sample stage and force signals.
An example of multimode measurement performed in silicon nanograss is shown in Fig. 4(c)-(e). Five consecutive measurements were made on the same sample location, from which the mean and standard deviations were calculated (solid and shaded area, respectively).
The interface area is shown in Fig. 4(c) as a function of sample stage displacement. The top-view images are postanalyzed in MATLAB to find the area of the interface in each frame of the measurement. For each frame, a binary image was produced by threshold. The area of the interface is calculated as the area of the largest filled blob. The displacement axis was set to zero at snap-in (the moment when the droplet first contacts the sample). Fig. 4(d) shows the forces acting at the interface. The total measured force F is shown in black, which can be decomposed as the sum of the water-air surface tension force F t acting on the perimeter of the wetting interface and the force due to Laplace pressure F P acting on the interface area where L CL is the contact line perimeter length, obtained through machine vision (green line in Fig. 4(c) inset); γ is the liquid surface tension; θ c is the average contact angle of the droplet with the interface; A is the interface area, shown in Fig. 4(c); and P is the Laplace pressure.
To estimate P, we measure the radii of curvature using side-view images [ Fig. 4(e), inset] using the Laplace pressure equation where R 1 and R 2 are the principal radii of curvature at any point of the air-water interface of the droplet. R 1 is estimated as the mean of the radii on each side of the droplet, which are obtained by fitting a circle to a segment of the edge of the droplet, detected with a binary threshold (red curves in Fig. 4(e), inset). R 2 is estimated as the horizontal half-width of the droplet. The mean contact angle θ c from the five measurements is shown in Fig. 4(f) as a function of interface diameter. The contact angle can be calculated from (6) by combining the top-view measurement of A and L CL , side-view measurement of P, and force sensor measurement of F. Three characteristic wetting phases can be identified: the advancing phase, shown in blue, during which the sample stage is raised toward the droplet. During this phase, the interface area grows and the contact line advances over the surface with an approximately constant contact angle. The transition phase, shown in black, starts after the sample stage reverses direction. The end of the transition phase was determined from the slope of θ c . During the transition phase, the contact line remains pinned and the area is approximately constant. The receding phase follows, shown in red, as the sample stage continues to move downward. During the receding phase, the interface area decreases continuously, and the contact angle is approximately constant. The mean advancing contact angle is 178.5 • ± 0.5 • and the mean receding angle is 169.9 • ± 1.3 • , where the uncertainties correspond to the standard deviation. We note that these are experimental uncertainties, where the contact angle noise was estimated to be 0.04 • as the standard deviation of ten 1-s periods taken evenly along the contact angle measurement.

VII. SUMMARY AND DISCUSSION
In this article, we present a force-sensing transparent droplet probe for the multimodal characterization of superhydrophobic surfaces. A liquid droplet is held at the end of a glass cantilever, while a top-view camera images the droplet-sample interface through the droplet. The glass cantilever doubles as a force sensor, which enables the simultaneous recording of droplet-sample interaction forces. The top-view images are analyzed with machine vision to obtain a continuous measurement of the interface area.
The multimodal measurement provides valuable opportunities to directly measure the state of the wetting interface. Force components from both surface tension and Laplace pressure can be measured separately. The contact angle of super-repellent surfaces can also be calculated with a great resolution by combining top view, side view, and high-resolution force sensing. These data may better inform material scientists and wetting researchers on how to better characterize and develop superhydrophobic materials. Other lighting strategies can also be explored, such as the use of polarizing filters and even fluorescence microscopy. Moreover, the transparent probe can also be applied to other optical microscopes, such as the laser scanning confocal microscope, to provide detailed 3-D imaging of the interface.

APPENDIX I PROBE FABRICATION
The components used to fabricate the probe are shown in Fig. 1(b). The 22 × 2.8 mm cantilever and 5 × 2.8 mm spacers are cut from a #0 glass coverslip (∼110 µm thickness) and the 20 × 5 × 1 mm protective probe cover is cut from a glass slide. All glass pieces are cut using a Disco DAD3220 dicing machine.
The back of the cantilever is coated with gold using a Cressington 108 auto sputter device, with care not to coat over the disk region and the back side where it will be glued to the probe.
A 10 × 4 × 4 mm stainless steel piece is assembled to the top of the glass protective cover to facilitate manipulation and mounting, with the help of a screw and a magnet.
To fabricate the undercut disks, a 100-µm-thick layer of SU-8 50 was spin-coated (1500 rpm, 30 s) on a silicon oxide coated wafer followed by 15 min at 95 • C soft bake on a hotplate, 20-s UV exposure using a Karl Suss MA6 mask aligner, 15-min post-exposure bake at 95 • C, and then development in PGMEA for 20 min. The disks were manually released using a scalpel. A microgripper was used to precisely place the disk on the cantilever glass piece at approximately 0.25 mm from the end of the glass slide.
All parts were assembled with UV curable optical glue, model Delo Photobond GB310, Delo.

APPENDIX II SAMPLES
The two silicon nanograss samples used were produced by a maskless cryogenic deep reactive ion etching process using an Oxford Plasmalab System 100 on a 4-in silicon wafer (⟨100⟩, p-type boron doped, >1 cm). The process parameters were 1000 W of ICP forward power, a temperature of −110 • C, 10 mTorr of pressure, and 7 min of etching time. For the nanograss in Fig. 2(b), the flow rates were: The Glaco sample in Fig. 2(c) was prepared by coating a microscope glass slide with Glaco Mirror Coat Zero spray (Soft99 Company) at room conditions. The sample was set on its side and let to dry.
The Maranta potted plant (Leuconeura Amabilis Mint), shown in Fig. 2(d), was purchased from local sellers. A test sample of the leaf was cut using scissors and attached to a glass slide using double-sided tape. The test sample was washed with purified water prior to measurement and let to dry for approximately 5 min.
The silicon micropillars in Fig. 2(e) were fabricated by cryogenic deep reactive ion etching with a silicon dioxide hard mask. The starting substrate was a ⟨100⟩ silicon wafer with 500-nm wet thermal oxide. The micropillar pattern was defined by UV lithography (AZ5214 photoresist, Süss MA6 mask aligner). The oxide was etched with reactive ion etching using an Oxford Plasmalab 80+ (Oxford Instruments, Bristol, U.K.), 18-min etching time, 200-mTorr pressure, 30-W power, 25-sccm CHF 3 , and 25-sccm Ar flows. The photoresist was then stripped by ultrasonication in acetone for 10 min. Next, the micropillars were etched using an Oxford Plasmalab 100 (Oxford Instruments, Bristol, U.K.). The micropillars were fabricated with anisotropic silicon etch (O 2 6 sccm, SF 6 40 sccm, forward power 3 W, ICP power 1050 W, 110 • C temperature, 8-mtorr pressure, and 24-min etching time). Afterward, the oxide mask was stripped in buffered HF, and the etch depth was determined by a profilometer (Bruker Dektak XT) to be 50 µm. The diameter of the pillars was 20 µm, and the pillars were in a square array with 60-µm spacing.