Determination of the hysteresis of the contact angle of wetting of boiling surfaces

. For a deeper understanding of the fluid dynamics and heat transfer in the transition layer, when studying the dynamics of a two-phase flow during boiling and a heat transfer crisis, i


Introduction
Heat-exchange devices of the new generation, as a rule, have high heat fluxes and impulse loads with relatively small sizes of fuel elements.This situation is typical for electric vehicles, avionics, industrial lasers, equipment for wireless telecommunications networks and radars, including defence ones.The 3D architecture of today's high-performance chip packages also requires nextlevel thermal management solutions.Liquid boiling in mini-and microchannels is a promising method for cooling electronic and microelectronic equipment [1].The use of the latent heat of vaporization during boiling provides a much greater cooling capacity than just a single-phase flow, which allows the use of small liquid mass flow rates.
World trends in the study of heat transfer processes are focused on the miniaturization of heat exchangers.The use of micro and nano coatings can significantly improve the energy efficiency of new generation heat exchangers.Graphene coatings and coatings based on highly thermally conductive nanotubes require detailed study.The effect of graphene coatings on high-volume boiling characteristics is currently being extensively studied.Researchers are trying to determine the mechanisms of heat transfer enhancement and find the most suitable method for applying graphene coatings, which would be easily scalable, inexpensive, and ensure the durability of coatings.Zhou et al. [2] when boiling water in a large volume, the surface with the optimal graphene layer made it possible to increase the critical heat flux by 104%, and the heat transfer coefficient by 73% compared to the uncoated copper surface.The improvement in heat transfer characteristics on this surface was explained by the formation of an interconnected multilayer graphene oxide film with high thermal conductivity and its moderate thickness, which contributed to the formation of bubbles and the rapid rewetting of local dry areas, which led to a delay in the onset of the film boiling regime.Ahn et al. [3] studied the effect of graphene film thickness on heat transfer during boiling in a large volume.The improvement of heat transfer on the graphene-coated surface asymptotically continued with an increase in the coating thickness to 150 nm, both in terms of the heat transfer coefficient and the critical heat flux.The increase in the heat transfer coefficient was explained by the decrease in wettability and the bending of the edges of the reduced graphene oxide flakes, which led to a decrease in the diameter of the detached bubbles and an increase in the frequency of bubble formation.The dependence of the critical heat flux on the thickness of the graphene film is explained by the authors by thermal conductivity: the film prevented the formation of hot local regions, which led to an increase in the critical heat flux.Boiling on graphene-coated surfaces was studied in [4] by soaking in a solution with graphene flakes.An increase in critical heat flux and heat transfer coefficient of 42% and 47%, respectively, compared to a smooth surface, was obtained with the shortest surface coating duration.The authors came to the conclusion that the change in the contact angles compared to the uncoated surface was not the main reason for the intensification, while the main reason was the increased surface roughness with a short exposure of the samples.The joint effect of a porous copper coating with graphene nanoplates was carried out in [5].Composite coating graphene-copper (GNP-Cu) was obtained by sintering to improve heat transfer when boiling in a large volume.An increase in critical heat flux and heat transfer coefficient of 91% and 438%, respectively, was observed compared to the uncoated copper surface.The porous structure of the composite surface contributed to the formation of very efficient liquid supply and vapor evacuation pathways, E3S Web of Conferences 459, 08001 (2023) https://doi.org/10.1051/e3sconf/202345908001XXXIX Siberian Thermophysical Seminar while the graphene particles (GNP) also contributed to the formation of a super-hydrophilic coating with a higher absorption rate.A clear correlation was observed between the bubble dynamics and the critical heat flux, as well as with the heat transfer coefficient.
The above review of works demonstrates that a deeper understanding of fluid dynamics and heat transfer in the transition layer is needed -in the region of the dynamic gas-liquid-solid contact line and the adjacent meniscus characterized by an apparent contact wetting angle [6,7].It is known that the surface morphology significantly affects the wettability [8,9] and the intensity of heat transfer during boiling.An important feature of boiling two-phase flows is the fact that the contact angle is dynamic, i.e. depends on the speed of the contact line.There are other factors that significantly affect the dynamic contact angle, such as roughness, morphology, porosity.It is currently almost impossible to correctly choose a universal relation for the dynamic contact angle in some specific situation.We can note the simplified model proposed by Kistler [10], in which the value of the contact angle is chosen based on the direction of movement of the contact line, on the basis of the equilibrium value of the contact angle and the capillary number.A more complex model is presented in [11].
The aim of this work is to analyse wettability, contact angle hysteresis, and surface morphology for further investigation of two-phase flow dynamics during boiling and heat transfer crisis.A graphene-coated copper substrate sample, a nanotube surface, and an uncoated copper surface for comparison will be considered.

Research methodology
The surface morphology of the studied samples was observed by scanning electron microscopy (SEM) in Jeol JSM 6700F (Jeol, Japan) in secondary electron mode at accelerating voltage of 15 kV at view field of 4,5x4,5 µm 2 .Micrograph of the Cu substrate obtained using a scanning electron microscope is shown in fig.1a.It can be seen that the surface is quite flat and there are groove traces on it from mechanical polishing.For the second sample, the copper surface was coated with horizontally oriented multi-walled carbon nanotubes by sputtering.The coating thickness was about 1 μm.The root-mean-square surface roughness was about 62 nm.Surface morphology of CNTs coating shown in fig.1b.Consisting from thin tubes, CNTs coating repeat and smooth the surface morphology of the copper substrate.The surface of the copper substrate was also coated with graphene by chemical vapor deposition technique [12].It is assumed that the synthesis of graphene on copper occurs through the process of surface adsorption [13,14].Polished (rms roughness about 50 nm) round copper columns 10 mm high and 20 mm in diameter were used as the substrate.The substrate was subjected to chemical polishing to reduce the surface roughness.The substrate was then cleaned in an ultrasonic bath.After cleaning, the substrate was placed in a CVD reactor and annealed for 25 minutes in a hydrogen atmosphere at a temperature of 1050°C.During annealing on the substrate surface, copper oxide was reduced to metallic copper, thus changing the crystal structure of the surface.After annealing, the reactor was evacuated and filled with hydrogen and methane.Then, to saturate the copper surface with carbon, the reaction zone was heated to a temperature of 1050°C and the gas mixture flow rate was set at 0.5-1.0ml/s.After 10 minutes, the gas mixture was pumped out of the reactor, the furnace was turned off and cooled.Using the method of Raman spectroscopy, it was obtained that the synthesized graphene is a multilayer structure (approximately 6-8 layers).Figure 1с shows the structure of multilayer graphene on a copper substrate.The wettability properties of all surfaces were determined using a KRUSS DSA-100 contact angle measuring device (Fig. 2).The digital camera of the device has a recording speed of 61 to 311 FPS.The maximum and minimum frame resolutions are 780 x 580 pixels and 780 x 60 pixels, respectively.The optical system has a magnification of up to 7 times.The minimum and maximum field of view is 3.7x2.7 mm and 23.2x17.2mm, respectively.The device is equipped with a high-temperature chamber and a high-pressure chamber, which were not used in these measurements.The Kruss Drop Shape Analyzer software for measuring the contact angle makes it possible to measure the contact angle using the sessile drop or trapped bubble method, Fig. 3. Measuring range: 1-180°, resolution: ± 0.1°, five measurements were taken in one second.To determine the shape of the drop, five main selection methods are used to describe the curvature of the drop shape: by the Young-Laplace equations, ellipse, circle, as well as by determining the tangent, height and width.In this case, the method for determining the tangent uses a polynomial approximation.For surfaces with micro-, nano-roughness, the apparent contact angle is determined.The advancing and receding contact angles are determined.These angles are determined depending on the direction of movement of the gas-liquid-solid line of contact.Further, the hysteresis of the contact angle was determined as the difference between these angles.For measurements, the sessile drop method of variable volume was used.Deionized, nano-filtered water was used, obtained in the laboratory using a Milli-Q device.The experiments were carried out at room temperature 25 ±2°C.

Measurement results
As can be seen from Fig. 3, the contact angle is formed between the tangent drawn to the liquid-gas surface with the vertex located at the point of contact between the two phases and the solid surface.This angle is always measured inside the liquid phase.Wettability is determined by the interaction of gas, liquid, and solid molecules.According to Young's equation, the equilibrium contact angle is determined by the surface tension of the liquid (σlg), the interfacial tension (σsl) between the liquid and the solid, and the surface free energy of the solid (σsg): The measurement of advancing (Θadv) and receding contact angle (Θrec) on a copper surface is shown in Fig. 4. A drop of liquid is dispensed with a special syringe, the needle of which is located inside the drop in close proximity to the working surface.To measure the advancing contact angle, a drop is pumped with liquid through a needle at a constant rate.To measure the receding contact angle, liquid is pumped out of the drop at a constant rate.From Fig. 4 it can be seen that the advancing contact angle significantly exceeds the receding contact angle.Figure 5 shows the results of measuring the contact angle for a polished copper surface.The contact angle of wetting is given depending on the number of measurements, which characterizes the direction of liquid supply, i.e. inside the drop or out of the drop.It is indicated up to which dimension the water flow increases and from which dimension it begins to decrease.The measurement of the advancing and receding contact angle on a copper surface coated with horizontally oriented multi-walled carbon nanotubes is shown in Fig. 6.It is also seen that the advancing contact angle significantly exceeds the receding contact angle.Figure 7 shows the contact angle measurements for a copper surface coated with horizontally oriented multiwalled carbon nanotubes.To measure the contact angle, we used the lowest possible liquid flow rates, i.e., velocity of the gas-liquid-substrate contact line, which by themselves had no effect on the value of the contact angle.It only mattered whether the liquid wetted the sample surface or receded.This fact of the absence of the influence of low liquid flow rates on the value of the contact angle was verified experimentally by changing the flow rate by a factor of two.The measurement of the advancing and receding contact angle on a copper surface coated with multilayer graphene is shown in Fig. 8.The advancing contact angle significantly exceeds the receding contact angle, which nevertheless has a rather high value.Figure 9 shows the contact angle measurements for a copper surface coated with multilayer graphene.

Discussion of results
Data analysis in Fig. 5, 7, 9 shows that at the first moment of measurements after the creation of a drop of the required size and the beginning of liquid pumping, the contact angle slightly increases or does not change.This is due to the fact that the creation of a drop is associated with surface wetting, i.e. already in this period, the contact angle of wetting has the essence of the advancing contact angle of wetting.Therefore, after the start of liquid pumping, the angle can practically not change.This angle practically does not change its value regardless of the pumping time.The maximum average values of this angle are taken as the advancing contact angle.Averaging was performed over at least 10-15 values.The maximum size of the pumped drop in the experiments was limited to 3-4 mm.The absence of the first 50-70 measurements on the graphs above is due to the fact that this period of time is necessary for the formation of a drop of the minimum size on the surface under study and fixation of the capillary in the central part of the drop.After the liquid is pumped out of the droplet, the contact angle begins to systematically decrease and eventually reaches a minimum value, which practically does not change during several measurements.The minimum values of this angle are taken as the receding contact angle.Averaging was performed over at least 10-15 values.The diameter of the capillary for supplying liquid to the drop was 0.5 mm.The measurement of the receding contact angle was stopped when the droplet diameter became commensurate with the capillary diameter, i.e. less than 1.5 mm.
The contact angle is measured on both sides of the drop.As a rule, measurements on the right and left sides of the drop practically coincide within the measurement error of ± 0.1°.From the data in Fig. 4, 6, 8 shows that in some cases they can differ markedly.This is especially true for measuring the receding contact angle.Figures 7 and 9 show that Θrec, while remaining within certain limits, changes periodically.In our opinion, this is due to the effect of contact line engagement [8].These figures show a local change in the contact angle, i.e.only on one side of the drop.Some scatter of data for Θadv in Fig. 5, 7, 9, apparently, is also associated with this phenomenon.
Thus, although the term "equilibrium contact angle, Θe" is often used in the literature and only one value for the contact angle is given in the articles, in practice there are two angles in measurements for different surfaces.The difference between these angles is called the contact angle hysteresis ΔΘ = Θadv -Θrec.The obtained data on the contact angles of wetting are given in Table 1.It follows from the data in Table 1 that for the studied surfaces, the hysteresis ranges from 58 to 74 degrees.The presence of the contact angle hysteresis plays an important role in the hydrodynamics of two-phase systems.For example, this phenomenon allows the droplet not to change the wetted perimeter with an increase in the body force by a factor of 600 during parabolic flights [8].Dry spots in thin liquid layers also become stable due to the contact angle hysteresis [15,16].

Conclusions
The analysis of the morphology and wettability by water of three surfaces, which are supposed to be used for further study of the dynamics of a two-phase flow during boiling and a heat transfer crisis, is carried out.A sample of a copper substrate coated with multilayer graphene, a copper surface coated with horizontally oriented multiwalled carbon nanotubes, and an uncoated polished copper surface for comparison are considered.The term "equilibrium contact angle" is often used in the literature, and in many experimental articles only one value for the contact angle is often given.In practice, only two characteristic contact angles can be measured in measurements for different surfaces.
It is shown that the hysteresis of the wetting angle for these surfaces is from 58 to 74 degrees.Moreover, the maximum value takes place for a smooth copper polished surface.
It has been found that the receding contact angle is characterized by noticeable fluctuations that significantly exceed the measurement error, which can be explained by the effect of contact line engagement [8].In our opinion, this is due to the chemical inhomogeneity of the near-surface layer and the inhomogeneity of the roughness.

Fig. 3 .
Fig. 3. Determination of the contact angle of wetting.

Fig. 4 .
Lying drop of variable volume, water.a), b)measurement of the advancing and receding contact angle on a polished copper surface, respectively.

Fig. 5 .
Fig. 5. Dependence of the contact angle on the time on a polished copper surface, water.The measurement frequency is 10 fps.The average value of the angle on the left and right is taken as the measured value.

Fig. 6 .Fig. 7 .
Fig. 6.Lying drop of variable volume, water.a), b)measurement of the advancing and receding contact angle on a copper surface coated with horizontally oriented multiwalled carbon nanotubes, respectively.

Fig. 8 .
Fig. 8. Lying drop of variable volume, water.a), b)measurement of the advancing and receding contact angle of wetting on a copper surface coated with multilayer graphene, respectively.

Fig. 9 .
Fig. 9. Dependence of the contact angle of wetting on the left side of the drop on the time on a copper surface coated with multilayer graphene, water.The measurement frequency is 15 fps.

Table 1 .
Measurement data of contact angle hysteresis.