Transitional behaviour between biphasic lubrication and soft elastohydrodynamic lubrication of poly(vinyl alcohol) hydrogel using microelectromechanical system pressure sensor

The soft hydrogel material is expected for a candidate material as biomimetic artificial cartilage with synergistic functionalities of adaptive multimode lubrication. In boundary lubrication mode of hydrogel material, the biphasic lubrication mechanism cooperatively exerts its functionality. In hydrodynamic lubrication mode, it is preferable that the lubricating surfaces be impermeable to trap the fluid pressure in contact surfaces, whereas the actual biphasic material like a hydrogel is a permeable material with surface porosity. It is indicated that the interstitial fluid pressurisation in the permeable biphasic material can contribute to significant fluid load support under lower sliding speed condition. So, the authors examined how the contrary fluid pressure effect appears in the transition from the boundary lubrication mode to soft elastohydrodynamic lubrication mode. In the experiment, a small pressure sensor was utilised to measure the in-situ fluid pressure in sliding condition. Although the experimental condition of this study was selective, the result showed a possibility of the negative effect of the biphasic surface, in which the permeable surface diminished the hydrodynamic fluid pressure. This means that one should manage and enhance the biphasic lubrication abilities in wide operation range when the hydrogel material was used as a load bearing material.


Introduction
In a human body, the contact load in the articulating bones reaches more than 10 times body weight, while relative sliding speed sometimes subsides nearly stationary. Under these severe and wide operating conditions, the synovial load-bearing system retains a very low friction coefficient of <0.03 and maintains its tribological functionalities over a whole lifetime in a healthy body. The joint diseases, e.g. osteoarthritis and rheumatoid arthritis, lead the deterioration of the joint functions, which causes severe joint pain and a limitation of joint mobility. The orthopaedic surgery on the joint prosthesis has been widely performed for the relief from joint pain and the recovery of the joint function as a load bearing system. The most successful articulating combination of the artificial joint material would be an ultra-high molecular weight polyethylene (UHMWPE) on hard materials, such as a cobalt-chromium-molybdenum (Co-Cr-Mo) alloy or ceramics. As the lubrication mode of the common artificial joint cannot always enter the hydrodynamic lubrication mode, the wear particle of UHMWPE involves severe biological reactions that sometimes cause the loosening of the artificial joint [1]. So, the improvement of the wear resistance of UHMWPE material has been studied using several approaches [2][3][4].
The natural synovial joint surfaces are covered by a soft articular cartilage to prevent direct contact with bones and redistribute contact pressure as first functionality. The soft articulating surface promotes the fluid film formation by soft elastohydrodynamic lubrication (soft-EHL) [5]. The further concept of the micro-EHL [6] explained the flattening of surface roughness asperities with the effective local fluid film lubrication even in the mixed lubrication transition with a low lambda ratio. The inclusion of the soft surface layer experimentally reduced the friction coefficient of an artificial hip joint by a specified stiffness range [7]. Another nature of the synovial articular cartilage is the hydrogel material with high water content up to 80 wt%. The weeping [8] and boosted [9] mechanism were proposed based on the frictional mechanism of hydrogel material in the past. It is well known that the articular cartilage shows the time-dependent compressive behaviour [10,11], which was explained by a 'biphasic model' [12]. In the biphasic model, the cartilaginous tissue was modelled by the mixed composition of solid and fluid phase. The interstitial fluid flows along the gradient of fluid pressure in the matrix, which causes the stress relaxation of articular cartilage. Once the biphasic matrix comes in contact with the counter surface, the interstitial fluid near the surface is trapped and pressurised by the contact load. In this situation, the considerable proportion of the contact load is supported by the fluid pressure of the tissue surface, which results in a low friction coefficient under an assumption of non-viscous fluid. This biphasic complex on frictional behaviour was called as 'biphasic lubrication mechanism' [13]. The biphasic lubrication framework successfully revealed the relationship between the constituent structure of the articular cartilage and consequent functionalities as a load bearing system [14][15][16][17][18][19][20][21].
The synovial articular cartilage has the capabilities for the compliant contact to promote soft-EHL and the biphasic lubrication mechanism. Other various lubrication mechanisms, including protein boundary films, hydration, surface amorphous gel layer, and so on, also play an important role to enhance the tribological functionalities, which is called 'adaptive multimode lubrication' [22,23]. As the articular cartilage is essentially the soft hydrogel material, the poly(vinyl alcohol) (PVA) hydrogel is expected for one of the candidate materials as biomimetic artificial cartilage with acceptable biocompatibility. So, various studies on PVA hydrogel as the artificial cartilage material have been conducted for the improvement of frictional properties and clinical applications. Author's research group reported several studies, concerning the potential of fluid film formation [24], boundary film in synovial fluid constituents [25], production processes with hybrid gel [26,27] and sterilisation effect on frictional properties [28].
In natural synovial joints, various lubrication mechanisms effectively maintain low friction and minimum wear over a wide operating range by synergistic functionalities of adaptive multimode lubrication. PVA hydrogel as artificial cartilage material is expected to mimic the adaptive multimode lubrication mechanism seen in the synovial joint. In boundary lubrication mode of PVA hydrogel, the biphasic lubrication mechanism would cooperatively exert its functionality concurrent with hydration and absorbed film lubrication. The time-dependent frictional behaviours of natural articular cartilage on the difference of lubricant constituents were explained by the biphasic finite element (FE) analysis with different solid-to-solid friction coefficients [29]. The frictional difference of the PVA hydrogels with different production processes, which were freeze-thawing (FT), cast-drying, and these hybrid gels, were also confirmed by biphasic FE analysis with different mechanical properties for each material [30,31]. While the increase of the friction coefficient with a sliding period may partly derive from dehydration or denaturation of protein lubricants, the transitional behaviour of the friction coefficient of PVA hydrogel in the boundary lubrication regime appeared to follow the frictional estimation of biphasic FE analysis. On the basis of the biphasic lubrication mechanism [32], the effective friction coefficient decreases with the increase of the proportion of fluid load support in a poroelastic contact area. Therefore, the friction coefficient in boundary lubrication mode of hydrogel would be influenced not only by the friction of the boundary lubrication film but also the fluid load support of the hydrogel contact surface as the biphasic mechanism.
The synergistic functionality of boundary lubrication and biphasic lubrication of PVA hydrogel was past examined under several sliding conditions. From the viewpoint of adaptive multimode lubrication, there appears another multimode conjunction between the biphasic lubrication and the fluid film lubrication. In hydrodynamic lubrication mode including squeeze film, the fluid pressure in an apparent contact area enough supports the total contact load, which results in a low friction coefficient under Couette flow. On the other hand, in biphasic lubrication mode, the surface fluid pressure as the interstitial fluid pressure under the apparent contact surface supports some part of the total contact load, in which the biphasic fluid pressure directly presses the counter surface. In these both situations, the fluid pressure plays an important role in the reduction of the friction coefficient, but the formation mechanism of the fluid pressure is completely different. In the hydrodynamic lubrication mode, it is preferable that the lubricating surfaces be impermeable to trap the fluid pressure in contact surfaces, whereas the actual biphasic material like PVA hydrogel is a permeable material with surface porosity. The permeable material surface may diminish the effect of hydrodynamic lubrication, although the permeable biphasic material has an ability to perform the biphasic lubrication. There is this conflicted or combined question in the concept of the adaptive multimode lubrication mechanism. So, we thought to examine how the effect of this circumstance appears in the transition from the boundary lubrication mode to soft-EHL mode. In this study, the frictional behaviour between the biphasic lubrication and hydrodynamic lubrication mode was experimentally observed by PVA hydrogel to determine whether the permeable surface affects the hydrodynamic lubrication regime. In the experiment, a small pressure sensor by a microelectromechanical system (MEMS) was utilised to measure the in-situ fluid pressure under sliding conditions. The MEMS pressure sensor would capture both the hydrodynamic pressure and the interstitial fluid pressure of the biphasic lubrication mechanism.

Materials and methods
In this study, physically cross-linked PVA hydrogels were prepared by the repeated FT method. PVA powder (Kishida Chemical Co., Ltd, Japan: Poval, 020-63185) as a raw material had a polymerisation degree of 2000 and saponification of 98.4-99.8%. The PVA powder was mixed in pure water at 20 wt% and dissolved at 95°C for 3 h in an autoclave. Then, the solution was stirred in 80°C water bath for more than 2 h to ensure the homogeneity and deaeration. The casting mould to form the hydrogel with 2 mm thickness was made of acrylic resin plate (Mitsubhishi Chemical Co., Ltd, Japan: Acrylite EX, t = 5 mm), in which the continuous casting surface of the production process was kept in the hydrogel casting surface. The hot solution was poured into the casting mould, and the FT gelation process was repeated 5 times at −20°C for 8 h and 4°C for 16 h. The apparent compressive modulus of PVA hydrogel by 8.2 mm square specimen was 0.52 MPa in 20% compressive strain at 1 s compression time, and equivalent water content was estimated as 79% in the past [25]. The details of the biphasic material properties of PVA hydrogel are shown in another report [33].
The friction coefficient and fluid pressure in contact area were simultaneously measured in wide reciprocating speeds from the boundary lubrication mode to fluid film lubrication mode. Fig. 1 shows the schematic drawing of experimental apparatus and the photograph of sliding part. The PVA hydrogel of 2 mm thickness was attached to the semi-cylindrical substrate by a cyanoacrylate adhesive. As the cylindrical radius of the rigid and impermeable substrate was 16 mm, the surface radius of the sliding specimen was 18 mm. The transversal width of the specimen was 20 mm, which were selected to enter the fluid film lubrication mode with a specific viscous lubricant in the maximum sliding speed of the apparatus. For the comparative experiment, another PVA hydrogel specimen with impermeable surface modification was prepared to prevent the surface seepage of the biphasic interstitial fluid pressure and the inflow of the hydrodynamic pressurised fluid.
In the impermeable surface model, the sliding surface of PVA hydrogel was covered by a low-density polyethylene film with 50 μm thickness as shown in Fig. 2. It may be difficult to see the difference in the photograph, but the covered PVA hydrogel specimen shows a light reflection of ambient illumination than a mat surface of normal PVA hydrogel. For the other experiment to observe the absolute hydrodynamic lubrication regime, an impermeable hard rubber specimen with the same 2 mm thickness (Waki Sangyo Co., Ltd., Japan: GR-07, black natural rubber) was also prepared as a reference. The compressive modulus of the black natural rubber used in this study was estimated as 5.1 MPa, which was measured in the same 20% compression strain at 1 s compression time.
The high speed and precise reciprocating motions were generated using a linear ball-screw stage (THK Co., Ltd, Japan: SKR33) that was actuated by a DC servomotor (Maxon Motor AG, Switzerland: RE35). The sliding motion was controlled by a state feedback control of 0.02 s time constant with an instantaneous 750 W overdrive for the direction turning phase of the reciprocating motion. The specimen was fixed to the upper movement part and slid on the lower counter surface at a speed of 1.56-400 mm/s in 38.69 mm stroke (77.38 mm sliding length in one cycle). The lower surface was an acrylic resin (Mitsubishi Chemical Co., Ltd, Japan: Acrylite EX, t = 10 mm) and was fixed on a ultra-low friction ball slider (THK Co., Ltd, Japan: LSP1052) to detect frictional force by a load cell (Showa-sokki Co., Ltd, Japan: DBJ-5N). The acrylic resin material for the lower counter surface was selected not only for an easy machining work but also for the management of the friction coefficient to enhance the difference between the actual hydrodynamic lubrication mode and the mixed/biphasic lubrication mode. Applied load was 1.8 N by the self-gravity force of the upper part under all sliding conditions. The lubricant was 3.3wt% PVA water solution of the same material of the PVA hydrogel shown above. The viscosity of the lubricant was estimated as 20 mPa s at 23°C, which was selected for the transition to fluid film lubrication mode at high-speed sliding. Experiments were executed at 23°C by a general room air-conditioner.
The MEMS pressure sensor (FISO technologies Inc., Canada: FOP-M) was embedded in the centre of the lower acrylic resin plate through 1.6 mm diameter hole to measure the local fluid pressure. As shown in Fig. 1, the measurement hole was reduced to 0.6 mm diameter at the sliding surface to eliminate a potential influence as a surface texture spot possibly. In this study, the contact length along the sliding direction was about 3 mm, where the average contact stress was estimated as 0.03 MPa. We thought that the diameter of the measurement hole was a compromising size in considering machining processes, material strength, orifice effects and so on. The measurement principle of the MEMS pressure sensor used in this study was the detection of the displacement of the MEMS diaphragm which deforms in about 16 μm at 300 kPa in the specification. It was preferable that the measurement hole was placed at the centre of the sliding track, and the lower acrylic plate should be placed at the centre of the linear ball slider for a force balance. So, we decided to make the path hole for the MEMS pressure sensor at the centre of the linear ball slider, which required disassembling of the ball slider. The sampling rate of the control unit for the MEMS sensor (FISO technologies Inc., Canada: FPI-HS) was 15 kHz in the specification. Since the sliding speed in the fluid film lubrication mode was estimated to be fast, the signals from the sensors were synchronously collected by a single control PC at 2 kHz sampling rate to capture the fast pressure change in the contact area sliding over the MEMS sensor. Since any small bubble in the measurement hole corrupts the resultant pressure data, the MEMS pressure sensor was carefully flushed by a pipetting treatment in a water bath.
The net fluid load support was calculated by the integration of the fluid pressure along the sliding direction with an assumption that the value in the transversal direction did not vary over experiments (the transversal direction means the axial direction of semi-column  substrate), as shown in Fig. 3. The remaining load support by the solid phase was used to calculate the effective friction coefficient with the friction coefficient of the solid-to-solid contact under the equilibrium condition. The specimen was positioned where the centre of the specimen passes at the position of the MEMS sensor. The intact specimens were first subjected to the running-in process, which was executed by 50 reciprocating cycles at a speed of 100 mm/s. A re-swelling period of more than 1800 s in pure water was arranged between each experimental sliding test. Then, the specimen started sliding from the high-speed sliding at 400 mm/s, which was thought to be in fluid film lubrication mode in this report. To prevent the surface change by wear, experiments of each sliding speed were two reciprocating cycles, and the data were collected from the second cycle. It was impossible to generate the completely ideal velocity profile in the turning period of the sliding direction under the high-speed sliding condition. Also, the frictional behaviour would be unstable just after changing the sliding direction, especially in the fluid film lubrication mode. So, the friction coefficient was calculated by the average friction in 25-35 and 75-85% of the sliding motion phase. It was difficult to select the solid-to-solid friction coefficient because the friction coefficient of hydrogel material in the boundary lubrication regime is thought to be dependent on the sliding speed especially in the adhesive hydrogel contact pair as called by elastic friction [34]. In considering this complex and from the experimental results of the impermeable surface specimen, the solid-to-solid friction coefficient was determined as follows. After a series of experiments, each hydrogel specimen was statically loaded with the experimental contact load of 1.8 N for 3 h to secure the equilibrium condition of interstitial fluid flow, where the interstitial fluid pressure would subside to zero. Then, the hydrogel specimen slid at 0.75 mm/s without any re-swelling period. The friction coefficient as the solid-to-solid contact was obtained from this extra low-speed sliding by the same calculation procedure as explained above. The typical experimental conditions are summarised in Table 1.

Results
As shown in Fig. 1, the frictional model was the reciprocating sliding on the plate. The transversal width of the cylindrical specimen was selected as 20 mm, and the reciprocating stroke was 38.69 mm. To cover the sliding surface enough, the lubricant volume of 4 ml was used in a single sliding experiment. The lubricant could stay on the hydrophobic acrylic resin plate with about 1.5 mm fluid thickness. When the cylindrical specimen was placed on the sliding plate, the lubricant was pulled to the specimen by meniscus phenomenon and kept around the specimen even under the high-speed sliding condition, which prevented the shortage of the lubricant. Fig. 4a shows the destination trajectory of the reciprocating motion. Since the DC servomotor had to drive the long ball screw with corresponding inertia, the acceleration phase was needed to change the sliding direction under the high-speed condition. The evaluation of the friction coefficient should be performed in the constant velocity phase in the reciprocating motion. Fig. 4b and c show typical fluid pressure measurement and friction in low (3.125 mm/s) and high (200 mm/s) sliding speed. The MEMS pressure sensor was placed in the centre of the reciprocating sliding pathway. In Fig. 4c, under high-speed sliding conditions, the pressure detecting position showed a little phase delay, which was caused by the motion delay of the type 1 state feedback control. As explained before, the friction coefficient was averaged in 25-35 and 75-85% of the reciprocating motion phase, where the friction coefficient was relatively stable than the other reciprocating phase. This averaging period was corrected with the control delay time and the actual sliding position from the position encoder in the apparatus. The measurement hole of the MEMS pressure sensor was positioned at 25 and 75% of the reciprocating sliding phase. As shown in Figs. 4b and c, the friction coefficient after passing the measurement hole was relatively stable until entering the next accelerating phase.
Since the sliding velocity around 25 and 75% of sliding phase was constant, the horizontal axis of Figs. 4b and c can be converted into the sliding position by the trajectory profile of Fig. 4a. Also, the sliding position of the cylindrical upper part was separately captured by the position encoder. Fig. 5 shows the pressure transition in the same position and the same length at (a) 3.125 mm/s and (b) 200 mm/s extracted from Fig. 4. In Fig. 5, the horizontal width of the graph is accurately equivalent to 8 mm sliding length. The red double-headed arrow on the right side of the graphs shows the 2 mm sliding length. In the slow sliding speed of (a) 3.125 mm/s, the span of the fluid pressure detection was ∼3.14 mm, which was indicated by green vertical lines in the graph. Under an assumption that the fluid pressure in Fig. 5a derived from the interstitial fluid pressure of the biphasic lubrication mechanism, the contact length would be the same 3.14 mm. The position of the pressure peak in (a) the slow sliding condition shifted a little to the forward position in the contact area, which was partly predicted in the study of biphasic hydrogel lubrication [30]. The experimental condition was carefully selected to enter in the hydrodynamic lubrication mode by the radius of the cylindrical specimen, the transverse width of the hydrogel specimen and the viscosity of lubricant in the maximum sliding speed of the experimental apparatus. In Fig. 5b the high-speed sliding condition at 200 mm/s, the lubricating mode would be in the hydrodynamic lubrication in this study. Even at the maximum  sliding speed of the apparatus, the specimen was surrounded with the lubricant by the fluid meniscus. The green vertical lines from the graph (a) indicated the exact same positions in the sliding pathway, which was verified by the position encoder with micrometre precision. Although the contact length might not be completely the same as that of (a) the slow sliding speed, the pressure generation was observed in the leading zone. In the trailing zone, the negative pressure was also detected as a feature of the hydrodynamic lubrication mode. In the experiment, apparent cavitation could not be visible in the trailing zone in the reciprocating motion. A little bulged shoulder as the soft-EHL mode might be accepted in the rear region of the contact area. Fig. 6a shows velocity dependencies of the friction coefficient of PVA hydrogel slid over the acrylic resin plate. To compare the friction coefficient with the proportion of fluid load support, the vertical axis was set to the linear scale, while the horizontal axis was the typical logarithmic one. Although not the all experiments could show the apparent increase of friction coefficient in the high-speed region, the lubrication mode would enter into the quasi-hydrodynamic lubrication mode at a higher sliding speed of 200 mm/s. At lower sliding speed (<100 mm/s), the friction coefficient increased along with the decreasing sliding speed. To determine whether this increase of the friction coefficient derived from the decrease of fluid load support, the proportion of the fluid load support was calculated by the integration of the transition of the local fluid pressure shown in Fig. 3. In a pure hydrodynamic lubrication mode, the fluid pressure of the central region in an apparent contact area is generally higher than that of the side region. As explained in Section 2, the transversal variation of the fluid pressure was omitted because we cannot divide the measured fluid pressure into the biphasic interstitial fluid pressure and the hydrodynamic effect. The proportion of fluid load support of in-situ experimental measurement is shown in Fig. 6b, where the same marks in the graphs correspond to the same experimental specimen. Since the value of the proportion of the fluid load support was calculated by the ratio of fluid support force to the total load, the value of 1 means that all of the load is supported by the fluid pressure. In the high-speed region than 200 mm/s, almost all of the contact load was supported by the fluid pressure. In the slowest sliding speed of 1.56 mm/s, the proportion of the fluid load support ranged from 0.4 to 0.6. Although the sliding condition was not the same, this value would be the acceptable range in comparison with the previous study including the biphasic computational estimation research [31]. In comparing these values with that in simple compression of PVA hydrogel material by the computational research, these experimental values were the lowest one. It means that half of the contact load would be supported by the interstitial fluid pressure in biphasic PVA hydrogel material in the well-swelling state. The effective friction coefficient m eff in biphasic lubrication theory [13] is formulated as where m eq is the equilibrium solid-to-solid friction coefficient in which all of the contact load is supported by the solid phase of the biphasic matrix; w is the fraction of the solid-to-solid contact area in microscopic view, and W p /W represents the interstitial fluid load  Fig. 6b. In this study, the value of w was set to zero under an assumption that the matrix was under completely mixed conditions and the direct solid surface in an intact state was small enough as shown under an actual experimental situation [13].
The solid-to-solid friction coefficient m eq was measured by each specimen, and the effective friction coefficient m eff was calculated with each m eq value. The average solid-to-solid friction coefficient was m eq = 1.042 + 0.084SD in N = 5, which ranged from 0.94 to 1.16. Fig. 6c shows the effective friction coefficient m eff calculated from the values in Fig. 6b the proportion of the fluid load support. The larger fluid load support resulted in lower friction coefficient. As shown in (1), the effective friction coefficient did not include the frictional drag of Couette flow in hydrodynamic lubrication. If the proportion of fluid load support W p /W is 1, the effective friction coefficient m eff results in 0 by (1). Since half of the contact load was supported by interstitial fluid pressure in lowest sliding speed in Fig. 6, the effective friction coefficient m eff was also the half of the equilibrium friction coefficient m eq . To compare the effective friction coefficient m eff with the experimentally measured friction coefficient, the m eff was overlaid with the experimental one in Fig. 7. The calculated effective friction coefficient showed adequate correlation with the experimental friction coefficient.
In the lower sliding speed (<100 mm/s), the fluid pressure for supporting the contact load would be generated by both the interstitial fluid pressure of the biphasic lubrication mechanism and the hydrodynamic lubrication pressure. In an extra attempt of the low sliding speed under 1.56 mm/s, a heavy stick-slip behaviour occurred from the beginning of sliding, where the friction coefficient was so unstable. Although the mechanism of this behaviour might be interesting from some points of view, we limited the lowest sliding speed at 1.56 mm/s in the experiment of the PVA hydrogel surface. For the verification and comparison of this study, another PVA hydrogel specimen with the impermeable surface modification, shown in Fig. 2, was also examined to exclude the surface seepage effect on the biphasic material contact. Although the tangential tensile stiffness of the impermeable specimen provoked some strengthening, the compressive stiffness would not show any large difference from the normal specimen within a short experimental time. To observe the quasi-pure hydrodynamic lubrication mode, the black natural rubber with 10 times stiffer modulus was also tested as an impermeable material. As seen in Fig. 8a, the impermeable specimen apparently showed the increase of the friction coefficient in the high-speed region than 200 mm/s, where the lubrication mode entered the quasi-pure hydrodynamic lubrication mode. Whereas the biphasic surface showed the increase of the friction coefficient with the decrease of the sliding speed (<100 mm/s) as shown in Fig. 6a, the impermeable surfaces in Fig. 8a retain a low level of friction coefficient until the sliding speed of 10 mm/s. In the low friction coefficient in the middle sliding speed from 10 to 100 mm/s, the fluid load support from the MEMS pressure sensor, as shown in Fig. 8b was much lower than that of the biphasic surface in Fig. 6b. While the boundary friction coefficient, which would be equivalent to the equilibrium friction coefficient of biphasic lubrication, ranged 0.4-0.6 in Fig. 8a, the calculated friction coefficient with the impermeable modification by the fluid load support in Fig. 8c did not show any correspondence with the experimental friction coefficient. In the middle sliding speed of the impermeable specimens, the lubrication mode would be the soft-EHL with the micro-EHL, since the lubricant could be trapped in the contact area by the impermeable surface than the biphasic permeable hydrogel surface. The MEMS pressure sensor could not capture the fluid pressure of the thin soft-EHL fluid film because the principle of the MEMS pressure sensor was to detect the deformation of the diaphragm.

Discussion
As for the experimental setup, the MEMS pressure sensor should not be placed in a moving part. The MEMS pressure sensor was  embedded in the fixed bottom plate, and the specimens were slid over the plate. In this sliding configuration, the method to realise the hydrodynamic lubrication regime was to increase the sliding speed of the reciprocating motion with a sufficient lubricant viscosity. The maximum sliding speed of 400 mm/s was achieved by the cycle time of 0.25 s with the 38.7 mm reciprocating stroke, in which the time of the half pathway of the reciprocating motion was only 0.125 s. To capture this fast motion, the overall sampling rate including the motion control was set to 2 kHz as the completely synchronous measurement of all devices. Taking account of the time lag of the state feedback control, the absolute position of the sliding motion could be determined over the experimental trials, as shown in Fig. 5. The friction coefficient was calculated by the average friction in 25-35 and 75-85% of the sliding motion phase, and the local fluid pressure was captured at the centre position of the reciprocating trajectory. In concerning the growth of the hydrodynamic lubrication film, the sliding distance of the twice the initial contact length was required for non-contacting operation in a start-up sliding of a compliant material [35,36]. It was also reported that the fluid film thickness was steady just after the sliding speed reached a constant velocity in a reciprocating motion [37]. In our experiment, the constant velocity region in the sliding trajectory was configured as 26 mm in one way of the reciprocating motion, and the contact length was about 3 mm. So, the hydrodynamic lubrication would be in a steady state at the centre of the reciprocating sliding motion under the high-speed sliding condition.
In this study, several experimental conditions were selectively determined to observe the biphasic lubrication mode under the high-speed sliding condition. While some of the PVA hydrogels showed a very low friction coefficient even in a normal saline lubricant [27], the friction coefficient of PVA hydrogel in this study was considerably higher than those studies in a low sliding speed. If the low friction PVA hydrogel was used in this study, it would be difficult to highlight the function of the biphasic lubrication mode near the hydrodynamic lubrication. As the low friction coefficient surface of PVA hydrogel has been produced by controlling the production process, we could also generate the high friction PVA hydrogel. The friction coefficient of hydrogels and soft materials depends on the surface properties and their interaction with the opposing surface, including roughness, hydrophobicity, dangling chains, electrolyte charge and a template effect of casting mould material [34,[38][39][40]. To obtain the high solid-to-solid friction coefficient of PVA hydrogel, the specific acrylic resin plate was utilised as the casting mould surface. Several resin materials as a counter surface resulted in a large friction coefficient around 1 in a ball on ring experiment [41]. In this study, the counter surface was selected as the acrylic resin plate, which caused very high adhesion to the PVA hydrogel.
The calculated effective friction coefficient by the proportion of fluid load support showed good agreement with the experimental friction coefficient as shown in Fig. 7. In the biphasic lubrication mechanism, the interstitial fluid pressure presses not only the contact surface but also the deformable solid phase around the pressurised fluid. Since this deformation of the solid phase relaxes the fluid pressure, there is a limitation to generate a high proportion of fluid load supported by interstitial fluid pressurization of biphasic theory without any secondary structure in unconfined geometry. Depending on the compressive condition, half of the total contact load would be supported by the fluid pressure in a simple unconfined compression of plain PVA hydrogel. Under an assumption that the proportion of fluid load support immediately after compression of well-swelling PVA hydrogel had a constant value of 0.5, the residual fluid pressure in Fig. 6b should be derived from the effect of the hydrodynamic lubrication mechanism. The MEMS pressure sensor successfully confirmed the fluid load support mechanism in conjunction with the biphasic lubrication and the hydrodynamic lubrication mode.
In the hydrodynamic lubrication mode, it is preferable that the rubbing surfaces be impermeable to trap the fluid pressure in contact surfaces, whereas the permeable biphasic material has an ability to perform the biphasic lubrication mechanism. The main purpose of this study was to confirm whether the biphasic permeable surface disturbs the hydrodynamic lubrication or not. For the comparison of the experimental measurement of the biphasic lubrication with the soft-EHL mode, the hydrogel surface was covered with the thin polyethylene film as the impermeable modification. The impermeable natural rubber with 10 times stiffer modulus was also tested to observe the pure hydrodynamic lubrication mode. In both permeable and impermeable surfaces, the increase of the friction coefficient was observed under higherspeed sliding condition than 200 mm/s. By the experimental settings of this study, the lubrication mode could enter the pure hydrodynamic lubrication mode under high-speed sliding condition. However, the obvious difference was seen in the middle sliding speed from 10 to 100 mm/s. In the middle speed, the impermeable specimens maintaining the friction coefficient at a low level, while the biphasic permeable specimens showed the increase of the friction coefficient with decreasing of the Fig. 8 Friction coefficient and the fluid load support of the impermeable specimens. The impermeable surface kept low friction coefficient in middle sliding speed from 10 to 100 mm/s a Experimental friction coefficient b Fluid load by MEMS sensor c Calculated friction coefficient by load partitioning mechanism sliding speed. Also, the fluid load support of impermeable specimens was much lower than the biphasic permeable specimens by the measurement of the MEMS pressure sensor. In this study, the water solution of the large molecular weight PVA (M W ≃ 8.9 × 10 5 ) was used as the lubricant to increase the viscosity sufficient for entering the pure hydrodynamic lubrication mode under high-speed sliding conditions. By the impermeable modification of the hydrogel surface, one of the explanations of the frictional difference in the middle sliding speed would be the change of the lubrication mechanism to a soft-EHL mode including micro-EHL mechanism from biphasic lubrication. The lubrication properties of water solutions of several high molecular weight polymers were reported with the viscosity dependence of shear rate (shear rate dependence of viscosity) [42]. While the polymer molecules were effective in shifting the mixed lubrication regime to lower sliding speed, the polymer solutions did not appear to contribute a significant effect to boundary lubrication itself on either the hydrophobic or hydrophilic surface. On the other hand, it was known that some biological constituents in synovial fluid were effective under boundary lubrication conditions in specific surfaces [43,44]. The polymer concentration in a contact area would be effective for the improvement of both fluid film formation and boundary lubrication properties. In this study, the impermeable surface model had changed not only the surface permeability but also the surface material as the low-density polyethylene. Although the interactions between different surfaces and lubricant were the interesting thing from the scientific viewpoint, it was beyond the scope of this study. In the middle speed of the impermeable surface model, the MEMS pressure sensor did not detect enough fluid pressure to support contact load. As the MEMS sensor detect the deformation of the micro-diaphragm, enough volumetric fluid could not be trapped from the thin fluid film of the soft-EHL mode or boundary lubrication film. The MEMS pressure sensor could detect the weeping flow from the biphasic surface of PVA hydrogel with measurable permeability in this study. While it might not be appropriate to separate the pure hydrodynamic lubrication from soft-EHL, the increase of the friction coefficient was partly observed even in the permeable hydrogel specimen under high-speed sliding conditions. The plenty fluid flow of the pure hydrodynamic lubrication condition enough overcame the seepage flow into the biphasic matrix. Although the experimental conditions in this study were so selective, the biphasic permeable surface disturbed the effective lubrication of impermeable surface in the middle sliding speed. However, the biphasic lubrication mechanism exerts its functionality just behind the pure hydrodynamic lubrication mode. So, we have to consider this situation in the tribological design of hydrogel materials as a load bearing surface.
There existed a difficulty to measure the friction coefficient of PVA hydrogel in a low-speed region <1 mm/s. In an attempt of the very low sliding speed, we experienced excessive stick-slip behaviour as if the sliding specimen hopped on the counter surface of an acrylic resin plate with apparent large noise. An example of the partial stick-slip behaviour is shown in Fig. 4b, which showed the friction coefficient at the sliding speed of 3.125 mm/s. The elastic friction model was previously proposed in the observation of the frictional behaviour of hydrogel material [34]. However, they also reported the difficulty of the friction measurement of the adhesive surface pair. One of the reasons of the excessive stick-slip would be partly derived from the deficiency of the total stiffness of the experimental apparatus with a high sensitivity force sensor. However, another soft component in this experiment was the soft hydrogel specimen itself with necessary thickness, which involved a tangential elasticity in the sliding direction. On the other hand, to discriminate the friction of the biphasic lubrication mechanism from the coexisting hydrodynamic lubrication, the higher solid-to-solid friction coefficient was required as the selective condition. In the elastic friction model, the friction force related to the number of adsorbed sites, which was related to the sliding speed rather than the contact load. In the preliminary experiment of this study, the lower contact load apparently resulted in the higher friction coefficient, which led the selective reason for the contact load in this study. While the low contact load kept the thickness of the elastic bulk part, high adhesive friction pulled the bulk surface in the tangential sliding direction. So, we could not achieve the measurement of the friction coefficient in very low sliding speed in our experimental settings. However, the solid-to-solid equilibrium friction coefficient m eq was measured without excessive stick-slip behaviour at the sliding speed of 0.75 mm/s. Before the measurement of the solid-to-solid friction coefficient, the specimen was exposed to the static load for 3 h to obtain the equilibrium condition of interstitial fluid flow. This preconditioning process decreased the thickness of the elastic bulk part with the consolidation of the hydrogel matrix, which would suppress the stick-slip behaviour. To extend the sliding speed to higher and lower regions, the experimental setup should be reconsidered including the sliding manner of the reciprocating motion.
The experimental result showed some variance as shown in Fig. 6a. The difference of the surface structure including roughness caused a peculiar Stribeck curve in the transition of the boundary lubrication regime with the consideration of micro-EHL [45]. While the specimens with a certain roughness [31] were prepared by the smooth surface of the acrylic resin plate as the casting mould, the further consideration of the surface roughness should be conducted in the future. In the additional frictional experiment, specimens showed good repeatability over all sliding speeds, not shown in this paper. So, another possibility of the variance of the frictional behaviour might be a local inhomogeneity of the PVA hydrogel produced by the repeated FT process with an uncertain growth of the freezing ice. In this study, the friction coefficients under each experimental condition were collected in the routine procedure, as explained in Section 2. The frictional behaviour in more long-term sliding was also interesting things especially in the conjunction region between biphasic lubrication and hydrodynamic lubrication. We experienced some extent of the recovery of the friction coefficient under mid-and high-speed sliding conditions in the extra sliding test after the equilibrium condition of PVA hydrogel. This recovery of the friction coefficient might be caused by reswelling due to the hydrodynamic pressure, which was recently pointed out by other research [46].
While the lubricant in this study was simply the solution of PVA powder, the synovial fluid contains several constituents. These proteins and phospholipids enhance the frictional abilities in the boundary lubrication regime [29].
Although the biphasic lubrication worked beside the pure fluid film lubrication mode, the permeable porous surface disturbed the effective lubrication of soft-EHL mode and micro-EHL mechanism under our experimental conditions. The lubricant fluid flowed into the biphasic hydrogel bulk and could not keep the hydrodynamic fluid pressure with the micro-EHL mechanism. Although the experimental condition of this study was so selective and unrealistic, the experimental result showed a possibility of the negative effect of the biphasic surface. So, we have to consider the extra mechanism to avoid or deal with this inconvenient situation. In the synovial joint system, it was said that macromolecules were trapped at the surface of an articular cartilage with a small pore size, which induced the increase of the concentration of lubricant constituents in the contacting surface of biphasic material [17] as called by 'boosted lubrication' [9]. If some of the macromolecules adhere to the PVA hydrogel surface and seal a part of the inflow, this situation helps to recruit the effective lubrication of soft-EHL in middle sliding speed. So, the further experiment with the phospholipid lubricant or the synovial fluid would be expected as one of the next trials. In this study, the high solid-to-solid friction was required to separate the activity of biphasic lubrication from the effective hydrodynamic lubrication. Since the well-defined lubricant reduces the boundary friction of the artificial hydrogel cartilage [47], we have to select the appropriate constituents for the lubricant in the further experiment of this study. The biphasic lubrication of the synovial articular cartilage in the conjunction of hydrodynamic lubrication was also the interesting thing, which could elucidate the design of artificial cartilage material as a load bearing system. In early trials, synovial articular cartilage with subchondral bone was once subjected instead of the PVA hydrogel specimen. However, any small dislocation of the cartilage specimen resulted in a large difference of the fluid pressure because actual articular cartilage has a curvature. Since the tissue thickness and mechanical properties would vary with each specimen, there were inevitable limitations in the experiment of synovial articular cartilage. One of the methods might be cutting off the cartilaginous tissue from subchondral bone and reshaping the tissue into a specified condition. The high solid-to-solid friction coefficient in this study was not a realistic situation because well-controlled PVA hydrogels with a low friction coefficient should be used for artificial articular cartilage. However, the biphasic lubrication mechanism arises in any other situation with the interstitial fluid pressure than the pure hydrodynamic lubrication mode. In other words, the biphasic lubrication mode widely delivers its functionalities with other effective mechanisms to reduce friction coefficient in adaptive multimode lubrication. The synovial articular cartilage has several functional compositions to realise a low friction coefficient, including a fibre-reinforced structure by a collagen network with position dependency and inhomogeneity, depth-dependent compressive modulus, compaction effect on permeability, amorphous surface gel layer etc. The combination of the PVA hydrogel with fibre-reinforcement as biomimetic artificial cartilage [33] successfully reduced the friction coefficient by the enhancement of the biphasic lubrication mechanism for a series of studies. The PVA hydrogel as the artificial cartilage material has more potentialities to reduce the friction coefficient and resist wear by importing the effective mechanism of the synovial articular cartilage.

Conclusion
In this study, the relationship of biphasic lubrication and hydrodynamic lubrication was observed by the in-situ measurement of fluid load support. The small MEMS pressure sensor was embedded in the lower plate, and the PVA hydrogel as a biphasic material was slid on the plate reciprocally in a wide range of sliding speed. The experimental results of the PVA hydrogel showed that the biphasic lubrication mode coexisted with the hydrodynamic lubrication mode as the mixed lubrication regime. Another specimen with impermeable modification kept a lower friction coefficient than the biphasic surface in middle sliding speed, where the impermeable surface would trap the fluid pressure in contact surfaces with thin fluid film thickness or the micro-EHL mechanism. Although the experimental condition of this study was so selective and unrealistic, the result showed a possibility of the negative effect of the biphasic surface. However, the fluid load support of the biphasic surface was estimated as the significant level at lower sliding speed. The biphasic lubrication mode affects the friction coefficient in wide operating range. So, we have to manage and enhance the biphasic lubrication mechanism in considering the artificial articular cartilage as a load bearing material.

Acknowledgments
This study was financially supported by the Grant-in-Aid for Specially Promoted Research of Japan Society for the Promotion of Science (JSPS) (KAKENHI:23000011) and the Grant-in-Aid for Science Research of JSPS (KAKENHI:16H03170).