Development of a setup to characterize capillary liquid bridges between liquid infused surfaces

Capillary liquid bridges (CLBs) are created when a droplet of liquid forms a stable link between two surfaces, usually solids. In nature, countless examples of water based CLBs can be found, from the cohesive force holding soil and sandcastles together¹ to the adhesion of small animals and insects to surfaces,^2–4 the function of our joints,⁵ and in several respiratory diseases.^6,7 In technology and industrial applications, CLBs are also ubiquitous in processes such as soldering,^8,9 lithography,¹⁰ oil recovery,¹¹ and cement drying,¹² with potential for medical processes such as stem cell and drug delivery.¹³ 

The behavior of CLBs is influenced by many environmental and physical factors as well as the fluid used to create the bridge. The exact shape of the CLB and the force it exerts on the contacting surfaces are determined by an interplay between the surface tension of the liquid, the shape of the surfaces, and the affinity between the liquid and the surfaces. Gravity also influences CLBs, but its effect only becomes noticeable at scales larger than the so-called capillary length (about 2 mm for pure water). Given the importance of CLBs in science and technology, considerable research aims at modeling^14–18 and experimentally characterizing their properties^19–21 over a wide range of relevant conditions.

Experimentally, a variety of setups have been developed to explore CLBs stretched between parallel or non-parallel solid plates. At the nanoscale, force measurements typically rely on atomic force microscopy^19,20 or similar devices.²¹ Nano-bridge sizes range from a few nanometers to hundreds of nanometers, and the associated capillary forces range from piconewton to tens of nanonewtons. Although highly precise spatially, such measurements do not allow for direct visualization for the CLB or characterization of its shape while being deformed. Asperities or chemical inhomogeneities of the surfaces can also dramatically affect the measurements which usually involve atomically flat, ideal surfaces that are not representative of most applications. In contrast, CLB measurements over the millimeter scale allow for direct visualization of the CLB evolution as the distance between surfaces changes.^22–28 At that scale, capillary forces are typically in the range of millinewtons^22,23 and the effect of gravity may need to be taken into consideration depending on the particular system considered.²⁹ Given the relatively large size of such CLBs, the geometry and chemical properties of the surfaces can be well controlled on the relevant scale, including via the introduction of chemical patches,^24,30 surface corrugations,³¹ or non-parallel geometries, such as spheres²³ and wedges.²⁵ 

While standard nanoscale and millimeter-sized “macroscale” measurements have enabled significant advances in the field, many phenomena involving CLBs fall in the in-between region, where capillary forces range between sub-micronewtons to hundreds of micronewtons. In this range, directly observing the CLB is usually still possible, but measuring the force it exerts on the contacting surfaces becomes challenging and requires bespoke experimental setups.³² Such setups are usually expensive, highly specialized, and unsuitable for routine measurements.

This gap is all the more problematic with the advent of liquid infused surfaces (LIS), where CLBs are only expected to induce micronewton force changes when extended, even at the millimeter scale. Since their discovery,^33–35 LIS have enabled important development in the field of surface science and wetting, with important implications for surface capillary phenomena.³⁵ The interest in LIS is motivated by a wide range of technological applications from anti-fouling properties to anti-icing,^36–38 antibacterial,^39–41 self-healing,^33,42 and anticorrosive properties.^43,44 Simulations have captured some aspects of CLBs formed between LIS,¹⁴ but experimental studies are lagging behind, owing to the difficulties associated with such measurements.

In the present study, we develop a novel setup to study CLBs between parallel plates with improved force sensitivity, down to the micronewton range. The plates can be functionalized with any desired surface, making the system suitable for measurements on LIS. The setup, built from relatively inexpensive and commercially available parts, is fully motorized for relative displacements of the surfaces over several millimeters. It is versatile and can be easily adjusted to suit different geometrical configurations or work in specific environments. It can incorporate multiple cameras working simultaneously (here two) for more accurate measurements, and a bespoke software is developed to drive the experiments and subsequently analyze the data collected from the camera and the force sensor.

We illustrate the measurement capabilities of the setup by tracking the changes in force and geometry associated with the extension and the compression of CLBs between salinized glass surfaces and between planar LIS.

Before describing in detail the setup developed, it is useful to briefly summarize some of the key details of typical measurements involving CLBs, including the observables necessary for quantitatively describing the CLB and the underlying theory.

The main geometrical parameters used to describe CLBs are (1) the angles θ₁ and θ₂ formed by the liquid and the contacting surfaces, (2) the height h of the bridge, (3) the radii of contact R_t and R_b at the top and bottom surfaces, respectively, and (4) the radii of curvature R₁ and R₂ of the surface of the liquid bridge (Fig. 1). R₁ and R₂ are shown in Fig. 1 at the point of contact between the liquid bridge and the top contacting surface.

The CLB exerts a capillary force on the contacting surfaces. The magnitude and direction of this force depend on the specific geometry of the system. Gravity is also present, and its effect may have to be taken into consideration, depending on the size and volume of the CLB. In larger CLBs, the gravity-induced differential hydrostatic pressure between the top and the bottom of the CLB results in an asymmetric shape.

In a typical experimental measurement, the geometry of a CLB is tracked by a camera while a given parameter (here the distance h between the surfaces) changes continuously. The associated capillary force F experienced by one of the contacting surfaces is also measured. The CLB geometry is usually extracted from 2-dimensional video images of the bridge, which have to be synchronized with the force measurements.

Most experimental measurements face several challenges. One key problem stems from assuming symmetry and uniformity over the entire CLB. This is implicit as we use a 2D image to extract all the geometrical parameters (θ₁, θ₂, h, R_t, R_b, R₁, and R₂) assumed to represent the bridge at equilibrium. For large CLBs, or CLBs experiencing pinning on the surface, this assumption may not be valid because the optical image may miss pinned points. However, the measured force is sensitive to such pinning points, resulting in a disagreement between the measured force and that calculated from the geometrical parameters. Liquid evaporation may lead to time-dependent changes in the force over longer measurements due to changes in the CLB’s volume. Using larger CLBs can reduce the relative importance of evaporation effects but at the cost of needing to take into account gravity. Alternatively, CLBs can be made of liquids less susceptible to evaporation (e.g., water–glycerol mixture instead of pure water^47,48) and make use of a controlled environment (e.g., humidity and temperature^49,50).

Measuring CLBs between LIS is more challenging for several reasons. First, the changes in capillary force as the CLBs are stretched are typically an order of magnitude lower than those for CLBs of the same size but involving non-LIS. Second, while LIS are of interest, precisely, for the absence of contact line pinning^51,52 and the ability of droplets to roll off easily,³⁵ these properties render CLB measurements more challenging due to increased bridge mobility. Additionally, the liquid layer of the LIS (typically oil) can create a visible ridge around the CLB–LIS contact regions or may cloak the whole bridge,⁵³ rendering precise determination of θ more difficult (Fig. 2). The contact angle must then be approximated either by fitting the bridge edge and extrapolating the obscured region [Fig. 2(b)] or by approximating the contact angle using geometrical arguments.¹⁸ When focusing on cases with small oil ridges, these two approximations converge to the same value. However, for larger oil ridges, their values can differ significantly, and it is important to employ consistent radii and contact angle definitions in Eqs. (1) and (2). For practical reasons, it is often convenient to define them at the droplet–lubricant–gas contact line.

The impact of the oil ridge on the measurements depends on the thickness of the LIS liquid layer, thus rendering the issue system dependent. The ridge may also impact the measurement of the curvature depending on which approximations are used, and its size can grow during the measurements (something that needs to be taken into account while studying changes in the contact angles). To overcome this issue, a solution with a dye dissolved in the droplet or the LIS liquid⁵⁴ can be used so as to highlight the contact line or contact angles. There is, however, some concern that dye molecules could affect the surface tension of the fluids and hence the contact angles measured.

The setup developed in this paper uses a standard design^22–24 with one of the surfaces fixed and the other motorized and suspended to a high-precision force sensor. Cameras provide direct visualization of the CLB’s geometry, with all pieces of hardware controlled and synchronized using the same computer software. While several hardware and software aspects of the development improve on existing setups, the key improvement is the force sensitivity (accuracy to 4 µN), with demonstrated measurements on CLB between LIS. This improvement also entails some limitations, which are discussed in Sec. III.

The key building elements of the setup are a micronewton sensitive force cell (Novatech Measurements Limited, St Leonards on Sea, UK), a high-quality digital camera (IDS Imaging Development Systems GmbH, Obersulm, Germany) and motorized stages (Thorlabs LTD., Ely, UK), all interfaced, synchronized and controlled using LabVIEW (National Instruments, Austin, TX, USA). Each item is listed in Table I with the key elements labeled as “essential” while optional improvements are labeled “optional.”

The different items are assembled as shown in Fig. 3. The force sensor (Novatech, F329 Deci-Newton Load cell), mounted on the vertical motorized stage (Thorlabs, KVS30/M), can operate symmetrically in both traction and compression. We opted for a top position with the sensor suspended to a custom-made holder. Both the top and bottom stages can be manually adjusted to change the sample position while loading, including the relative tilt angle (usually around 0.5°) of the bottom plate. This is useful to apply minute corrections of the plate parallelism. Removable plates can be screwed into the force sensor, allowing for different surfaces to be easily and stably mounted. Suspending the force sensor has a number of benefits: it protects against liquid ingress while using very mobile droplets, prevents oil shed during longer experiments or due to droplet rolling contaminating the sensor, and gives the sensor some protection from the user, who is less likely to knock or touch it. In this way, the sensor is only ever contacted by droplets that are gently brought into contact using the z-stage. The custom-built holder is attached to a thick post (Thorlabs, 300 mm post) to hold the entire unit steady as measurements are taken. An optional horizontal stage (Thorlabs, PT1/M—25.0 mm translation stage) can be used for shearing experiments (not used in this paper).

The main camera (IDS, UI-5880CP Rev. 2 GigE CMOS camera^55,56) takes a video of the capillary bridge during the stretching experiment at 5 fps (or higher as required). It is focused so as to track accurately the edges of the CLB and angled with respect to the plates to get a good view of the top contact angle and the bridge reflection. The reflection provides a convenient way of determining the position of the surface contact accurately. Since experiments are conducted using identical contacting surfaces, tracking the bridge geometry at its top interface is sufficient to derive all the meaningful parameters for modeling in the absence of gravitational effects. The images from the video are time-stamped for synchronization with the force sensor data and subsequently post-processed using a bespoke python script to automatically extract the contact angles and radii of curvatures (see Sec. IV).

An optional secondary camera (Dino-lite AM7915MZT—EDGE, Almere, The Netherlands) offers a synchronized side view of the CLB. It is primarily used for measuring the initial plate separation but can also be used to track droplet movement in the transversal direction to the plane imaged by the main camera. This is useful to monitor possible lateral motion of the CLB (and if necessary, bring suitable corrections) and to ensure that the radii measured are correct. The second camera also helps in identifying pinning events missed by the primary camera while working with standard surfaces. From both cameras, the diameter and the surface curvature of the droplet can be accurately quantified for each frame during post-processing.

All the hardware components of the setup interface with LabVIEW, where a bespoke program controls their movement and collects all the data synchronously to ensure accurate timestamping of each component (see Sec. 2 of the supplementary material). The choice of using LabVIEW is motivated by the fact that it easily interfaces with the control software of most instruments, and many companies provide dynamic-link library (dll) and driver files such that the full capacity of all the instruments can be utilized without the need for machine-level programming.

The entire setup is placed in a Perspex box (custom built) with an anti-vibration stand (Thorlabs, B4560A—Nexus Breadboard) to prevent environmental changes from affecting the measurements. The Perspex box and the anti-vibration table shield the delicate force sensor from uncontrolled environmental effects and reduce the noise in the system. The box also allows for the local environment (temperature and humidity) to be controlled around the capillary bridge.

In a standard CLB stretching or compression experiment, the measurements are conducted as follows:

1. The two surfaces of interest are prepared on circular glass coverslips (Agar Scientific, 24 mm) and glued onto a custom-built thin metal mount using fast curing air dry glue (Reprorubber Thin Pour, Bowers Group, Camberley, UK). After 2 hours of curing, the surfaces and metal mounts are screwed into place in the static baseplate and the force sensor of the setup. The whole setup is then left to equilibrate for an hour before the measurements begin.

2. The camera and the light source are adjusted to ensure suitable visualization of the CLB for the desired experimental conditions.

3. The force sensor may be zeroed to remove the offset due to the weight of the sample and mount. For measurements where only the change of force is of interest, the system offset can simply be removed at the stage of data processing, leaving relative force measurements.

4. A droplet is placed onto the lower plate and brought gently into contact with the force sensor.

5. The force sensor and the camera begin recoding data. The measurement effectively commences approximately 1–2 mins after the first contact, to allow the force sensor to be fully at equilibrium before starting to collect meaningful data.

6. The stage can be set to move at a particular velocity and over a particular distance.

7. The stage can be set to repeat the stretching/compression motion as required.

8. After completion of the experiment, the timestamped data from each instrument are outputted as a text file (force) or a video file (camera) for post-processing.

9. The data are passed onto a python script for semi-automated post-processing and extraction of the geometrical parameters.

All the code for data acquisition and processing is available in Secs. 2 and 3 of the supplementary material. A brief description is also given below.

Setup control: Development of a LabVIEW setup to control the different pieces of equipment is relatively straightforward and based on the dll files provided by the different manufacturers or existing LabVIEW modules. The software controls the motion of the different stages (vertical, lateral, and tilt angle) as well the cameras and the data acquisition with timestamping.

Depending on the set of data, the analysis procedure may occasionally fail to extract properly the geometrical parameters due to a variety of external factors, such as unfavorable light reflections and intensity or a particular positioning of the CLB. This typically translates as large, unjustified variations of the parameters between consecutive images (in particular, in the contact angle and radius of curvature). If this occurs, a pre-processing step may be needed whereby certain image features or frames are removed by hand to assist in the edge detection. The fitting area may also be decreased to remove features close to the bridge edge that may interfere with the detection.

In an ideal experiment, the measured and calculated forces would be exactly the same. In reality, however, we usually find that the force sensor has a small but measurable constant offset (typically 20 µN) when compared to the forces calculated from the CLB geometrical parameters using Eq. (1) (Fig. 5). While negligible for measurements involving solid surfaces, this offset needs to be taken into account when comparing calculated and measured forces with the CLB between LIS. Practically, the experimental offset value is quantified in an objective and systematic manner for a given dataset by fitting the experimental data to the calculated data (least squares error minimization for the whole set). The process is illustrated in Fig. 5, where both experimental and calculated forces are given for an aligned set of data. This procedure was carried out systematically thereafter, and the data are displayed with the offset removed from the experimental measurement so as to allow better comparison of the absolute force values. The origin of the offset may be due a variety of factors and appears to depend on the day and type of measurement conducted. This suggests that it could result from daily variation in the load cell calibration due to external parameters (temperature and humidity) or due to the position of the CLB during its setup. However, given its small offset value, the fact that it is constant over a set of data, and the possibility to compensate for it, we do not see this as a major issue.

To illustrate the capabilities of the setup, we conducted some CLB measurements with surfaces composed of hydrophobic dimethyldichlorosilane-treated glass (DMS glass) and with LIS. The DMS glass was prepared by vapor deposition as described in Ref. 58. The LIS were prepared following an established protocol as described elsewhere⁵⁹ and had an oil layer thickness of ∼6 µm to limit oil ridge effects. During a measurement, the CLB is first extended by increasing the distance between the surfaces and subsequently returns to its initial position. The results are compared in Fig. 6, showing a good agreement between the measured and calculated forces derived from the CLB geometry. Movies of both experiments are available in Sec. II of the supplementary material.

Figure 6 illustrates the capabilities of the setup developed: both DMS glass and LIS induce a similar contact angle for the CLB and both bridges have similar dimensions, but the force variation while stretching experienced in both cases differ by a factor of ∼5. As expected, the contact angle hysteresis is much lower for LIS compared to DMS glass. This can be seen in the videos in SM2 of the supplementary material, which shows that when the contact line of the CLB on LIS is highly mobile while pinning is often seen for the DMS glass.

The force sensor is based on a load cell and is hence unavoidably affected by time dependent creep.⁶⁰ In practice, this means that rapid changes to the CLB geometry take several seconds to equilibrate in the associated force measurement. This should be taken into consideration while performing measurements with this setup because it imposes a limitation on the measurable CLB stretching and compressing velocities. We acquired the data shown at relatively slow stretching/compressing velocities (less than 0.01 mm/s), which provided a good agreement between the measured and calculated force values [Fig. 7(a)]. In contrast, the same measurement repeated ten times faster (stretched/compressed at 0.1 mm/s) results in a significant deviation between the measured and calculated forces [Fig. 7(b)]. The measured force becomes affected by a convolution with a time dependent creep, artificially lowering the value of the measured force and preventing equilibrium measurement.

Another interesting feature that can be explored is the pinning of CLBs on solid surfaces. The force is measured globally for the entire bridge and is, therefore, always sensitive to pinning, which often appears as an unexpected force evolution and a deviation from the theory (Fig. 8). Such pinning is, however, not always visible with the camera. This is because the camera effectively captures only a 2D projection of the 3D CLB, which can create some difficulty for interpreting the results. By adjusting the side camera so that it can visualize the whole triple line of the CLB, it is possible to determine where pinning likely occurred (Fig. 8).

Oil ridges can arise on LIS with a thick surface oil layer. Experimentally and for the type of LIS used here, this typically occurs when the oil layers exceed 12–14 µm (Fig. 9). The ridge appears as an obscured region where the CLB contacts the LIS’ surface; ridges are mobile and can grow during measurements. The presence of ridges leaves a smaller region for fitting the CLB’s edge. To some extent, this can be mitigated by adapting the analysis software so that it takes into account the entire bridge to extract the geometrical parameters rather than only the region near the top of the oil ridge (see Sec. 3 of the supplementary material).

The measurement setup developed in this paper is designed to overcome the difficulties associated with studying CLBs between LIS. It also provides a modular set of components that offers flexibility with the ability to conduct many different types of CLB investigations. The key features of the setup are the integrated measurement of all variables, the high sensitivity of the force sensor, and the custom-built analysis software to extract the relevant information from the experimental data.

The force measurement is sensitive enough to quantify the small force variations associated with experiments on LIS and could also be used to probe force variations associated with smaller liquid bridge deformations on conventional surfaces. The data can then be processed to high temporal accuracy with up to 20 images per second and 10 force sensor readings per second. Care must be taken to ensure that measurements are not affected by time dependent creep. While unavoidable in load cells, it can be mitigated by controlling the CLB stretching/compression velocities.

The system, having motorized stages that can move in all three directions (x, y, and z), is not limited to the simple stretching experiments shown here but can also perform shearing experiments or combinations of thereof. The position of the stages can be controlled with 0.1 µm accuracy, if necessary. The isolation of the setup in a Perspex box allows for control of the local environment around the CLB (e.g., humidity or temperature).

The accuracy of the calculations is currently limited by several factors. First, there is only one projection from which to measure the droplet geometry at any given time. Adding a second or third camera with a similar resolution could significantly improve the analysis by offering an average picture of the CLB and help identify pinning events. The camera themselves can also be improved to avoid limitations inherent to the number of pixels available for the data analysis. This can be easily addressed by upgrading the camera with a model that has higher speed and resolution. The orientation of the cameras can also be readily adapted to view the footprint of the CLB or a side view depending on the needs of the experiment.

Finally, the flexibility of the setup makes it an ideal tool to adapt to different types of systems. With measurements involving LIS, for example, large extensions can lead to higher droplet mobility and a smaller signal on the force sensor. Hence, a compromise has to be found in order to achieve repeatable measurements. For longer sets of measurements, using a glycerol solution instead of water reduces evaporation to a workable level over the timescales of the experiment.

In conclusion, we propose a fully motorized setup to track the characteristics of CLBs between any two surfaces of interest. The setup is relatively inexpensive, comparable to the cost of an analytical balance. Its configuration is flexible, and it is particularly suitable for measurements were a high force sensitivity is required.

The supplementary material contains two video files of the example successful measurements (description is available in Sec. SM1), the LabVIEW scripts for operating the setup and capturing the data (Sec. SM2), and the Python scripts for the data analysis (Sec. SM3).

The authors would like to thank Gary Wells for his advice on equipment purchase and 3D printing components. They would also like to thank the electronic and mechanical workshops in the Department of Physics for creating and advising on many of the custom parts mentioned in the text. S.J.G. gratefully acknowledges the EPSRC for funding through the SOFI (Soft Matter and Functional Interfaces) Center for Doctoral Training (Grant No. EP/L015536/1).

The authors have no conflicts to disclose.

S.J.G., H.K., and K.V. designed the experiments. S.J.G. performed all the measurements. S.J.G. analyzed the results with help from H.K. and K.V. S.J.G., H.K., and K.V. wrote the paper.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.