The silicone oils were purchased from Sigma Aldrich. The viscosity classification in centistokes refers to their viscosity at room temperature. The used oils had a viscosity of 10, 20, 50, and 100 cSt, respectively. Six test skis were supplied by Norwegian ski manufacturer Madshus and were identical 192 cm skate test skis with a medium grind with an S_a of 3.0 μm, as shown in Figure 1. Commercial fluorine-free spray-application glide waxes (HS6 and HS10) were supplied by Swix.

The friction measurements were conducted in our full-scale linear ski tribometer. The construction and assessment of precision and accuracy of the tribometer were recently published by our group (Auganæs et al., 2022). The data acquisition system has been updated and now consists of a Compact RIO 9054 (National Instruments, USA) with a four-channel NI-9237 simultaneous bridge module connected to the amplified vertical and horizontal loads cells. An 8-meter magnetic encoder system (LM15, RLS Merilna tehnika, Slovenia) with a 50 μm resolution was connected to the NI-9411 digital module, and the data is transferred wirelessly to the computer in the control room. For this study, the adjustable sampling rate (0–10 kHz) was set to 5 kHz. For the friction testing, the ski speed was 6 m/s, with a 1.5 m sinusoidal-ramped acceleration profile to reduce vibrations. At each temperature, all skis were tested in three sets of three runs, i.e., all skis were first run 3 runs, then the entire series was repeated twice until n = 9 for every ski. This was done to distribute effects of track polishing across all the skis of the series.

The snow used for the linear tribometer was laboratory-grown dendritic snow, produced at −20 °C by evaporation-crystallization. The fresh snow was evenly distributed and compacted in the friction track and left to sinter for 16 h before starting the friction measurements. For the test on wet snow, aged snow was used. This snow was 1 week old laboratory-grown new snow which was sifted and distributed evenly in the tribometer by a steel blade and left to sinter for 16 h. On the day of testing, the cold room temperature was set to 5 °C 4 h before the testing started. The compaction of the snow surface before testing was done at 1 m/s by repeated runs at increasing normal load (50, 100, 200, 300, and 400 N). Then the track was worn in by increasing the speed by 1 m/s increments stepwise up to 6 m/s and lastly performing six repeated runs at 400 N at 6 m/s.

Snow humidity was measured with a Snow Moisture Meter Type 011 (DOSER Messtechnik GmbH & Co.KG, Germany) while the snow density was measured with the SLF Snow Sensor (FPGA Company GmbH, Switzerland). These measurements were conducted immediately after each experiment series, and the reported values are averages of five measurements equally spaced throughout the 3.5 meter measurement region. Contact angle measurements were recorded along the ski running direction with the MSA Flexible Liquid (KRÜSS GmbH, Germany) using distilled water.

To get a meaningful estimate of the glide performance of silicone oils, they were tested alongside a ski waxed with commercial liquid gliders suitable for each temperature. The term liquid glider refers to the state in which it is applied to the ski by aerosol spray. After application, the solvents evaporate, leaving a hard wax coating. One ski was left completely untreated in all measurements to establish the baseline glide performance of the sole material. This ski is referred to as “bare UHMWPE sole” or “reference.”

The application of the silicone oils was monitored by first weighing the amount of oil applied to the ski, and subsequently weighing every Fiberlene paper used to distribute and wipe the skis. By volume, 1 g of silicone oil which was distributed over the entire ski sole and left for 15 min. Then the sole was wiped with Fiberlene (Swix, Norway) paper until no more oil was visually removed, leaving an average of 50 mg of silicone oil, regardless of viscosity. Over the area of one ski, this equals 60 μg/cm² or a 600 nm thick silicone oil layer assuming a uniform distribution. Before each friction test, the skis were placed in the cold lab for 1 h to equilibrate thermally to the testing temperature. Silicone oil was reapplied for each temperature. The liquid glide waxes were applied by spraying the ski, waiting 15 min for the solvent to evaporate then wiping off the sole with Fiberlene until no more wax was visually removed. While this is not the recommended application procedure for these products, it avoids mechanical brushing and ensures the structure of the ski remains comparable to the other skis.

The temperature and relative humidity of the air alongside the snow temperature, density, and humidity for the testing conditions are given in Table 1.

The contact angle of water on a surface is a measure of hydrophobicity and is affected by the chemical properties of the material and the surface structure. In Figure 2, the contact angles of the oiled skis are plotted alongside the contact angle of a ski with a commercial wax and the unwaxed reference ski. Selected images from each series of measurements are presented in Figure 3.

To establish the six test skis used in the study were identical, a friction test was performed before treatment with oil or the reference wax. The temperature for this test was −8 °C, and the snow was fresh dendritic snow. The average coefficient of friction for the six skis was 0.0607 with a standard deviation of 0.009. The individual performances of each ski with corresponding error bars are given in Figure 4.

The effect of the silicone oil treatments was tested at three temperatures and snow conditions ranging from −10 °C and dry snow to +5 °C wet snow. The average coefficients of friction at all temperatures are plotted in Figure 5 while the values and standard deviations are given in Table 2. At the lowest temperature of −10 °C, the silicone oils increased the coefficient of friction on average by 24% compared to the unwaxed reference ski. The liquid glide wax HS6 reduced the coefficient of friction by 5%, while the friction coefficient of the untreated reference ski was only marginally increased from the baseline test conducted at −8 °C. Among the silicone oils, there was a weak trend of reduced friction with increased viscosity.

At the intermediate temperature of −1 °C the snow had more pre-existing water than at −10 °C, but still considered dry with a Doser snow humidity value of 17%. Under these conditions, the skis treated with silicone oils showed no benefit from a more hydrophobic surface and surprisingly increased the coefficient of friction by 44–57% while the commercial HS10 wax reduced the friction by 6%. Also at this temperature, the higher viscosity silicone oils were slightly better, albeit with higher standard deviations.

Under melting conditions (air temperature of 5 °C), all skis performed better than on colder dry snow, and here the silicone oils reduced the friction by about 10% compared to the untreated reference ski. The conventional liquid glider Swix HS10 reduced the friction by 20%.

The contact angles increased for all treatments compared to the bare UHMWPE reference, and the skis treated with the conventional glide wax HS6 had the highest contact angles. For the silicone oils, increased oil viscosity gives higher contact angles. This can be rationalized by the fact that higher viscosity silicone oils have higher surface tension, and therefore yield higher contact angles when in contact with water (Barca et al., 2014). Higher water contact angles means increased water repellence, which especially under wet conditions is favorable for reducing ski-snow friction.

To measure the ski-snow friction and the effects of the different silicone oils, the skis were tested in a linear full-size ski tribometer (Auganæs et al., 2022). When the friction of the skis was tested prior to application of any products, we found the baseline performance to be practically identical. The six skis were therefore considered to be a good test set to investigate the effect of silicone oils. The average friction coefficient of the untreated skis of 0.060 represents, in our experience, skis with below average gliding properties and would therefore have potential for improvements.

At −10 °C, the silicone oils significantly increased the friction [t₍₁₆₎ p < 0.001] while the conventional wax reduced the friction [t₍₁₆₎ p = 0.001]. At these temperatures, there is little liquid water generated by frictional heating, causing a comparatively high portion of the friction to stem from solid-solid contact. Although the main function of a liquid lubricant is to reduce solid-solid contact, it also can induce a new source of resistance, namely shear forces in the lubrication film. In addition, the oil can contribute to an increase in the real contact area. The dry friction from solid ice-UHMWPE interactions is still relatively low when compared to systems such as stainless steel-UHMWPE (Yousif et al., 2010). Therefore it appears that the benefit of reducing solid-solid contact between the snow and UHMWPE by silicone oil lubrication gets overruled by the introduction of shear forces and increased contact area.

A theoretical calculation of the magnitude of the shear forces is possible by assuming laminar flow in the silicone oil layer, see Figure 6C. The friction force from the shear stress within the lubricant layer, F_shear, can be calculated with Equation 1, where τ is the shear stress, A the real contact area in m², μ is the dynamic viscosity of the oil in N·s/m² and H is the thickness of the silicone oil film in meters. U_ski is the ski speed relative to the snow in m/s and U_slip is the wall slip. So that the wall slip can be expressed as a fraction of the ski speed, we define U_slip = a · U_ski, where a is the wall slip factor which can be set between 0 and 1.

To get an estimate for the shear friction some assumptions are required. The two contact zones of the loaded ski have a combined length of 43 cm and the ski width is 4.4 cm, dictating the apparent contact area to be 189 cm². The real contact area (of ski in contact with snow during sliding) is assumed to be 1% of the apparent contact area (Theile et al., 2009; Mössner et al., 2021). While the low real contact area is a result of the coarseness of the snow and the structured ski surface, both surfaces are assumed perfectly flat in the points of contact. The dynamic viscosity of a 100 cSt silicone oil with a density of ~1 g/cm³ converts to 0.1 N·s/m², and the thickness of the oil layer is calculated from the amount of oil applied on the ski and is 600 nm. Under noslip conditions, which is highly unlikely considering the icephobic nature of silicone oils, the calculated shear force is 190 N. This corresponds to a very high friction coefficient of 0.475, meaning this system must have significant wall-slip. Starting with a realistic friction coefficient for this system of 0.08, the shear force would equate to 32 N assuming shear is the sole resistance mechanism, and this would require a wall-slip factor of 0.83.

These calculations show that viscous shear in oil films of realistic thicknesses can quickly lead to high resistance forces between skis and snow. As no change in friction coefficient was observed over the course of the experiments, it is reasonable to conclude the oil did not wear away at a significant rate, and consequently the wall-slip factor must be high. Furthermore, as the shear force calculation is proportional to viscosity it is intriguing that the measured total friction appears not to be. This can be explained by the higher viscosity oils having a higher degree of wall-slip causing the two contributions cancel each other.

Bearing in mind the friction values of the untreated and commercial wax skis were practically unchanged compared to the values at −10 °C, the considerable increase for the silicone oil skis at −1 °C is intriguing, and contrary to common conceptions in ski waxing.

Our explanation of this notable friction increase on warm dry snow stems from changes in the snow. Cold dry snow has sharper edges and slower metamorphism compared to warmer snow, which means the snow in the experiment at −1 °C has more rounded features. In turn, this means the contact area of a ski sliding over warm snow can be larger than on cold snow. The shear forces from the liquid silicone lubricants are proportional to the real contact area between the ski and the snow. The two scenarios are illustrated in Figures 6A,B. The commercial HS waxes are considerably harder coatings than pure silicone oils, and therefore no detrimental effects due to shear friction were observed.

The competitive advantage of fluorinated glide products is largest when the snow humidity is high, and the silicone oils did significantly reduce the ski-snow friction under these conditions [t₍₁₆₎ p < 0.025] compared to the untreated ski. This can be attributed to the increased hydrophobicity of the sole material, greatly reducing the friction contribution from capillary suction. The static water contact angle of the conventional wax was even higher than for the silicone oils. In combination with the lack of viscous shear, the conventional HS waxes outperformed the silicone oils also on the warmest and wettest of skiing conditions.

While the air temperature was 5 °C during these tests, the snow, which is undergoing a phase change, maintained 0 °C throughout the experiment. While all cold snow is relatively dry, snow around 0 °C can vary greatly in humidity. This is often also the case during competitions, where racers pass through colder shaded parts of the track as well as sun-soaked areas. Consequently, glide products need to be highly specialized for specific conditions to give a competitive advantage while simultaneously maintaining a good baseline performance when outside the ideal temperature or humidity window. For the case of pure silicone oils, this performance window appears to contain only warm temperatures and humid snow, as shown in Figure 7. In the authors' opinion, it is unlikely that liquid silicone oil lubricants will have a significant potential for UHMWPE-snow lubrication.

On the other hand, by employing silicone oils as additives in other coating matrices one may be able to retain the wet snow properties from the silicone oils while avoiding the detrimental effects under dry conditions. As the effects in this study were obtained with very low quantities of oil, we consider the viability of silicone oils as additives as realistic.