Study of the Contact and the Evaporation Kinetics of a Thin Water Liquid Bridge between Two Hydrophobic Plates

The evaporation of sessile water droplets on hydrophobic surfaces is a topic which led to numerous investigations. However, how does the liquid behave when the evaporation occurs between two of these particular substrates? The drying stage is governed by capillary phenomena which takes place in a confined space. In the field of material shaping, it is also possible that some regions of a green body exhibit hydrophobic properties. As part of a better understanding of the local mechanisms during drying, liquid bridges have been reproduced in an ideal case. Drying kinetics and parameters measurements from 303 to 343 K (relative humidity of 55%) of deionized water liquid bridges between two plates of hydrophobic substrates are presented. Experimental work was carried out using a specific device to create liquid bridges, coupled with image analysis within an adapted instrumented climatic chamber. While the volume and the exchange surface of liquid bridges decrease regularly throughout the process, contact angles constantly diminish and more significantly at the end. This is different from the evaporation between two hydrophilic plates. From these measurements, the change of curvature of the liquid bridges during evaporation is highlighted.


Introduction
Hydrophobic materials arouse interest as their applications are widespread, from limiting friction in the aeronautic field, self-cleaning surfaces or modifying heat transfer properties. The main interesting characteristics are then the static con-tact angle and tilting angles. However, how does the liquid evaporate from these surfaces? The behavior of a liquid deposited on a solid substrate depends on its wetting properties. The investigation of liquid/solid interfaces was widely discussed in the literature [1] [2], but still remains a current topic. Wetting phenomena, and the resulting surface forces are responsible for many crucial effects in material science, such as capillary actions (adhesion forces between a liquid and a solid or between two solids) and dynamic liquid flow (impregnation, drying) [3] [4]. Among the different types of contacts that can be realized, an increasing interest appears for the study of hydrophobic surfaces (contact angle with water > 90˚) [5] [6] [7]. These surfaces often mimic nature, for instance the super-hydrophobic surface of a lotus leaf (Figure 1(a)). Such materials can be created using several methods, among which surface treatments, coatings or by controlling the initial composition. These water-repellent surfaces have widespread and practical applications, as self-cleaning materials, limiting the fog or the deposition of dirt, preventing frost formation. Recently, hydrophobic materials, coatings, textured surfaces were used in microelectromechanical systems and in microfluidic fields. Indeed, they promote dropwise condensation instead of liquid spreading, which prevents water damage in electronics ( Figure 1(b)). In the case of a microfluidic device, they greatly facilitate liquid flow by eliminating the capillary forces, whereas hydrophilic materials usually prevent liquid displacement at local scales (Figure 1(c)). In this study, the evaporation of liquid bridges between two hydrophobic substrates and under various temperatures of the drying air is investigated. In particular, focus is made on the local capillary phenomena during the departure of the liquid phase.
When temperature evolves, surface tension at the liquid/gas interface is modified [8]. Recently, experimental studies pointed out that relative humidity was (a) (b) (c) Figure 1. Three examples for the use of hydrophobic surfaces: (a) an almost spherical water droplet deposited on an hydrophobic lotus leaf, the leaf surface has a multiscale texturing with spikes at a micrometric scale and wires of stearic acid at a nanometric scale which produce superhydrophobicity (image acquistions realized with an optical camera and ESEM equipment described in the materials and methods section); (b) hydrophobic materials are used in electronic devices in order to prevent any damage from water or water based liquids; (c) microfluidic channel using hydrophobic materials in order to ease the flow in confined geometries.

Materials and Methods
We encourage the interested reader to find more details about the specific device used in this study in our previous work [11].

Climatic Chamber
Experiments are made within an environmental chamber presented in Figure 2, at a given temperature between 303 and 343 K (accuracy of 0.1 K) and a fixed relative humidity of 55% (accuracy of 0.1%) which are controlled by computer.
The zero diopter glass door allows the observation of the liquid bridges during the drying stage.
In order to create liquid bridges in hydrophobic contacts, a specific module was created and is described in the following section.

Liquid Bridges Creation
A detailed view of the specific liquid bridges creation module is presented in Figure 3 and illustrated in the case of a liquid bridge between two hydrophobic substrates. This module includes a rotating movable part attached to a fixed  frame. The movable part can make a vertical translation using a 20 mm ± 1 μm of travel micrometer, and a rotation with an accuracy of 0.1˚ along an axis perpendicular to that of the translation. The two required substrates are fixed on the system and their parallelism is checked using the optical camera. After a pendant drop was slowly deposited on the lower substrate, the upper substrate is moved towards the drop and the liquid bridge is created. An Eppendorf Multipette ® plus allowed to create pendant drops with an initial volume of 4 μL with a precision of 1%. Deionized water (conductivity < 1 mS•m −1 ) was used for drops and for the water tank providing humidity into the climatic chamber, thus the studied liquid and surrounding vapor have the same composition. Water density is of 1.000 ± 0.005 g•mL −1 at 293 K and for the presented work it can decrease to 0.977 ± 0.005 g•mL −1 at 343 K.

Substrates
In this study, four different substrates have been used. To illustrate the transition between hydrophilic and hydrophobic contacts, silicon wafer substrates were

Image Acquisition
A high resolution monochrome camera with charge-coupled device (CCD) was used, model UI-148SE-M from manufacturer IDS Imaging. The camera has a 5 M pixel 1/2" sensor, a resolution of 2560×1920 pixels and a rate of 6 images•s −1 .

Liquid Bridge Volume and Area Evaluation
The volume and the area of the liquid bridge during drying are evaluated. These measurements consist in a three steps procedure. First, liquid bridges with an initial volume of 4.0 μL ± 0.1 μL were produced and observed during drying (varying the initial volume is investigated in our previous work in the case of hydrophilic contacts [11]). The dimensions are given in Figure 5  Liquid bridges are observed until they break. No measurements are performed after the liquid bridges breaking. The measurements presented in the following section are realized at a fixed relative humidity of 55%.

Contact Angle Hysteresis
Before any evaporation study, the behavior between the different substrates was  Figure 6, accompanied with the corresponding images. In the case of silicon wafer (Figure 6(a)), the four initial contact angles are about 42˚. By compressing the liquid bridges to a separation distance of 0.5 mm, contact angles slightly increase to 44˚. Then, stretching make them decrease to about 30˚.
Finally, the contact angles remain constant with a value around 30˚ until the liquid bridge breaks.
For PTFE substrates (Figure 6(b)), upper and bottom contact angles do not behave in the same way. After the contact is realized, the upper contact angles proposed so as to observe the liquid bridges during evaporation.

Liquid Bridge Volume and Exchange Surface Evolution
Liquid bridges have been created between four pairs of parallel and identical plates (silicon wafer, PTFE, organosiloxane gel, superhydrophobic coating). As presented in the hysteresis study, the substrates can present hydrophilic or hydrophobic contacts with deionized water. Thus, the resulting shape of the liquid bridges differs from one pair of substrates to another, as illustrated Figure   7.
From the image acquisition, the evolution of different geometrical parameters was followed ( Figure 8).
In this study, the liquid bridges height used is 0.5 mm. The initial inserted volume to create the liquid bridge was 4 μL. From these conditions, liquid bridges were evaporated, at temperatures from 303 K to 343 K and at a fixed relative humidity of 55 % (variations of relative humidity were previously discussed in a recent study [11]). The results are given in Figure 9.    (Figure 9(d)) are higher (>2 mm 2 ). This is due to the formation of a droplet which still presents a hydrophobic state between the two substrates.
These different variations are dictated by the nature of the contact between the substrates and the liquid. In order to gain a better understanding of the drying behavior, the observed contact angles were measured. The results are the subject of the following section.

Contact Angle Evolution
From image acquisition, the four contact angles of each observed liquid bridge were evaluated by image analysis. Compared to the hysteresis study presented in the first part, here the liquid bridge is compressed to a height value of 0.5 mm.
When evaporating, the liquid bridge volume decreases and according to the wettability of the contact, it can be more and more in tension, which is similar to the stretching stage previously described. The results between silicon wafers come from a previous study and are presented in Figure 10. In a first step, from the initial values usually between 20˚ and 40˚, contact angles slightly decrease.
Then, when the liquid bridges become unstable and are about to break, the contact angles decrease drastically. The behavior does not change with temperature.
One of the four contact angles may present a different evolution compared to the others, due to the pinning of the contact line around the observed region, as noticed for the liquid bridge evaporation at 313 K. This reveals a local change of the surface state.
The results obtained on PTFE substrates are presented in Figure 11. Initial contact angles values are usually between 60˚ and 80˚. Whatever the temperature is, the behavior is unchanged. Unlike the silicon wafer substrates, the four contact angles decrease during all the drying process. Figure 10. Evolution of the four contact angles of liquid bridges between two plates of silicon wafer, from 303 K up to 343 K at fixed relative humidity of 55% and a liquid bridge height of 0.5 mm. Figure 11. Evolution of the four contact angles of liquid bridges between two plates of PTFE, from 303 K up to 343 K at fixed relative humidity of 55% and a liquid bridge height of 0.5 mm.
The same behavior is observed in the case of organosiloxane gel substrates ( Figure 12), from initial contact angles values around 100˚ to the separation values under contact angles values of 50˚.
This decrease in contact angle is reflected by the change of curvature of the deionized water liquid bridge through the drying stage, where the exchange surface evolves from a convex shape to a concave shape, as illustrated in Figure 13 in the case of organosiloxane gel substrates at a temperature of 323 K and a fixed relative humidity of 55%.
The results obtained on super hydrophobic substrates in Figure 14. Initial contact angles values are usually between 130˚ and 150˚. Between two superhydrophobic plates, the contact angles almost do not vary and the wettability conditions stays hydrophobic, except at the very end of the liquid bridge existence where a slight decrease is observed before creating a unique residual sessile drop on one of the two surfaces, contrary to the other three substrates. However, at Figure 12. Evolution of the four contact angles of liquid bridges between two plates of organosiloxane gel, from 303 K up to 343 K at fixed relative humidity of 55% and a liquid bridge height of 0.5 mm. Figure 13. Evolution of curvature of a 0.5 mm height deionized water bridge between two plates of organosiloxane gel, at a temperature of 323 K and a relative humidity of 55%. Generally, a change of curvature during drying occurs for the substrates with the largest gaps when realizing the hysteresis study, according to Figure 6. The liquid develops a greater affinity with the substrates for these surfaces, which leads to suggest that these particular evolutions are not necessary due to the rugosity but mostly to their surface chemistry.

Research Interest and Future Work
This study points out that even in the particular case of hydrophobic contact, a higher affinity for those particular substrates will lead to more hydrophilic con-  [20].
Yet, there is still no general approach to reproduce all the effects due to the inte-raction between the liquid and the air or the substrate. This study is part of a project which aims at providing data for these new innovative models.

Conclusion
Using a specific device to create liquid bridges within a humid environment and between hydrophobic surfaces, values of geometrical parameters, namely the volume, the exchange surface and contact angles of liquid bridges as a function of the drying time have been evaluated for temperatures from 303 to 343 K and a fixed relative humidity of 55%. Drying time decreases when temperature increases. The measurement of the four contact angles at a given time reveals that they don't always follow the same trend, due to different substrate surface states.
More precisely, a change of curvature is observed in the case of hydrophobic substrates. This suggests that even in the case of a liquid contained between locally hydrophobic regions, an affinity or a pinning can occur during drying, leading to classic concave menisci shapes observed in the case of hydrophilic contacts. Finally, the proposed study aims at providing new data for innovative models close to real cases, such as liquid flows and liquid evaporation in the particular case of hydrophobic materials.