The theory of the surface wettability angle in the formation of an oil film in internal combustion piston engines

doi:10.21203/rs.3.rs-2609101/v1

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The theory of the surface wettability angle in the formation of an oil film in internal combustion piston engines

https://doi.org/10.21203/rs.3.rs-2609101/v1

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published 24 Nov, 2023

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In internal combustion piston engines, the formation of an oil film is completely different than in industrial machines. The molecular adhesion force at the interface between the surface coating of engine parts and the lubricating oil determines the load-carrying capacity and the ability to form a lubricated film. The geometry of the lubricating wedge between the surfaces of the piston rings and the cylinder wall is created by the thickness of the oil film and the height of the ring's coverage with lubricating oil. This condition is affected by many parameters characterizing the engine operation and physical and chemical parameters of the coatings of the cooperating pairs. For lubricant particles reaching high energies higher than the potential energy barrier for adhesive attraction at the interface, slippage occurs. Therefore, the value of the contact angle of the liquid on the surface of the coating depends on the value of the intermolecular force of attraction. According to the author, there is a strong relationship between the contact angle and the lubrication effect. The paper shows that the surface potential energy barrier is a function of the contact angle and contact angle hysteresis (CAH). The innovation of the work consists in examining the contact angle and CAH in the conditions of thin layers of lubricating oil in cooperation with hydrophilic and hydrophobic coatings. The thickness of the lubricant film was measured under various speed and load conditions using optical interferometry. The work shows that CAH is a better interfacial parameter to correlate with the effect of hydrodynamic lubrication. The paper presents mathematical relationships in relation to a piston engine, various coatings and lubricants.

Physical sciences/Materials science

Physical sciences/Engineering

Physical sciences/Engineering/Mechanical engineering

friction losses

contact angle hysteresis

film thickness

critical shear stress

wettability

In internal combustion piston engines there are changes in hydrodynamic pressure in the engine work cycle. These changes have a special effect on the coverage of the piston, piston rings and cylinder liner with an oil film. The value of these changes depends on many geometrical parameters of the engine's structural elements, parameters of its operation and chemical parameters of the lubricating liquid. The properties of the surface of the material, mainly hardness, roughness, Young's modulus and surface energy, also have a significant impact on the distribution of the oil film. Many authors focus their attention on the design of the surface topography, ignoring the important parameter, which is the hydrophilic and hydrophobic properties of the coatings. The impact of these parameters, as indicated by the author's earlier works, is very important and should not be overlooked [1]. Contact angle hysteresis (CAH) is one of the most important and classic elements of liquid droplet wetting in tribological systems. There are many papers on CAH determination [2],[3],[4]. According to the papers [5], [6], [7], [8], it is recognized that significant contact angle measurements can be used to calculate constant surface tensions. In recent years, numerous methods have been used to measure the contact angle [9], [10], [11], [12]. The most important surface parameters include: self-cleaning, adhesion, low friction, wettability, hydrophobicity and/or hydrophilicity and surface energy. They are of great importance for the properties of coatings and base materials as well as lubricants. The parameters of these bodies are largely negligible in most works on the tribological behavior of pairs of cooperating internal combustion engines and industrial machines. They are not fully taken into account in most theoretical works and simulation models. The parameters of coatings used in internal combustion engines, such as surface energy, microgeometry, hydrophilicity, hydrophobicity, contact angle, contact angle hysteresis, have been described in a small number of articles.

The results and implications of these studies differ and it is difficult to determine their credibility at the theoretical level [13], [14], [15]. Experimental comparisons were also carried out, but on different scales and hydrodynamic conditions or nanoscale contacts [16], [17]. Works on macroscale contacts express more similar results [18], [19], [20], [21], [22], [23]. An additional limitation of these results when it comes to engineering models is the fact that the experiments were sometimes performed in non-engineering conditions, i.e. model surfaces or model liquids [19], [20], [21]. Studies using surfaces similar to those used in internal combustion engines and oils have been presented in [20], [22], [23]. Although the number of scientific works is constantly increasing in the field of wetting, there is still a lack of full understanding of the phenomena occurring in internal combustion engines. The lack of important parameters in the models and various theories correlating with each other will make a big deal discrepancy in research results. as well as important models and theories correlating various parameters, resulting in frequently observed exceptions. This often applies to mapping the surface stereometry of cooperating elements, kinematics and dynamics of elements working in the main mechanism and engine timing. Inaccuracy of gas and liquid flow descriptions, lack of appropriate input data reflecting the engine operating conditions, in particular the heat load implied by the thermodynamics of fuel-air mixture combustion. Currently, there are almost no scientific works on simulation models of cooperation of pistons and piston rings with the cylinder surface with the introduction of wettability data, hydrophilic and hydrophobic properties, full surface stereometry and the phenomena of simultaneous flow of liquid and gas through the nanospaces of rubbing pairs. Research using the engine was conducted by the author for the first time and described in detail in [1]. According to the author determining and controlling the CAH is of great importance to the operation of these tribological systems.

Several experimental papers have been developed in the area of lubrication theory using CAH. Thanks to them, it is possible to learn some mechanisms of operation when applying this theory to internal combustion engines. Molecular dynamics (MDS) simulations were performed in the work [24]. It was found that the ultimate slip increases with a larger wettability angle of the coating. The value of the slip length reaches up to thirty molecular diameters. This is the case for a contact angle of approximately 140°. Using the MDS for the water model, the wettability angle is the parameter that defines the slip control [25]. It was assumed in the research that the exponential characteristic defining the relationship between the slip length and the value of the wettability angle for liquid-repellent surfaces represents the rate of increase in the slip length. In another paper [26], measurements of the liquid penetration force between the sphere and the hydrophilic and hydrophobic coating were performed. The penetration substance was glycerol. The measurement was performed using a surface force apparatus (SFA). Slip occurred only in non-wet conditions. The particle image speedometer method can also be used to identify the occurrence of limit slip [27]. In this work, the apparent speed of sliding was noted when water flowed through a hydrophobic channel. An apparatus for dynamic surface forces to measure the interaction forces in water was used in work [28] The authors of this paper observed that water slippage increases with hydrophobicity. The study of the slip and its length in a Newtonian fluid using the SFA method was performed in [29]. With regard to kinematic pairs lubricated hydrodynamically at low loads, studies were carried out in [30],[31] Glycerol and n-hexadecane lubricants were used. To a large extent, most studies on the interaction of the surface of a material with a liquid involve the measurement of drainage or hydrodynamic force. A comparison of the ability to form a lubricating film for different surfaces is presented in [32]. Interferometry was used to measure the micro scale with high accuracy. As part of these measurements, it was found that a surface characterized by high wettability and a small contact angle produces a greater thickness of the lubricating film. This is related to the intermolecular attraction of the lubricating liquid to the surface layer of the coating. The results were inconclusive. In the papers [33],[34] different hydrodynamic drainage forces were obtained for the flow of water on a fully wetted tribological system. In the work [35] it was established that the coefficient of friction under EHL lubrication conditions does not depend on the hydrophobicity of the coating. The test was carried out on a PDMS target with a ball. Despite this, the results showed that in the boundary lubrication regime, the coefficient of friction decreased with the decrease of the contact angle. In the work [36], the hydrodynamic force was measured in various liquids with the surface covered with alkylsilane and the AFM colloidal probe. It was assumed that the slip length decreased with the contact angle for non-polar liquids, when the value of the contact angle was in the range of about 10° to 40°. For polar liquids with a contact angle of 60° to 100°, a slight relationship was found between the contact angle and the slip length. In these works, various conclusions were drawn regarding the influence of wettability. It should be noted that the lubricant flow in labyrinth seals or bearings is dynamic, while the contact angle is a static parameter reflecting the wettability range.

The aim and innovation of this work is to compare the effectiveness of the contact angle and CAH in correlation with hydrodynamic lubrication on the example of a labyrinth seal using standard coatings and lubricating oils used in engines. According to the author, these results are only credible when comparing tribological and engine bench tests. The results of this work show the essence of the problem of hydrophilic and hydrophobic interactions on the decomposition of the oil film. With modern technologies for creating coatings and additives to lubricating oils, this may be the future in reducing friction losses in internal combustion engines.

In order to carry out the tests, an optical station was built for testing sliders with a constant inclination in accordance with the work [37]. Sliding friction is achieved by means of a glass disk rotating on a stationary inclined slider. The angle of inclination can be freely adjusted depending on the desired results. The thickness of the oil film is measured by interferometry. The initial reflection of the incident beam at the liquid-solid interface is supported by a sputtered chromium coating on the glass surface. When the disk rotates, the hydrodynamic effect causes the slider to lift. In the test, the number of interference fringes is identified to determine the slope. When the test is turned off, the slider falls freely to the disk surface. The exact determination of the film thickness for a given reference speed in accordance with the shift of kinematic pairs in the internal combustion engine is based on the change in the order of the fringes and the intensity of the selected point of the interferogram during the period stopping with a multi-beam intensity approach [38]. In a piston internal combustion engine, the average thickness of the oil film under load conditions, e.g. the expansion stroke, does not exceed 10 µm and this maximum value was adopted in experimental studies. Measurement uncertainty for this stand was less than 8 nm.

In the experimental study, a glass disc covered with a layer of chromium and SiO2 was used to ensure appropriate resolution conditions for the optics and surface protection. The reflectivity of the chrome coating is about 20%. In the test, 5 different coatings were sprayed on the slider of the device. The size of the slip plane is 5.15 mm by 10.20 mm. Material properties and their roughness are summarized in Table 1. Steel intended for the production of rings (slider 1) was used as the basic material in the test. It is stainless steel 1.4112 (X90CrMoV18) with high hardness and abrasion resistance. Various multi-layer and single-layer nanocoatings were applied to this steel (sliders 2–5). Hydrophobic and hydrophilic coatings are adopted. The roughness of all samples is measured in nanometers. Three lubricants, 65 wt % glycerol, 99 wt % glycerol and a lubricating oil, were used as base fluids. The properties of these greases are shown in Table 2. The contact angle and CAH were measured in the test of these lubricants on the surfaces of accepted test specimens. Depending on the sample, a drop of liquid needs a short exposure time to stabilize the optical parameters of the drop. It lasted a maximum of 10 seconds. The measurement was considered valid after stabilization. The test was carried out 5 times for the same liquid and a given sample. For this purpose, a measurement error of no more than 3.5% was obtained for all test samples and lubricants. Before testing, all samples were bathed in an ultrasonic cleaner in 99% alcohol. Contaminants were removed using a special cloth absorbing liquid time and solid impurities. The slider was dried for about 3 minutes.

Table 3 summarizes the results grouped for different liquids and base materials. For ideal conditions, a unique contact angle of a liquid drop on a perfectly smooth and flat solid surface can be expected based on Young's equations [39]. For experimental test conditions, a range can be measured contact angles. The upper and lower limits of the range are given by increasing or decreasing contact angles. The hysteresis of the contact angle CAH can be represented as the difference between the increasing and decreasing contact angle CA. The studies used the sedentary method to determine CAH. A droplet of the test liquid with a volume of less than 10 µl was deposited on the surface layer of the steel or coated steel sample. Liquid was added to the drop until the line of contact shifted. At the appropriate moment, a measurement was made for the advancing contact angle. Alternatively, liquid was taken from the droplet. At the time of retraction, the contact angle was reached as the line of contact moved. The tests were carried out at an ambient temperature of 17.0 ± 0.5°C and a humidity of 30 ± 1%. A new glycerol was used for each research group. It is well known that glycerol is hygroscopic. Therefore, a time change in viscosity of 99 wt.% was established. glycerol solution. It was assumed that in the area of research his the viscosity would only drop by 1.1% in 20 minutes. During the test, the viscosity of all liquid samples was constant. No greater changes in viscosity than 0.1% were recorded, therefore it was assumed that the viscosity of the liquid samples was unchanged.

Materials were adopted due to divergent contact angle properties with similar material properties. Some of the materials are described in publications [1],[40],[41]

Table 1

Properties of base materials and counter samples
Slider type	Surface layer	Bulk material	Roughness (nm)	The number of layers
1	Steel X90CrMoV18	Steel X90CrMoV18	123±3	0
2	AlTiN/CrN/Cr/…CrN/Cr	Steel X90CrMoV18	121 ±4	1 – AlTiN, 5 – CrN, 5 - Cr
3	AlN/CrN/…/AlN/CrN	Steel X90CrMoV18	108 + 3	6 – AlN, 5 - CrN
4	CrN/AlN/…/CrN/AlN	Steel X90CrMoV18	139±4	5 – CrN, 5 - AlN
5	Glass	Cr	4±0.3	1 - Cr
6	Glass	SiO₂	5±0.4	1 – SiO₂

In a piston internal combustion engine, as part of the movement of the piston in the cylinder sleeve, there is a variable instantaneous speed of the moving kinematic pairs. This is due to the reciprocating movement of the piston. The ring pack moves stochastically in the piston grooves. Therefore, it is difficult to determine the mutual position of the moving planes of the piston and piston rings relative to the cylinder surface. Nevertheless, it is possible to determine their mutual position with high probability, depending on the dynamic viscosity of the lubricant, the geometry of all elements of the main engine mechanism, the rotational speed of the crankshaft and the thermodynamic conditions in the combustion chamber. The distribution of the thickness of the oil film between the piston rings and the cylinder wall is affected by a number of engine operating parameters [42]. On the basis of simulation and experimental data, it is possible to determine the approximate thickness of the oil film between the given engine components. The smallest film thickness occurs between the upper piston ring and the cylinder wall. On average, it ranges from 0.1 to 15 µm, depending on the engine stroke, shaft speed and other parameters characterizing the engine load conditions. As is well known, oil parameters play a very important role here and affect the value of hydrodynamic pressure and the possibility of mixed friction or boundary friction conditions.

In the tests, the measurement of the thickness of the lubricating film was performed. Different loads were assumed for selected slider sets with applied coatings and lubricating fluid. The angle of inclination was constant during the test run. The name of the slider comes from the name of the coating. During the interferometric test, the number of fringes at different speeds is read and analyzed. In the test, the same number of evenly arranged fringes shifted on given interferograms with different speeds means that the slider inclination was unchanged at the time of the test and no elastic deformation of the contact surface of the kinematic pairs was observed. All tests were carried out in the conditions of hydrodynamic lubrication, reflecting the conditions of fluid friction between engine components. Experiments with 65% by weight of glycerol were performed using various sliders with a constant load of 5 N and a constant slope of 1:1875. As with the inclination of the plane ring relative to the cylinder face for symmetrical and asymmetric parabolic shapes.

Table 2

Properties of lubricants used in the tests
Lubricant	Refractive index	Dynamic viscosity (22°C, mPas)
Oil	1.46	840
99% Glycerol	1.47	704
65% Glycerol	1.45	14

Table 3

contact angle and contact angle hysteresis surface materials and lubricants
Lubricating liquids	Zipper surface material	Contact angle CA (°)	Contact angle hysteresis CAH (°)
65% Glycerol	Steel X90CrMoV18	${39.2}_{-5.4}^{+7.8}$	${46.5}_{-3.2}^{+2.3}$
65% Glycerol	AlTiN/CrN/Cr/…/CrN/Cr	${32.1}_{-5.8}^{+6.4}$	${\text{48,7}}_{-2.1}^{+2.2}$
65% Glycerol	AlN/CrN/…/AlN/CrN	${38.5}_{-4.6}^{+5.5}$	${\text{45,2}}_{-2.4}^{+2.3}$
65% Glycerol	CrN/AlN/…/CrN/AlN	${61.7}_{-4.8}^{+54}$	${\text{24,5}}_{-1.4}^{+1.4}$
65% Glycerol	SiO₂	${53.1}_{-7.7}^{+8.4}$	${35.1}_{-2.9}^{+2.6}$
65% Glycerol	Cr	${66.8}_{-5.4}^{+5.1}$	${34.9}_{-2.4}^{+1.7}$
99% Glycerol	Steel X90CrMoV18	${46.3}_{-4.6}^{+4.8}$	${47.4}_{-1.1}^{+1.1}$
99% Glycerol	AlTiN/CrN/Cr/…CrN/Cr	${42.7}_{-3.2}^{+4.1}$	${45.2}_{-1.3}^{+1.5}$
99% Glycerol	AlN/CrN/…/AlN/CrN	${45.2}_{-3.7}^{+2.4}$	${47.4}_{-1.0}^{+1.4}$
99% Glycerol	CrN/AlN/…/CrN/AlN	${69.8}_{-3.4}^{+2.8}$	${35.2}_{-1.1}^{+1.2}$
99% Glycerol	SiO₂	${62.3}_{-4.3}^{+3.8}$	${33.8}_{-1.3}^{+1.6}$
99% Glycerol	Cr	${74.6}_{-3.6}^{+4.2}$	${47.4}_{-1.9}^{+1.1}$
Oil	Steel X90CrMoV18	${26.1}_{-5.9}^{+5.8}$	${31.2}_{-1.8}^{+1.6}$
Oil	AlTiN/CrN/Cr/…CrN/Cr	${12.4}_{-2.2}^{+3.4}$	${28.8}_{-1.4}^{+1.2}$
Oil	AlN/CrN/…/AlN/CrN	${20.6}_{-1.5}^{+1.8}$	${30.9}_{-1.2}^{+1.7}$
Oil	CrN/AlN/…/CrN/AlN	${54.6}_{-1.6}^{+2.1}$	${18.7}_{-1.9}^{+1.6}$
Oil	SiO₂	${46.7}_{-1.1}^{+2.1}$	${26.6}_{-1.1}^{+1.3}$
Oil	Cr	${56.2}_{-2.7}^{+1.5}$	${25.1}_{-1.2}^{+1.2}$

Figure 1 shows the variation of film thickness versus speed for the 65 wt% test. glycerol solution. In order to better understand the issues of hydrophilicity and hydrophobicity, two theoretical layer thickness-velocity curves were additionally plotted on the film thickness. In the study, also for the purpose of systematizing the results, the theoretical Reynolds equations were calculated on the basis of a full two-dimensional solution of finite differences for surfaces covered with a lubricating film. The plotted theoretical curve read in the absence of slippage is equivalent to the classical Reynolds equation. (1). Theoretical results for full slip conditions were calculated using the extended Reynolds equation model with boundary conditions corresponding to full slip as in the case of equation. (2) [43]. Eq. (2) uses the critical stress slip model. In this model, stresses of this type are assumed to be zero. Comparing the terms of the equation on the right side of both equations, including one with boundary conditions for full slip (Eq. 2) was found to be only half of that with boundary conditions without slip. As a consequence of these findings and assumptions, it can be assumed that the theoretical thickness of the layer under the boundary conditions of full slip is smaller. The results of this are shown in Fig. 1.

$$\frac{\partial }{\partial \text{x}}\left({h}^{3}\frac{\partial \text{p}}{\partial \text{x}}\right)+\frac{\partial }{\partial \text{y}}\left({h}^{3}\frac{\partial \text{p}}{\partial \text{y}}\right)=6u\eta \frac{dh}{dx}$$

The sliders of the device made of steel X90CrMoV18 and AlN/CrN/…/AlN/CrN provided a high layer thickness, which coincided with the classic theory of non-slip hydrodynamic lubrication. The highest layer thickness results were also obtained for the AlTiN/CrN/Cr/…/CrN/Cr coating. It is an innovative highly complex multi-layer coating created by the author in such a combination based on theoretical assumptions in order to obtain special wetting properties. The thickness of the lubricating film created by the SiO₂ and Cr sliders was almost the same and slightly smaller than that of the AlTiN/CrN/Cr/…/CrN/Cr, AlN/CrN/…/AlN/CrN and steel X90CrMoV18 sliders. The thickness of the lubricating film created by the CrN/AlN/…/CrN/AlN coated slider was the lowest. In this case, its change with speed is perfectly correlated with the theory of hydrodynamic lubrication for full slip conditions. This shows that the molecular bonds of CrN/AlN/…/CrN/AlN and the lubricant are weak. The difference in the test conditions was the surface roughness. Other parameters for all test trials, such as slider inclination, liquid parameters are the same.

The surface roughness of the CrN/AlN/…/CrN/AlN slider is higher than for the other coatings (Table 1). Nevertheless, the roughness of this coating is almost an order of magnitude less than the measured minimum layer thickness. Slightly lower roughness was obtained for the Steel X90CrMoV18, AlTiN/CrN/Cr/…/CrN/Cr and AlN/CrN/…/AlN/CrN coatings. Cr and SiO₂ coatings had the lowest roughness. Nevertheless, this parameter did not significantly affect the thickness of the oil film in relation to coatings steel X90CrMoV18, AlTiN/CrN/Cr/…/CrN/Cr and AlN/CrN/…/AlN/CrN.

Assuming these surface properties, it can be said that the small thickness of the lubricating film layer obtained with the CrN/AlN/…/CrN/AlN slider cannot result from high surface roughness. Otherwise, a higher roughness of the applied coating would increase the hydrodynamic effect leading to increased coating thickness. In this arrangement, the thickness of the lubricating film layer generated on the slider surface depends on interfacial and surface effects.

The relationship between the thickness of the lubricating film and the contact angle and CAH is shown in Fig. 2. According to the accompanying figures, it can be concluded that the film thickness decreases significantly with the increase of the contact angle. For the materials adopted, it can be concluded that they coincide with the general conceptual assumption, with the exception of Cr and SiO₂. For this coating, the contact angle is the second largest among all the adopted variants of sliders, but it produces a considerable thickness of the lubricating film.

Based on Fig. 3, it can be assumed that the correlation of the thickness of the lubricating film layer and CAH is much better than in the case of CA. It performs much better in the predictability of the lubricating film for individual materials. CAH shows a more stable and rectilinear nature of the waveform. In the case of Fig. 3, slight deviations of SiO2, Cr and CrN/AlN/…/CrN/AlN from the approximation waveform can be noticed. An additional approximation of CA was performed using a sixth-order polynomial and in the case of CAH using a fourth-order polynomial.

Differences between the CrN/AlN/…/CrN/AlN sliders and the AlTiN/CrN/Cr/…/CrN/Cr sliders, which represent the two extreme abilities of forming a lubricating film, are shown in Fig. 4. They were verified by carrying out tests with 99 wt. glycerin. The introduction of glycerol from 65 to 99% by weight allowed to increase the viscosity. The test was performed for 5 and 10 N. The slope was 1:1650. The results of two different loads are shown in Figs. 4 and 5 for the same coatings. The measurement results including the AlTiN/CrN/Cr/…/CrN/Cr coating thickness of the slider are well correlated with the theoretical anti-slip curves in the specified speed range for two loads. However, the film thickness generated by the CrN/AlN/…/CrN/AlN slider is much smaller. Due to the large measurement errors of the interference images of the CrN/AlN/…/CrN/AlN slider at low speeds, Figs. 4 and 5 show only the thickness of the lubricating film layer measured at higher speeds starting from 5 mm/s. The minimum coating thickness shown in Figs. 4 and 5 is still about five times greater than the roughness of the CrN/AlN/…/CrN/AlN slider given in Table 1. It is therefore assumed that there is no direct contact between the two cooperating surfaces of the selected kinematic pairs.

A significant reduction in the thickness of the lubricating film for the CrN/AlN/…/CrN/AlN coating on the slider surface can be attributed to the hydrophobic properties of this coating and the intensification of the repulsion of lubricant particles at low feed speeds. Hysteresis of the surface contact angle of CrN/AlN/…/CrN/AlN and AlTiN/CrN/Cr/…/CrN/Cr with 99% by weight glycerol is 35.2° and 45.2°, respectively, as shown in Table 3. It is assumed that the higher the value of the CAH parameter, the greater the thickness of the lubricating film. Figures 4 and 5 show an interesting phenomenon where the resultant thickness of the lubricating layer obtained by the slider with the CrN/AlN/…/CrN/AlN coating is smaller than the theoretical full slip curves. Therefore, the test was repeated for the Olalphaolefin oil. This oil has approximately the same dynamic viscosity value as 99% by weight. glycerol. However, these substances have different polarity values. Olalphaolefin oil is a non-polar oil while glycerin is polar. This will extend the range more comparison and will allow to assess the possibility of influencing the thickness of the oil film in the operating conditions of a piston oil engine.

Figures 6 and 7 show the change in the thickness of the lubricating film layer for oliphaolefin oil in relation to the speed of movement at an inclination (slope: 1:1820) for loads of 5 and 10 N. In this case, all accepted materials were used. Sliders with the material steel X90CrMoV18, AlTiN/CrN/Cr/…CrN/Cr, AlN/CrN/…/AlN/CrN and CrN/AlN/…/CrN/AlN were tested for the same measurement conditions. In these coatings, there is a large variation in the contact angle CA, respectively: 26.1°; 12.4°, 20.6°, 54.6°. In the case of CAH, these values are respectively 31.2°; 28.2°; 30.9°; 18.7°. The first three shells have divergent CAs but have very similar CAH values. Therefore, it is necessary to carefully analyze which of the parameters more closely reflects the theoretical prediction of CA or CAH thickness. The courses of the film thickness distribution for CAH correspond well to the classical theory of non-slip hydrodynamic lubrication. The difference in the contact angle between the material CrN/AlN/…/CrN/AlN and AlTiN/CrN/Cr/…/CrN/Cr is CA = 35.2°. In the case of sliders made of steel X90CrMoV18 and AlN/CrN/…/AlN/CrN, the difference is CA = 5.5°. The Cr coating has a CA = 56.2° and a CAH of 25.1°. The SiO2 coating has a CA lower by 7.9° than the CrN/AlN/…/CrN/AlN coating.

The thickness of the lubricating film layer for the oil produced by selected sliders: at different speeds is shown in Figs. 8 and 9. The presented results prove that the CAH more closely reflects the relationship of the kinematic node for the effect of hydrodynamic lubrication produced by various sliding surfaces. This proves that CAH allows better establishment of hydrodynamic lubrication conditions between two surfaces. In this arrangement, CA is worse. In assessing the credibility of introducing the results of experimental research into mathematical models related to hydrodynamic lubrication, in assessing hydrophobic and hydrophilic properties, it is very important. Therefore, CAH gives a greater chance of credibility of changes in the oil film thickness in the elements of the cooperating kinematic pairs of the engine. As CA gives greater deviations from the values of theoretical models and approximation functions.

The results of sliders coated with steel X90CrMoV18, AlTiN/CrN/Cr/…CrN/Cr and AlN/CrN/…/AlN/CrN correlate very well with the classical theory of non-slip hydrodynamics for both 1 and 2 N loads. of the CrN/AlN/…/CrN/AlN slider is, however, significantly lower than for all sliders. The values of the film thickness in relation to the speed are characterized by a significant dispersion of values and non-uniformity of the course. This coating has hydrophobic properties, while 3 coatings have hydrophilic properties. Between them there are oil film thickness distributions for Cr and SiO₂. However, they have a more even distribution of film thickness values relative to the speed of the slider. The difference in the thickness of these layers resulting from different surfaces. In this case, it corresponds well with their CAH, but not with the contact angle CA. In the author's opinion, this is the answer which parameter is more important in improving the model of the hydrodynamic theory lubrication. In addition, the results shown in Fig. 4.5, 8 and 9 indicate an unexplained phenomenon where the thickness of the film produced by the CrN/AlN/.../CrN/AlN slider with 99% wt. glycerol or oil is much lower than the theoretical full slip values. It is difficult to explain this phenomenon of stochastic course of values for hydrophobic coatings.

In the work [43], a detailed analysis of the influence of the non-wetted, stationary surface of the sliding object on the hydrodynamic properties was carried out using the model of critical shear stresses. In this work, the conditions of boundary slip were defined: full slip (τc = 0), one-way slip (finite-valued constant τc applied to the entire static surface of the slider) and directional slip (slip or no slip and slip direction depended on the local pressure gradient at the boundary). The tests were carried out on the basis of one-dimensional flow. Studies of this type on two-dimensional flows are presented in [44]. They describe changes in the dimensionless load capacity W* where (${Wh }_{0}^{2}$/(Uη${B}^{2}$L) with respect to the dimensionless critical value of the shear stress τc* (h₀ τc /Uη) for different inclinations of the rubbing pairs.

Large critical shear stresses τc*>1 correspond to non-slip conditions and the resistance curves approximate Reynolds load values. The size of the ability to transfer the hydrodynamic load, i.e. to create a lubricating film, decreases when the limit slip begins on the stationary surface of the slider covered with any material. The disappearance of the hydrodynamic effect in the initial phase proceeds very quickly with increasing slip, which is indicated by the decrease in τc*. Soon this phenomenon is reduced to a minimum and the lubricating film-forming capacity increases again to further reduce τc*. Such a description is particularly important in the case of correcting the slip values for various materials used for the elements of kinematic pairs of internal combustion engines. This is the basic condition for the planned shaping of the oil film in terms of surface coverage and the thickness of the lubricating film obtained.

Figure 1 shows that the thickness of the lubricating film layer generated by the CrN/AlN/.../CrN/AlN slider with 65% wt. glycerol solution coincides with the theoretical full slip curve (i.e. τc = 0). This means that the critical shear stress of an EGC slider surface lubricated with 65% wt. values that lead to a significant reduction of the hydrodynamic effect, i.e. load support, as shown in Fig. 9. As a result, the thickness of the lubricating film layer formed by the CrN/AlN/.../CrN/AlN slider with 99% wt. glycerol or oil is much less. Under such conditions, the direction of lubricant slip in the pre-surface area of the slider is directed towards the inlet, which results in reduced grease pick-up and leads to a lower thickness of the lubricant film than under full slip conditions. The two glycerol samples have similar chemical properties, but a large difference in dynamic viscosity. In this case, 99% by weight of glycerol has a higher viscosity. Greater Critical Shear Stress 99% weights of glycerol on the surface layer of the CrN/AlN/.../CrN/AlN slider material can be attributed to its higher dynamic viscosity with respect to 65% by weight. glycerol.

The results of the experiment for selected sliders with different surface materials show the influence of surface properties of various materials in terms of CA and CAH on hydrodynamic lubrication. The ability of the hydrodynamic formation of a lubricating film is related to the adhesive force between the liquid and the solid surface. It takes place under conditions of fluid friction in the separation of cylinder walls, piston rings and piston. The conditions of mixed friction and the values of generated forces depending on the operating conditions are not taken into account here. Lubricant particles are able to slide or relative to any surface of the coating applied to the engine component only when these particles overcome the energy barrier. Its value depends on the adhesion of the lubricant particles and the coating. These parameters are determined using CAH and CA. The size of the energy barrier depends on the interfacial properties of the coating and the lubricant.

In paper [45], based on the basic principles of thermodynamics, the energy barrier equation was derived. It is expressed using CA and CAH:

$$E=\frac{R}{{2}^{\frac{7}{3}}}{\left(CAH\right)}^{2}f\left(\theta \right)$$

Where:

$$f\left(\theta \right)=\frac{{\left(1+cos\theta \right)}^{2}}{{\left(1-cos\theta \right)}^{1/6}{\left(2+cos\theta \right)}^{4/3}}$$

Calculations of the energy barrier E can be made using the parameters θ and CAH. However, the value of this parameter does not change significantly for the range from 20° to 140°. The parameter f(θ) practically remains unchanged in this range. To a large extent, the value of the energy barrier is due to the CAH. In the case of materials used in the construction of kinematic elements of internal combustion engines, it is assumed that a contact angle greater than 90° means that the surface of the material is hydrophobic. Therefore, for the operating conditions of combustion engines and the maximum piston speeds achieved, which are temporarily much higher than in the test, the hydrophobic properties of the coatings do not necessarily have to be worse in terms of the formation of a lubricating film than for the hydrophilic coatings.

Based on the formula (1), it is established that the smaller the CAH, the lower the barrier value. The main reason for this condition is the molecular interaction between the lubricating liquid and the surface layer of the coating. Limit slip occurs only above CA 140°. Slip length increases also occur above this value. A number of works on the methodology of research to assess the validity of the use of CA and CAH are given in [47–52]. According to the author, the research methodology adopted and the results obtained prove the significant potential of the theory of material selection in terms of CA and CAH in industrial use in internal combustion engines in order not only to obtain durability of these assemblies and low wear, but also to significantly reduce hydrodynamic friction losses occurring between main components of internal combustion piston engines.

In internal combustion piston engines, the oil film is shaped depending on many parameters of engine operation, macro and micro geometry of assemblies, properties of liquids and materials. Currently, the latest trend is to assess the possibility of designing the thickness of the oil film and covering the sliding surfaces of the rings, piston and cylinder sliding surfaces with an oil film using the phenomena of hydrophilic and hydrophobic coatings. The influence of these parameters on the shape of the oil film and the surface wettability of the kinematic couple materials is difficult to assess in dynamic conditions. There are two interfacial parameters: contact angle and hysteresis contact angle, whose effectiveness in assessing these phenomena was compared in terms of their correlation with the hydrodynamic effect of lubrication. Several coating materials with varying degrees of hydrophilic and hydrophobic features, with different CA and CAH parameters, and three liquids, polar and non-polar, were used in the tests, which provided contact angles from 12° to 75°. In the evaluation In order to predict the thickness of the oil film, it was found that the key parameter is the CAH hysteresis of the contact angle, which more closely reflects the phenomena of oil film formation than the CA contact angle in terms of hydrophilic and hydrophobic characteristics. The results of these studies also reflect the basic theory of thermodynamics. It was found that the critical shear stresses constituting the limit slip barrier depend on the dynamic viscosity of the lubricant. This discovery will allow future researchers to delve further into the hydrophilic and hydrophobic properties of coatings in oil film formation and design that have not been considered so far. This is very important due to the further process of reducing mechanical friction losses of the engine while maintaining the durability of kinematic assemblies.

B - Breadth of slider bearing (in x direction)

E - Potential energy barrier

L - Length of slider bearing (in y direction)

h - Film thickness

R - Radius of spherical liquid drop on solid surface

p - Fluid pressure

U - The speed of the puck in a given direction

τ_c - Critical shear stress for slip

η - Dynamic viscosity of lubricant

x - Shift coordinate

y - Transverse coordinate of the shift

Author Contributions

Conceptualization, P.W; methodology, P.W. investigation, P.W; writing—original draft preparation, P.W; writing—review and editing, all authors; funding acquisition, P.W. All authors have read and agreed to the published version of the manuscript.

Data availability: All data generated or analyzed during this study are included in this published article.

Conflict of Interest: Author(s) declare that they have no conflict of interest for this manuscript.

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The theory of the surface wettability angle in the formation of an oil film in internal combustion piston engines

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Lubricating liquids	Zipper surface material	Contact angle CA (°)	Contact angle hysteresis CAH (°)
65% Glycerol	Steel X90CrMoV18	\({39.2}_{-5.4}^{+7.8}\)	\({46.5}_{-3.2}^{+2.3}\)
65% Glycerol	AlTiN/CrN/Cr/…/CrN/Cr	\({32.1}_{-5.8}^{+6.4}\)	\({\text{48,7}}_{-2.1}^{+2.2}\)
65% Glycerol	AlN/CrN/…/AlN/CrN	\({38.5}_{-4.6}^{+5.5}\)	\({\text{45,2}}_{-2.4}^{+2.3}\)
65% Glycerol	CrN/AlN/…/CrN/AlN	\({61.7}_{-4.8}^{+54}\)	\({\text{24,5}}_{-1.4}^{+1.4}\)
65% Glycerol	SiO₂	\({53.1}_{-7.7}^{+8.4}\)	\({35.1}_{-2.9}^{+2.6}\)
65% Glycerol	Cr	\({66.8}_{-5.4}^{+5.1}\)	\({34.9}_{-2.4}^{+1.7}\)
99% Glycerol	Steel X90CrMoV18	\({46.3}_{-4.6}^{+4.8}\)	\({47.4}_{-1.1}^{+1.1}\)
99% Glycerol	AlTiN/CrN/Cr/…CrN/Cr	\({42.7}_{-3.2}^{+4.1}\)	\({45.2}_{-1.3}^{+1.5}\)
99% Glycerol	AlN/CrN/…/AlN/CrN	\({45.2}_{-3.7}^{+2.4}\)	\({47.4}_{-1.0}^{+1.4}\)
99% Glycerol	CrN/AlN/…/CrN/AlN	\({69.8}_{-3.4}^{+2.8}\)	\({35.2}_{-1.1}^{+1.2}\)
99% Glycerol	SiO₂	\({62.3}_{-4.3}^{+3.8}\)	\({33.8}_{-1.3}^{+1.6}\)
99% Glycerol	Cr	\({74.6}_{-3.6}^{+4.2}\)	\({47.4}_{-1.9}^{+1.1}\)
Oil	Steel X90CrMoV18	\({26.1}_{-5.9}^{+5.8}\)	\({31.2}_{-1.8}^{+1.6}\)
Oil	AlTiN/CrN/Cr/…CrN/Cr	\({12.4}_{-2.2}^{+3.4}\)	\({28.8}_{-1.4}^{+1.2}\)
Oil	AlN/CrN/…/AlN/CrN	\({20.6}_{-1.5}^{+1.8}\)	\({30.9}_{-1.2}^{+1.7}\)
Oil	CrN/AlN/…/CrN/AlN	\({54.6}_{-1.6}^{+2.1}\)	\({18.7}_{-1.9}^{+1.6}\)
Oil	SiO₂	\({46.7}_{-1.1}^{+2.1}\)	\({26.6}_{-1.1}^{+1.3}\)
Oil	Cr	\({56.2}_{-2.7}^{+1.5}\)	\({25.1}_{-1.2}^{+1.2}\)