Self‐Sustaining 3D Thin Liquid Films in Ambient Environments

Abstract

Thin liquid films (TLF) have fundamental and technological importance ranging from the thermodynamics of cell membranes to the safety of light-water cooled nuclear reactors. The creation of stable water TLFs, however, is very difficult. In this paper, the realization of thin liquid films of water with custom 3D geometries that persist indefinitely in ambient environments is reported. The wetting films are generated using microscale “mounts” fed by microfluidic channels with small feature sizes and large aspect ratios. These devices are fabricated with a custom 3D printer and resin, which were developed to print high resolution microfluidic geometries as detailed in Reference 26. By modifying the 3D-printed polymer to be hydrophilic and taking advantage of well-known wetting principles and capillary effects, self-sustaining microscale “water fountains” are constructed that continuously replenish water lost to evaporation while relying on surface tension to stabilize their shape. To the authors’ knowledge, this is the first demonstration of stable sub-micron thin liquid films (TLFs) of pure water on curved 3D geometries.

Graphical Abstract

The creation of thin liquid films of water with custom 3D geometries that persist indefinitely in ambient environments is reported. The wetting films are generated using microscale 3D-printed capillaries fed by microfluidic channels with small feature sizes and large aspect ratios. These devices are fabricated with a custom 3D printer and resin.

Thin liquid films have both fundamental and practical importance in biology, chemistry, and physics. In biology, for example, TLFs are used to study pulmonary surfactants, lipid bilayers, and proteins.^[1–5] In physics, they are used to study film formation, film rupture, film stability, and film thermodynamics.^[6–10] TLFs can form in symmetric systems, in which the film is bounded by identical particles (e.g. soap films in air), or asymmetric systems, in which the TLF is bounded by different particles with potentially different phases (e.g. wetting films).

While the literature on TLF’s is vast, including 10 separate reviews on different aspects of TLF’s published simultaneously^[1], some common trends are worth highlighting to place the present results in context. Experimentally, the most widely used method to create wetting TLF’s is to force a bubble through a capillary, thereby creating a thin meniscus which is brought into contact with a polished planar surface.^[2] This method has several advantages: the planar surface allows for straightforward optical interferometry to determine film thickness, and the glass capillary allows for adjustments to the disjoining pressure via a micrometric pump. Furthermore, the planar geometry allows for close correspondence with theoretical predictions of disjoining pressure, film thickness, and line tension, properties which govern the thermodynamic behavior of the film but are difficult to calculate in curved geometries^[3]. For these reasons, this method and others similar to it have been used almost exclusively to study the static and dynamic properties of TLF’s. There are several disadvantages, however, such as the inability to form films with arbitrary 3D geometries and direct exposure to ambient environments.

The importance of water thin films has been highlighted in the recent literature, but to date their creation has been difficult owing to the instabilities caused by high evaporation rates and high surface tension.^[6,11,12] Instead, most studies of water TLFs require surfactants to reduce surface tension and use controlled humidity, temperature, and/or pressure environments to form and maintain a stable TLF.^{[2,6,11–18]} Relatively few studies of water TLFs have been performed without additives, none of which have achieved film stability without carefully controlling the surrounding environment.^[11,12] Furthermore, as noted above nearly all reported wetting TLFs of water have planar geometries constructed following the methods pioneered by Scheludko and Platikanov over 50 years ago.^[13,14]

Here we present devices that overcome these limitations by relying on well-known principles of microfluidics and surface wetting, and build upon recent work demonstrating 3D-printing of Scheludko cells and the construction of stable thin water bridges.^[19–22] As shown in Figure 1(a), the balance of surface tension and adhesion forces lead to an apparent contact angle θ* in structures where a liquid-vapor interface meets a solid-liquid interface, such as ours.^[23] As shown in Figure 1(b), these same forces also lead to well-known wetting in a capillary of radius r, causing fluid to rise to a height h as seen in Equation 1, where ρ is the density of the liquid, γ is the liquid-air surface tension, and g is the acceleration due to gravity.

$$h=\frac{2\gamma \text{cos}\left({\theta }^{*}\right)}{\rho gr}$$ (1)

Figure 1.

Wetting principles. a) Apparent contact angles. b) Capillary forces. c) Apparent resin contact angles before and after O₂ plasma treatment.

In our device design, shown in Figure 2 and Figure 3, we construct a nozzle with a central capillary that has a physical height less than h, allowing water to fill the capillary. At the top of the capillary, a microdroplet may be formed by applying external pressure, as shown in Figure 2(a) but is nominally pinned by the corner boundaries at the top of the capillary. ^[24] By exposing the polymer surface to an oxygen plasma, however, the apparent contact angle may be reduced, as shown in Figure 1(c), and water may overcome the pinning, thereby wetting the surface as shown in Figure 2(b). Such a film, however, will undergo rapid evaporation and become depleted. As shown in Figure 2(c), this depletion is eliminated by allowing the film to self-replenish from a local reservoir connected to a closed wetting path. Such a film is self-sustained by surface tension and wetting effects alone, requiring no external pressure. This has the practical advantage of creating a thin film whose shape is also entirely determined by local intermolecular forces and gravity. By creating the device at a sufficiently small scale, where a low Bond number ensures that surface tension is much stronger than gravity, very stable TLFs may be constructed.^[25]

Figure 2.

Design motivation cross sections. a) Microdroplet pinning at nozzle opening. b) Thin wetting film. c) Our passively replenishing thin film device.

Figure 3.

Fabricated device. a) CAD rendering of device with cutout to show channels. b) Scanning electron micrograph of printed device. c) Optical image of operating, wetted device.

There are two primary conditions for successful device operation:

1. The rate of water replenishment must be must faster than that of evaporation.

2. The water must overcome the corner boundaries introduced by the 3D printing process to completely wet the surface.

First note that the Bond (Eötvös) number ΔρgL²/γ for our devices is approximately 10⁻⁶, indicating that the surface tension forces dominate gravity in these devices. Ignoring gravity, some simple calculations can provide an understanding of the evaporation rate relative to the rate of water flow through the capillary.

The evaporation rate around the spheroid may be approximated using Fick’s law:

$$\frac{dm}{dt}=\rho \frac{dV}{dt}=-D\int \nabla c\cdot dS=-D\int \frac{dc}{dn}dS,$$

Where m, ρ, V are the mass, density, and volume of the liquid, n is the normal vector, D is the diffuision coefficient of the vapor, and c its concentration. We can approximate the concentration gradient at the air-liquid boundary as

$$\frac{dc}{dn}\approx \frac{c_0-c_{\infty }}{r},$$ (3)

Where r is the radius of the wetted spheroid and c₀ and c_∞ are the vapor density at the air-liquid interface and at infinity. This then gives an evaporation rate of approximately

$$\frac{dm}{dt}=4\pi rD\left(c_0-c_{\infty }\right),$$ (4)

which is proportional to the radius of the spheroid. Using our device parameters of r = 145 μm, D = 0.282 cm²/s, and c₀ = 23 g/m³, and c_∞ = 0 (to model the fastest possible evaporation rate), we obtain dm/dt = 1.18μg/s. Thus to maintain a constant shape on the spheroid, the device must be capable of drawing much more than 1 – 2 μg of water from the reservoir every second. The penetration length L of a liquid through a capillary in time t can be calculated using the Washburn equation:

$$L=\sqrt{\frac{\gamma \mathit{\text{rtcos}}\left(\theta *\right)}{2\eta }},$$ (5)

where θ* is the contact angle, γ is the surface tension, r is the radius of the capillary, and η is the dynamic viscosity of the liquid. Inserting our device parameters we obtain V/t = 1.34 mg/s. This is approximately 1000 times larger than the water lost due to evaporation, and accounts for the stability of the device.

The more constraining condition is (2), requiring water to completely wet the device and overcome pinning at the corner boundaries. The condition for a liquid with a native contact angle θ* to invade a corner boundary and thus wet the surface is that the solid-liquid angle must exceed a critical angle θ^C defined by

$${\theta }^C=\left(180-\varphi \right)+\theta *,$$ (6)

where ϕ is the angle of the corner boundary relative to a flat surface. This implies that a very hydrophilic device is desirable to reduce the critical angle. Experimentally we found that the plasma treatment along with the fillet at the top of the capillary is sufficient to enable complete wetting of the device.

Figure 3(a) shows a 3D rendering of our device design with a cutout to show the channels. Using OpenSCAD, a free open-source scripting 3D modeling software, we designed a conical frustrum with a 140 μm diameter vertical channel. A rectangular channel cutting through the bottom of the frustrum allows water to enter the vertical channel from the base. At the top of the frustrum is a spheroid with a 290 μm diameter. To decrease pinning, a circular fillet was added at the sphere and frustrum interface. Another fillet was added to the top of the sphere interfacing the sphere and the vertical channel.

The devices were fabricated using a recently developed custom 3D printer^[26–28], and the fabrication process is described in the Experimental Section below. Figure 3(b) shows scanning electron micrographs of a printed device. Each vertical layer in the print is 3 μm, and is visible in the images. Notably, the custom digital light processor stereolithographic (DLP-SLA) 3D printing process creates many pixel and layer corner boundaries on the surface of our devices, which are visible in the SEM images. As described above, we enable the wetting film to overcome these boundaries by exposing the devices to an oxygen plasma in a Technics PEII plasma etcher for two minutes at 200 W. This reduces the apparent contact angle on the device polymer from 43° to 11° as shown Figure 1(d). The contact angles were measured using DropSnake, an open source program which uses B-splines to determine the contact angle.^[29] The reduction in contact angle is temporary, lasting 8–10 hours, after which apparent contact angle reverts to its nominal value when exposed to air contaminants. However, when stored in water the apparent contact angle remains small and hydrophobic recovery diminishes. ^[30,31]

Figure 3(c) shows an optical image of a functioning device, wetted with approximately 10 μL of deionized water with a resistivity of 18 kOhms.

To study the thickness and stability of the TLF in our devices, we obtained computer vision images of dry and wet devices and performed digital subtraction as shown in Figure 4 and Figure 5. We note that many studies use interferometric imaging to measure the disjoining pressure and film thickness.^{[6,10,11,13–19,32–35]} Though interferometric techniques can be more accurate, they usually require at least one surface of the film be planar, thus making them unsuitable for analyzing our 3D devices.

Figure 4.

Steps for film thickness analysis through digital subtraction. Raw color images converted to grayscale, then black and white pixels using a binary thresholding function with midpoint of averaged values in paired yellow boxes (rows). Dry device image with standard 125 μm optical fiber for calibration, images of device in dry and wet states for subtraction (columns).

Figure 5.

(a) Example grayscale slices of dry and wet state device images used for film thickness measurements. Threshold value indicated in red and transition region in cyan on both the plot and the grayscale slices. Yellow boxes and lines show where on the device the 40-pixel samples were taken. Film thickness is the difference between the two red pixel positions. (b) Mechanical probe of film thickness at a single location, details described in text.

We perform several steps to achieve digital subtraction with maximum resolution. First, raw color images of a device in dry and wet states were captured (Figure 4 first row) using the same imaging setup describe above. A dry device image with a standard optical fiber of diameter 125 μm is also captured for calibration. The color image is then converted to grayscale with pixel values ranging from 0 to 255 (Figure 4 second row) using the Open Computer Vision library in Python. A binary thresholding function then converts each pixel to either black or white (Figure 4 third row). To obtain a threshold, grayscale pixel values within the paired yellow boxes shown are averaged and the midpoint of the two averages is used as the threshold.

An example of a horizontal grayscale slice of an image and the result of the threshholding function is shown in Figure 5, with the calculated threshold value indicated in red. To capture the images, we used a microscope objective with a numerical aperture (NA) of 0.28, giving a lateral Rayleigh resolution 0.61 λ / NA of approximately 1.4 μm. This matches well with the measured 80% transition values of 1.6 μm for the dry device and 1.4 μm for the wet device shown in cyan in Figure 5.

The CMOS camera used has a 0.16 μm pixel size, which is well below the diffraction limit.

We note, however, that the resolution limit in our setup is determined by the pixel size of the camera, not the Rayleigh limit of the imaging system, as demonstrated using similar thresholding techniques^[36]. This is because we are subtracting the centroids of single well-defined transition curves from light to dark for two separate images (wet and dry) rather than resolving two closely spaced objects simultaneously illuminated, as shown in Figure 5. The resolution enhancement is similar to any optical technique that relies on shifts in well-defined response functions, such as the sinusoidal signals from optical interferometers, which can measure relative distances much shorter than optical wavelengths.

An estimate of the film thickness was obtained by subtracting the thresholded edges of the wet and dry images. To obtain film thickness measurements as a function of time, video images were captured and processed in the same fashion. To further reduce noise, we averaged the film thickness over 9-frame intervals. Using this computer vision technique, we were able to analyze the dynamics of the film in a variety of scenarios including equilibrium and non-equilibrium states. Table 1 lists the repeatability of the film thickness at three locations on the device under static conditions for five independent measurements. To obtain each measurement, the device was dried and then re-wet with a small volume of water and allowed to come to an equilibrium state. The results indicate a highly repeatable film thickness, approaching the 0.16 μm limit of the camera, near the middle of the structure where the thinnest film is present. The increased repeatability of the thinnest films is expected since thicker films are influenced more by gravity and the amount of water in the reservoir.

Table 1.

The repeatability of the formation and measuring of the film thickness of our device is demonstrated through five independent measurements taken at different locations on the spheroid of the device.

Film thickness measured at device spheroid [μm]
Measurement #	Top	Middle	Bottom	Neck
1	2.19	0.53	1.62	15.91
2	2.29	0.54	1.79	15.76
3	2.28	0.56	1.42	16.63
4	1.94	0.54	1.73	16.98
5	2.16	0.53	1.54	14.12

Long term TLF stability was also measured, as shown in Figure 6 and Figure 7, which shows the film thickness of a single wetted device over approximately 2-hour measurement period. During the measurement period, the TLF was occasionally disturbed from equilibrium and allowed to relax back to its equilibrium state. This was achieved by dropping small amounts of water to the top of the wetted device using a 10 μL pipette, and appear in the data as spikes in the film-thickness measurements. Near the end of the 2-hour experiment, water in the reservoir was allowed to evaporate in order to observe the film depletion during drying of the device. We note that the TLF thickness is robust to disturbances and remained stable in an ambient environment for the duration of the experiment.

Figure 6.

Long term film thickness stability. Standard deviation in yellow superimposed onto raw film thickness data.

Figure 7.

a) Long-term film stability at four device locations, showing robustness despite disturbances to film equilibrium introduced by dropping water on the device the device. Spikes in each of the four plots show disturbances introduced by dropping water on device. b) Wetted device with submerged device edge shown by white vertical line. Colored horizontal lines indicate where measurements were taken. c) Diagrammatic description of pixilation effects of the CMOS camera leading to data discretization, explained in the main text. d) Images of device at three time stamps during the evaporation of water from the device reservoir. e) (top) Data from red plot in panel (a) vertically magnified to show data discretization from camera pixilation. (bottom) Discretized horizontal shift in device from hygroscopic absorption of water, showing that discretization in film measurement is due to camera pixilation.

Owing to the finite pixel size of our CMOS camera, the film thickness measurements are discretized into 0.16 μm increments. This is especially noticeable for the thinner film thickness, as shown in Figures 6–7. Figure 7 diagrammatically describes the effect of camera pixelation on the measured data and is explained below.

The measurement is further complicated by hygroscopic swelling of the device polymer during the duration of the experiment. The PEGDA material is a polymer with molecular-scale voids making up approximately 2.5% of the total volume^[37]. As water is absorbed into these voids, material strain causes the device edge to move within the camera frame over time. This movement is carefully tracked in our computer vision analysis, and the horizontal shift of the device over time can be seen in the lower (black) plot of panel (e) in Figure 7. As the device edge shifts, it traverses the pixel divisions of the CMOS camera as shown in panel (c) of Figure 7, resulting in pixelation instability. We note that the resulting 0.16 μm “jumps” are seen at all film thickness and represent the level of uncertainty of any individual measurement before averaging.

By tracking the vertical motion of the device from hygroscopic swelling we can quantify the diffusion coefficient of water within our custom PEGDA polymer. Figure 8 shows the vertical strain recorded in the device during the two-hour experiment reported in Figures 6–7. Since the horizontal device dimension is significantly less than the vertical dimension of the device and the base layer of PEGDA, the strain resulting from hygroscopic swelling is much larger vertically than horizontally, as shown in Figure 8.

Figure 8.

Vertical strain caused by hygroscopic absorption in the PEGDA. Note that spikes correlate to intentional reservoir disturbances, as explained in the main text.

To measure the film thickness accurately, we accounted for both the vertical and horizontal strain by tracking the position of unique features of the image throughout the measurement. Specifically, we used the light shining through the center of the wetted device which can be seen in the bottom center of Figure 7 as our tracked feature, and tracked the offset of each frame relative to a reference frame using a mean squared error (MSE) statistical estimator, resulting in an error of 1.4% throughout thousands of frames.

To analyze the rate of hygroscopic swelling, we fit the measured strain to a one-dimensional solution of Fick’s second law:

$$\frac{m\left(t\right)}{m_{sat}}=1-\frac{8}{{\pi }^2}\sum _{n=1}^{\infty }\frac{1}{{\left(2n-1\right)}^2}exp\left\{-{\left[\frac{\left(2n-1\right)\pi }{2L}\right]}^{2}Dt\right\} ,$$

where m(t)/m_sat is the mass ratio of the device at any given time to a completely saturated device, L = 800 μm is the vertical dimension of the PEGDA polymer, and D is the fitted mass diffusivity, which we report to be 6.29×10⁻¹¹ m²s⁻¹ with a 2% error in the fit. Since absorbed mass is known to have a linear relationship with hygroscopic strain in similar polymers, we also infer the coefficient of hygroscopic swelling, β, to be 16.5.

As a second measurement to verify the accuracy of the video analysis method described above, we used an optical fiber with an etched end of known dimensions to mechanically probe the fluid film thickness. The fiber probe was mounted on a stage with 20 nm relative position accuracy and the position of the fiber tip at the edge of the dry device edge was recorded. The fiber tip was then retracted, the device wet with water, and then the fiber tip translated horizontally until wetting of the fiber occurred. The method is illustrated in panel (b) of Figure 5, and agrees remarkably well with the image analysis technique.

In conclusion, we have demonstrated for the first time the creation of sustained, thin liquid films of water in curved geometries. We characterized the film thickness and stability and showed that it is stable even in the presence of evaporation and disturbances in an ambient environment.

The results show that devices demonstrated in this work are able to maintain a submicron curved TLF of water even while open to ambient environments and in the presence of external disturbances. To our knowledge, no other technique of creating a TLF is capable of such a level of control over the shape of the TLF and suggest that this technique may be robust enough for use in portable systems, such as lab-on-a-chip applications.

It is anticipated that several fundamental and applied studies may now be possible using this new technique. For example, recent discoveries have shown that the effective surface tension of liquid films is dramatically reduced when the film thickness is less than approximately 1 μm.^[33,38,39] To date this effect has only been studied in planar geometries, but our devices may allow for studies in curved geometries relevant to many biological systems.

As a final observation, we note that we also tested our device with other fluids with much lower evaporation rates, such as paraffin oil. In such cases, the device was also able to sustain TLF with similar characteristics, indicated potential applications using a variety of fluids.

Experimental Section

To fabricate the devices, which have very challenging dimensions, we used a custom digital light processor stereolithographic (DLP-SLA) printer with a 385 nm LED light source and a pixel pitch of 7.6 μm in the plane of the projected image.^[26] We used a custom photopolymerizable resin consisting of poly(ethylene glycol) diacrylate (PEGDA, MW258) with a 1% (w/w) phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (Irgacure 819) photoinitiator and a 2% (w/w) 2-nitrophenyl phenyl sulfide (NPS) UV absorber. The 3D-printed devices were fabricated on diced and silanized glass slides.^[26] Each slide was prepared by cleaning with acetone and isopropyl alcohol (IPA), followed by immersion in 10% 3-(trimethoxysilyl)propyl methacrylate in toluene for 2 hours. After silane deposition, the slides were kept in toluene until use. Each build layer of the print is exposed to a measured optical irradiance of 21.2 mW cm⁻² in the image plane for 400 ms. After printing, unpolymerized resin in interior regions is gently flushed with IPA, followed by device optical curing for 30 minutes in a custom curing station using a 430 nm LED having a measured irradiance of 11.3 mW cm² in the curing plane.

Images are captured with with a CMOS color camera with a resolution of 1280 × 1024 pixels through a 10X plano apochromatic microscope objective with a numerical aperture (NA) of 0.28 and a flood light source with a center wavelength of approximately 650 nm