- Email: [email protected]
Friction of human skin against smooth and rough glass as a function of the contact pressure
ARTICLE IN PRESS Tribology International 42 (2009) 1565–1574
Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Friction of human skin against smooth and rough glass as a function of the contact pressure S. Derler a,, L.-C. Gerhardt a, A. Lenz a, E. Bertaux a, M. Hadad b a
Laboratory for Protection and Physiology, Swiss Federal Laboratories for Materials Testing and Research (Empa), Lerchenfeldstrasse 5, CH-9014 St. Gallen, Switzerland Laboratory for Materials Processing and Characterization, Swiss Federal Laboratories for Materials Testing and Research (Empa), Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland b
a r t i c l e in fo
abstract
Article history: Received 21 July 2008 Received in revised form 22 November 2008 Accepted 28 November 2008 Available online 9 December 2008
The friction behaviour of human skin was studied by combining friction measurements using a tri-axial force plate with skin contact area measurements using a pressure sensitive film. Four subjects carried out friction measurement series, in which they rubbed the index finger pad and the edge of the hand against a smooth and a rough glass surface under dry and wet conditions. The normal loads were varied up to values of 50 N, leading to skin contact pressures of up to 120 kPa. The analysis of the pressure dependence of friction coefficients of skin for contrasting sliding conditions allowed to determine the involved friction mechanisms on the basis of theoretical concepts for the friction of elastomers. Adhesion was found to be involved in all investigated cases of friction between skin and glass. If adhesion mechanisms predominated (skin against smooth glass in the dry condition and skin against rough glass in the wet condition), the friction coefficients were generally high (typically 41) and decreased with increasing contact pressure according to power laws with typical exponents between 0.5 and 0.2. Contributions to the friction coefficient due to viscoelastic skin deformations were estimated to be relatively small (o0.2). In those cases where the deformation component of friction played an important role in connection with adhesion (skin against rough glass in the dry condition), the friction coefficients of skin were typically around 0.5 and their pressure dependence showed weak trends characterised by exponents ranging from 0.1 to +0.2. If hydrodynamic lubrication came into play (skin sliding on smooth glass in the wet condition), the friction coefficients were strongly reduced compared to dry friction (o1), and their decrease with increasing contact pressures was characterised by exponents of o0.7. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Skin tribology Sliding friction coefficient Contact area Adhesion Deformation Hydrodynamic lubrication
1. Introduction The friction behaviour of human skin is determined by the complex interplay of material and surface properties of the skin as well as the contacting material, and strongly depends on the contact parameters (e.g. pressure and sliding velocity) and the presence of substances such as water, sweat or skin surface lipids at the interface [1–3]. To a large extent, the current knowledge on the tribology of skin resulted from dermatological studies on the effects of skin care products [4–7]. However, the frictional properties of skin are of general importance in connection with mechanical contacts of the human body with external materials, e.g. when touching and handling objects or when wearing clothes and accessories. In several recent studies on skin tribology, specific practical cases such as friction contacts between hand and object [8–10] or
Corresponding author.
E-mail address: [email protected] (S. Derler). 0301-679X/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2008.11.009
between skin and textiles [11,12] were analysed by in vivo measurements. The typical experimental set-up in these studies was to rub the skin against objects and surface samples attached to a multi-axial force plate or a force transducer in order to measure normal and friction forces and to determine friction coefficients. An alternative approach consists in the use of a tribometer with which (mostly spherical) probes made of different materials are slid over the skin of subjects [13,14]. This measurement technique was applied to characterise the general friction properties of skin [15,16] and to study the contribution of the stratum corneum to the friction of skin [17]. Human skin shows viscoelastic material properties similar to those of a soft elastomer [2,18,19]. Therefore, theoretical concepts for the friction of elastomers [20,21] were applied to interpret experimental data for the friction of skin. Under dry conditions, adhesion at the skin/material interface as well as deformation of the skin and the soft sub-surface tissue contribute to the coefficient of friction (two-term model of friction) [1]:
m ¼ madhesion þ mdeformation
(1)
ARTICLE IN PRESS 1566
S. Derler et al. / Tribology International 42 (2009) 1565–1574
The friction of skin is considered to be mainly determined by adhesion, while deformation is normally believed to be unimportant [2,22,23]. Applying the contact theory of Hertz [24], Wolfram derived the following expression for the adhesion component of friction
madhesion / N 1=3 E2=3
(2)
where N denotes the normal load and E the elastic modulus of skin [23]. A decrease of friction coefficients with increasing normal load according to m / N1=3 is consistent with experimental studies in which the friction of dry skin was investigated using solid probe materials [25–27]. Friction coefficients that decreased with increasing load were also observed in experiments, in which spherical probes were slid on wet skin [22]. In order to estimate the contribution of viscoelastic skin deformations to friction (hysteresis), Johnson et al. [2] applied the approach of Greenwood and Tabor [28]. In contrast to the adhesion component of friction (Eq. (2)), the contribution due to hysteresis is expected to increase with normal load:
mhysteresis / N
þ1=3
1=3
E
(3)
It is usually experienced in everyday life that the friction of skin increases with hydration, e.g. due to sweating. This was explained by the fact that moist skin becomes softer and is characterised by a lower elastic modulus so that adhesion is increased (Eq. (2)) [23]. In addition, human skin swells due to water uptake, leading to a smoothing of the skin surface and an increased microscopic contact area in friction contacts [22]. In a recent study, Gerhardt et al. systematically varied the hydration state of the skin of the volar forearm in 22 subjects and found a highly positive linear correlation between skin moisture and friction coefficients against textiles [29]. When the skin is saturated and excess water accumulates in the interface, capillary bridges between the skin and the countersurface might be relevant to a certain degree, but with further increasing amounts of water lubrication phenomena will become more and more important. Dowson [1] described various types of lubrication that are relevant in connection with human skin. Hydrodynamic lubrication is characterised by the complete separation of the sliding surfaces by a liquid film. Under these conditions, the adhesion component of friction is replaced by a contribution due to viscous friction 1 V V mviscous ¼ Z (4) A¼Z p1 N h h where N denotes the normal load, Z the viscosity of the fluid, h the film thickness, V the sliding velocity, A the apparent contact area and p the contact pressure [1]. Depending on contact conditions as well as fluid film thickness in relation to the surface roughness of the skin and the contacting material, mixed lubrication or boundary lubrication can take place. The former lubrication regime is characterised by the coexistence of dry and wet contact zones, the latter by molecular surface films influencing the friction behaviour. It is a common empirical approach to express measurement data for the friction force F in the form F ¼ k Nn , where k corresponds to the conventional friction coefficient at unit normal load, N denotes the normal load and n is termed the load index [22]. The friction coefficient as a function of the normal load is then given by
mðNÞ ¼ k N n1
(5)
In the logarithmic form logðmÞ ¼ logðkÞ þ ðn 1Þ logðNÞ, this equation can be used to determine the exponent n1 (and the load index n) by linear regression and to test if the friction measurement data can be attributed to a predominant friction
mechanism. According to Eqs. (2)–(4), friction mechanisms such as adhesion, deformation or hydrodynamic lubrication should be indicated by distinctive exponents of 13, þ13 and 1, respectively. In this study, the friction behaviour of human skin was studied as a function of the contact pressure by combining friction measurements using a tri-axial force plate with contact area measurements using a pressure sensitive film. Four subjects carried out compression tests and friction measurement series, in which they rubbed the skin of two different anatomical sites against a smooth and a rough glass surface under dry and wet conditions. The objectives were (1) to analyse the pressure dependence of the friction of skin for contrasting cases (dry/wet, smooth/rough) and to determine the involved friction mechanisms and lubrication regimes and (2) to test how far theoretical concepts developed for the friction of elastomers are applicable to describe the experimental data found for human skin.
2. Experimental 2.1. Friction measurements The friction behaviour of the human skin was investigated for two anatomical sites, namely the pad of the index finger and the edge of the dominant hand. Two females and two males with ages between 23 and 45 y (four of the authors) carried out friction measurement series, in which they repeatedly rubbed their skin against a smooth and a rough glass surface using normal loads of up to 50 N. The skin slid over distances between 5 and 8 cm within periods of 0.5–1.5 s, leading to sliding velocities between 5 and 10 cm/s. Two subjects carried out the experiments with a pulling motion and the other two with a pushing motion, holding the finger and the hand in a stretched position (Fig. 1). When measuring friction coefficients for the skin of the finger pad, the index finger was inclined at angles between 301 and 451 to the counterface. The glass plates were attached to a quartz 3-component dynamometer Kistler, type 9254 (dimensions 15 cm 10 cm). The normal and the friction force were measured using charge amplifiers (Kistler, type 5011), and Dynoware software (Kistler, type 2825A-02) was used to acquire the friction and normal force with a resolution of approximately 25 mN at a sampling rate of 125 Hz. Measurements were carried out over periods of 20 s, allowing a subject to conduct a sequence of friction movements at varied normal loads. In the process, the subjects controlled the applied normal load by means of an analogue voltage meter. Figs. 2a and b show typical results measured in one friction experiment. Individual friction coefficients were determined for each single friction movement by analysing the peaks of the normal and friction force signals over intervals of 0.1 s. The variation of friction coefficients within these time intervals was characterised by typical (median) standard deviations of 0.02. For each glass surface and each anatomical site, the subjects carried out at least 10 friction measurements under dry and wet conditions. In the wet condition, the glass surfaces were covered by a film of deionised water with a thickness of approximately 1 mm. All friction experiments took place at a temperature of (2371) 1C and a relative humidity of (5075)%. The subjects were acclimatised to the laboratory climate for at least 10 min prior to the measurements. The skin of the subjects was cleaned with ethanol before each measurement series. In addition, the dry glass surfaces were cleaned with ethanol before each friction experiment. 2.2. Contact area measurements In order to measure the apparent contact area between the skin and a flat surface as a function of the normal load, a pressure
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
1567
surface profile was 0.0570.01 mm for the smooth glass and 45.075.6 mm for the rough glass. The surface topography of the skin was analysed by an optical profilometer based on white-light (Cotec, AltiSurf 500), using silicone replicas (negatives) of the anatomical sites investigated. Surface scans were carried out for samples of size 5 mm 5 mm, using a lateral resolution of 10 mm and a vertical resolution of 10 nm. Fig. 3 shows examples of the skin surface structure at two anatomical sites for two subjects. 3. Results 3.1. Apparent contact area of skin as a function of the normal load
Pushing motion
Pulling motion
Fig. 1. Measurement of sliding friction coefficients for the skin of the index finger pad (a) and the edge of the hand (b) against glass. The sliding directions corresponded to pushing and pulling motions of the arm.
sensitive film (Tekscan, model 5051; sensor density: 62 elements per cm2) was combined with the force plate. The subjects placed the index finger and the edge of the hand on the pressure sensitive film (using the same stretched position as in the friction tests) and gradually increased the normal load (Fig. 2c). The subjects checked the applied normal load by means of an analogue voltage meter. The pressure distribution of the skin and the normal force acting on the force plate were simultaneously recorded using a sampling rate of 125 Hz. From the measured pressure distributions, the apparent contact area of the skin could be determined with an estimated uncertainty of 70.2 cm2. For each anatomical site investigated, the four subjects carried out series of six experiments over periods of 20 s, in which the applied normal forces ranged up to 50 N. A typical result of a contact area measurement is shown in Fig. 2d.
2.3. Surface characterisation Glass surface samples were cut from a plate of technical glass. An untreated sample represented the smooth glass surface, and a sample with random surface roughness was produced by means of sandblasting. A mechanical profilometer (Mahr, Perthometer M1) was used to measure standard roughness parameters for the two glass surfaces. The parameter Rz, characterizing the average height difference between highest peaks and lowest valleys in a
Results of the compression tests for the finger pad and the edge of the hand are shown in Fig. 4. For both anatomical sites, the measurements of the contact area as a function of the normal force showed a satisfying reproducibility for the same subject (4a). The averaged results revealed differences between the four subjects, but showed the same qualitative behaviour (4c), characterised by a steep initial increase of the contact area with normal load (in the force range of up to 1 N in the case of the finger and within about 10 N in the case of the edge of the hand). At normal loads between 45 and 50 N, maximum skin contact areas of about 15 cm2 were observed for the edge of the hand and of about 4 cm2 for the index finger pad, leading to maximum mean contact pressures of about 40 and 120 kPa, respectively. For all subjects and skin sites, the averaged curves were fitted with empirical functions of the form AðNÞ ¼ a þ b N1=4 þ c N with adjusted R2-values between 0.94 and 0.99 (Fig. 4b and d). The resulting fit functions (4d) were used to relate normal forces to skin contact areas and to calculate mean contact pressures for the subsequent analysis of the friction behaviour of skin (Sections 3.2 and 3.3). The mean contact pressure of the skin linearly depended on the normal load in most cases (Fig. 4e). The deviations from the linear relationship observed in some cases (Figs. 4e and f) were probably due to slight positional changes of the hand during the compression tests. 3.2. Friction coefficients of skin for different subjects and anatomical sites More than 4500 single sliding friction coefficients ranging from about 0.05 to 5 were determined from the friction measurements performed by all subjects. The highest friction coefficients of skin were found against dry, smooth glass (2.1871.09; range: 0.39–5). On the wet, smooth glass surface, the friction coefficients were considerably lower (0.6170.37; range: 0.07–2.12). When rubbed against the rough glass surface, the investigated skin sites showed relatively low friction coefficients of 0.5370.22 (0.03–1.42) under dry conditions and values of 1.4370.57 (0.32–4.56) under wet conditions, respectively. The skin of the edge of the hand showed systematically lower friction coefficients than the skin of the finger pad (Fig. 5). For contact pressures in the range from 10 to 30 kPa, the average differences were between 0.3 and 0.7, depending on the glass surface and the presence of water. In the case of the edge of the hand, the measurement results of the four subjects were comparable for all glass surfaces and test conditions. In contrast, the friction behaviour of finger pads seemed to depend on the direction of the sliding motion. For pulling motions of the finger, the pressure dependence of the friction coefficients was more pronounced. Comparisons between the results of the different subjects are shown in Fig. 6 for the example of the rough glass surface in the wet condition.
ARTICLE IN PRESS 1568
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Friction coefficient
Force (N)
20 Normal Force Friction Force
15 10 5 0
2.0 1.5 1.0 0.5 0.0
0
5
10
15
20
0
5
10
15
20
Normal force (N)
35 30 25 20 15 10 5 0
Contact area (cm2)
Force (N)
Time (s)
4 3 2 1
1 cm
0 0
5
10
15
20
0
5
10
Time (s)
15
20
25
30
Time (s)
Fig. 2. (a) Normal force and friction force as a function of time, measured in a friction experiment on smooth glass in the wet condition. The subject (#, 31 y) rubbed the right index finger on the substrate, using different normal loads for the individual sliding movements. (b) The resulting friction coefficients (m) varied with the applied normal force. The plots c and d show results of the simultaneous measurement of the applied normal force (force plate) and the contact area (pressure sensitive film) for the index finger of the same subject. An example of the pressure distribution at a certain time is illustrated in the insert of plot d. The independent force and contact area measurements were synchronised via initial peaks resulting from a short touch.
mm 0
1
2
mm 3
4
5
0
0
0.5
0.5
1
1
1.5
1.5
1
2
0
1
2
2.5 3
3 3.5
4
4
4.5
4.5
5
5
3
4
5
5 mm 1
2
mm 3
4
5
mm
0
mm
4
2.5
3.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
3
2 mm
mm
2
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Fig. 3. Surface structure of the skin at the finger tip (left) and the edge of the hand (right) for two subjects (pictures above: #, 45 y; pictures below: ~, 23 y). Concentric ridges are characteristic for finger pads while first and second order furrows are visible for the skin of the edge of the hand.
ARTICLE IN PRESS
15
Contact area (cm2)
Contact area (cm2)
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Hand
10 5
Finger 0 0
10
20
30
40
15 Hand
10 5
Finger 0 0
50
10
15 Hand
5 Finger 0
30
40
50
15 Hand
10 5
Finger 0
0
10
20 30 40 Normal force (N)
0
50
100
10
20 30 40 Normal force (N)
50
100
80
Pressure (kPa)
Pressure (kPa)
20
Normal force (N)
Contact area (cm2)
Contact area (cm2)
Normal force (N)
10
1569
Finger
60 40 20
Hand
0
80 Finger
60 40 20
Hand
0 0
10
20 30 40 Normal force (N)
50
0
10
20 30 40 Normal force (N)
50
Fig. 4. Apparent contact area measured as a function of the normal load: (a) measurement results for the pad of the index finger and the edge of the hand for one subject (#, 31 y), (b) average curves for the finger and the edge of the hand, calculated from the six measurements shown in plot a, (c) comparison between the average curves of the four subjects (pink curve: ~, 23 y; red curve: ~, 27 y; blue curve: #, 31 y; green curve #, 45 y), (d) fits of the average curves for the four subjects. Relationship between normal force and mean contact pressure: (e) average curves for the four subjects and (f) linear fits of the pressure-force curves.
Fig. 5. Comparison between the friction coefficients of the skin for the finger and the edge of the hand when rubbed against smooth glass in the wet condition. Normal (a) and logarithmic plot (b) of the pressure dependence. The measurement results of all subjects are plotted.
The uncertainty of the friction measurement results was estimated on the basis of differences between successive data points in plots of friction coefficients versus contact pressure
(Figs. 5–7) for the same subject, skin site, glass surface and test condition. The statistical analysis indicated that the measured friction coefficients were typically scattered around the fitted
ARTICLE IN PRESS 1570
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Fig. 6. Friction coefficients of the skin of four subjects on rough glass in the wet condition. In the case of the index finger pad (a, b) the friction behaviour depended on the sliding direction ( and J: pulling motion; ’ and &: pushing motion). The skin of the edge of the hand (c, d) showed comparable results for all subjects.
trends with average standard deviations of about 0.1 for skin against dry, rough glass and against wet, smooth glass, of about 0.2 for skin in contact with wet, rough glass and of about 0.5 for skin against dry, smooth glass. 3.3. Pressure dependence of the friction of skin In most cases, the measured friction coefficients of skin strongly depended on the contact pressure. Fig. 7 exemplarily shows the measurement results for one subject. In the experiments on the dry, rough glass surface, the friction coefficients of skin were practically constant or depended slightly on the contact pressure. In contrast, the friction coefficients systematically decreased with increasing contact pressure in the experiments on dry, smooth glass as well as in all experiments carried out under wet conditions. In order to characterise the load-dependence of the friction of skin, the experimental data was assumed to follow a power law mðpÞ ¼ k pn1 , analogous to Eq. (5). The exponent n1 was determined by linear regression of the logarithmic data (as shown in the Figs. 5b, 6b and d and 7b and d). Results for the exponent n1 are given in Table 1. On the basis of the previous literature on the friction of skin (Section 1), the obtained exponents can be associated with different predominant friction mechanisms (see Section 4). 3.4. Skin surface characteristics The topographical measurement data of the skin replicas were analysed concerning the surface roughness parameters Ra and Rz
(Table 2). For all subjects, the skin surface on the index finger pad was found to be rougher (mean Rz values between 62 and 99 mm) than that on the edge of the hand (mean Rz values ranging from 33 to 73 mm).
4. Discussion 4.1. General The friction coefficients between skin and glass measured for two skin sites in four subjects ranged from about 0.05 to values greater than five and strongly depended on the glass surface roughness, test conditions and skin area. In this study, the skin was rubbed against two different flat glass surfaces attached to a tri-axial force plate, while in previous investigations glass lenses or spheres (radii of curvature in the range of centimetres) with smooth surfaces were slid over the skin of the volar forearm [2,22,26]. Direct comparisons between measurement results are further complicated by differences in the sliding velocities and the applied normal loads. We measured friction coefficients of skin over a wide range of contact pressures up to 120 kPa, covering practical cases of mechanical contacts of the skin, e.g. when touching or gripping hard objects or assessing the roughness of surfaces [11]. The analysis of the friction behaviour of skin on different glass surfaces (smooth and rough) and contrasting conditions (dry and wet) indicated various friction mechanisms which are combined in different ways. The measured friction coefficients systematically depended on the mean contact pressure (determined from the apparent contact area as a function of the normal load), so that a classification became possible on the basis of the load index
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
1571
Fig. 7. Sliding friction coefficients of the skin of one subject (#, 31 y) against smooth and rough glass under dry (a, b) and wet conditions (c, d).
Table 1 Exponents n1 determined from linear fits to the logarithmic data mðpÞ ¼ k pn1 for the skin of all subjects and anatomical sites when rubbed against smooth and rough glass under dry and wet conditions. Exponent n1
Skin site
Subject
Smooth glass
Rough glass
Dry condition
Finger
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.96 –0.79 –0.26 –0.15
+0.15 +0.10 –0.03 –0.09
Hand
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.56 –0.48 –0.19 –0.32
(–0.21) +0.04 +0.04 +0.17
Finger
~, 23 y ~, 27 y #, 31 y #, 45 y
–1.42 –1.05 –0.70 –0.74
–0.80 –0.63 –0.34 –0.36
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.87 –1.44 –0.73 –0.79
–0.26 –0.48 –0.45 –0.37
Wet condition
Hand
The value given in brackets is based on a small range of applied contact forces.
(Eq. (5)) as described in the following. For a common treatment of the two investigated skin areas, the pressure dependence of the friction coefficient (characterised by the exponent n1) is studied instead of the relationship between friction force and normal force (characterised by the load index n).
4.2. Friction mechanisms of skin under dry sliding conditions 4.2.1. Dry friction of skin against smooth glass For contact pressures of 2072 kPa, the mean friction coefficients of finger pads in contact with the smooth glass surface were
2.2570.82. For the edge of the hand, the corresponding friction coefficients were 1.2170.34. The exponents n1 for the edge of the hand ranged from 0.56 to 0.19, indicating the importance of adhesion in the friction mechanism, for which an exponent of 13 would be expected (Eq. (2)). In the case of the two subjects who rubbed the skin of their finger pads using a pushing motion, the exponents n1 of 0.26 and 0.15 were close to the results for the edge of the hand. For the subjects pulling their fingers over smooth glass, however, the exponents were 0.96 and 0.79, respectively. Different deformation of the skin and the finger pad in pulling and pushing motions probably contributed to the differences in the friction behaviour. Effects of moisture (sweat) in the skin/glass interface could not be excluded during the experiments.
4.2.2. Dry friction of skin against rough glass In dry sliding friction contacts with the rough glass surface, the investigated skin areas showed mean friction coefficients of 0.6370.22 (finger) and 0.3870.03 (edge of the hand) for contact pressures of 2072 kPa. Typically, the measured friction coefficients slightly increased with the contact pressure and were characterised by exponents n1 between 0.09 and +0.17 (the result for the edge of the hand of one subject was not taken into account, because the small range of applied normal loads did not allow a reliable regression analysis). The case of pressureindependent friction coefficients was physically explained by a linear increase of the real contact area between the asperities of rough surfaces in contact with increasing pressure [20,30]. As the microscopic contact areas between surface asperities grow and more and more new surface asperities come in contact with increasing pressure, the mean pressure at the contact zones remains constant. Friction coefficients increasing with the contact pressure, on the other hand, can be associated with a mechanism that involves skin deformation (Eq. (3)). Tang et al. [16] attributed the contribution of skin deformations to friction to the penetration and ploughing of surface asperities of a hard material into the skin surface. In our experiments, however, we neither observed
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
damages to the skin nor visible modifications of the skin surface, even though each subject on average carried out more than 550 individual friction measurements per investigated skin area. Therefore, we assume that ploughing and abrasion of the skin surface were less important as friction mechanisms than viscoelastic skin deformations (hysteresis), resulting from cyclic deformations of the skin due to glass surface asperities sliding over the skin surface. Adams et al. [22] who investigated the skin of the volar forearm, estimated an order of magnitude of 0.05 for the hysteresis component of skin friction. Among the four subjects and investigated skin areas, the most pronounced increase in dry friction on rough glass was found in the case of an edge of the hand (#, 45 years; reflected by n1 ¼ +0.17, Table 1). In the pressure range of up to 35 kPa, the total friction coefficient increased from 0.32 to 0.45, from which a maximum contribution of mhysteresis 0:13 can be estimated. Based on the two-term model of friction (Eq. (1)), the adhesive component of the friction coefficient can then be assumed to lie around 0.3. Thus, even if measurable contributions due to viscoelastic skin deformations are evident, adhesion remains an essential friction mechanism. Compared to dry friction contacts against smooth glass, the adhesion of skin is significantly reduced when in contact with the rough glass surface, indicating a smaller real contact area between the skin and glass surface asperities. 4.3. Friction mechanisms of skin under wet sliding conditions 4.3.1. Wet friction of skin against smooth glass The mean friction coefficients at contact pressures of 2072 kPa on smooth glass in the wet condition were 0.6670.32 for finger pads and 0.2170.05 for skin on the edge of the hand. The exponents n1 ranged from 1.44 to 0.70 and indicated an influence of the sliding direction of the skin. Pushing motions showed exponents between 0.79 and 0.70 and pulling motions values from 1.44 to 0.87. The relatively low friction coefficients, especially those found for the edge of the hand, as well as the high absolute values of the exponents n1 indicated aqueous lubrication effects (Eq. (4)). On the other hand, stick–slip phenomena occurring in some of the friction experiments with finger pads indicated that the lubricating water films can be penetrated by the surface elevations of the skin during the sliding processes. The maximum friction coefficient due to hydrodynamic lubrication of the skin can be estimated by Eq. (4), using the minimum fluid film thickness derived from the theory of soft EHL (or isoviscous-elastic hydrodynamic lubrication) [22,32]. The regime of soft EHL is characterised by significant elastic deformaTable 2 Skin surface roughness parameters determined from skin replicas (negatives) of the anatomical sites for the four subjects investigated.
tion of the solids, but relatively low contact pressure, so that the viscosity of the fluid film is not increased [33]. Johnson et al. [2] discussed the lubrication of skin by water films on the basis of an expression which was used to estimate the minimum film thickness for a smooth elastomer sphere sliding in a fluid on a rigid flat surface [34]. Fig. 8 shows the results of an analogous calculation which was adopted to the case of finger pads and the edge of the hand, in comparison with calculations using the formulae for soft EHL. For parameters representing the experimental conditions, the minimum water film thickness ranged from 1 to 3 mm. The calculated results for mviscous strongly decrease with increasing contact pressure, showing values around 0.005 for a pressure of 20 kPa. For contact pressures up to 30 kPa, fingertips show slightly higher values of mviscous than the edge of the hand. Linear regression analysis of the logarithmic version of the data shown in Fig. 8 indicates that the pressure dependence of mviscous is characterised by exponents in the order of 1. Even though considerations based on soft EHL provide a general picture that is qualitatively consistent with the trends of the measured friction coefficients, the contributions due to hydrodynamic lubrication alone are too small to explain the friction behaviour of wet skin on smooth glass quantitatively. Because the surface roughness of the skin (Rz between 30 and 100 mm) is much greater than the thickness of hydrodynamic films as estimated above, it can be assumed that water films between skin and smooth glass are only formed locally, while dry contact zones coexist in other regions (mixed lubrication). In the dry contact zones, adhesion is expected to be important for the sliding friction behaviour while stick–slip effects indicated that skin deformations are an essential factor at the same time. At the highest contact pressures applied by the individual subjects when rubbing different skin areas against the smooth wet glass surface, the average friction coefficients were 0.1470.03 (range: 0.07–0.18), which is in the range of the maximum hysteresis component estimated from the measurement data of one subject for the edge of the hand in contact with dry rough glass (Section 4.2). The skin of finger pads and the edge of the hand showed similar friction coefficients against smooth wet glass at maximum contact pressures, being 2–3 times higher in the case of the fingers. For comparable contact pressures, the skin of the finger pads showed greater total friction coefficients, and
0.04
0.03 viscous
1572
0.02
Subject
Skin site
Ra (mm)
Rz (mm)
~, 23 y
Index finger Edge of hand
27.074.7 18.573.0
94.1717.1 73.0712.7
0.01
~, 27 y
Index finger Edge of hand
32.7710.3 8.671.8
98.6720.2 32.776.0
0.00
#, 31 y
Index finger Edge of hand
26.673.6 22.474.0
94.5714.4 71.6714.7
#, 45 y
Index finger Edge of hand
18.973.7 10.072.0
61.8712.6 39.177.2
The given mean values and standard deviations are based on the analysis of 40 surface profiles in different directions.
0
20
40 60 Contact pressure (kPa)
80
Fig. 8. Calculated values of mviscous for fingertips and the skin of the edge of the hand when sliding with a velocity of 7.5 cm/s in a water film on wet smooth glass, assuming an elastic modulus of 15 kPa for both skin areas [31]. The effective radii of curvature were assumed to be 13 mm for fingertips and 30 mm for the edge of the hand. Calculations according to [2,34] (m: fingertips; : edge of the hand) are compared to the results for soft EHL (D: fingertips; J: edge of the hand). Data for the radius of the contact area as a function of the normal force were determined from the experimental results shown in Fig. 4.
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
higher deformation contributions are plausible due to the rougher skin surface. 4.3.2. Wet friction of skin against rough glass When rubbed against the wet rough glass surface at contact pressures of 2072 kPa, the skin of finger pads showed a mean friction coefficient of 1.0870.40 and the edge of the hand a slightly lower mean value of 0.8870.08. In the case of fingers, the exponents n1 were 0.80 and 0.63 for pulling motions and 0.36 and 0.34 for pushing motions, respectively. For the edge of the hand the exponents ranged from 0.48 to 0.26. Both the magnitudes and the trends of the friction coefficients point to adhesion as the predominant friction mechanism, although lubrication effects might have influenced the measurement results for finger pads pulled over the wet rough glass surface. The deformation component of friction is considered to be similar as in the friction experiments performed on dry rough glass (Section 4.2), i.e., small compared to the adhesion component. In order to compare the friction between skin and a rough glass surface under dry and wet conditions, it is useful to express the friction force as F ¼ A S, where A denotes the contact area and S the shear strength of the adhesive contact. As skin swells and becomes softer with water uptake (Section 1), a decrease rather than an increase of the shear strength is normally expected in adhesive contacts of wet skin. An increase in the adhesion and friction of wet skin therefore must necessarily be associated with an increase of the real contact area. One mechanism increasing the real contact area between wet skin and a rough surface is the softening of the hydrated skin and the stratum corneum in particular, making the skin surface more compliant and conforming to penetrating hard asperities. Another mechanism leading to an increased effective contact area is provided by the interfacial water, e.g. by filling tiny surface cavities and bridging microscopic gaps between the skin and glass asperities. Compared to the case of dry friction of skin on rough glass, the presence of water in the interface increased the sliding friction coefficients by a factor of ca. 2 for both the finger pads and the edge of the hand. It is interesting to note that the discussed mechanisms to increase the real contact area of wet skin only worked on the rough glass surface. In contrast, on smooth glass the presence of water seems to cause a reduction of the shear strength due to skin softening and the local development of lubricating films, so that the friction coefficients are strongly decreased compared to the dry situation.
1573
literature, we assumed equal and constant elastic properties for the two skin areas and used an elastic modulus of 15 kPa, which lies in the range of recently published data for the skin of the volar forearm [31]. The skin and the sub-surface soft tissue show nonlinear material behaviour [10] as was also evident from the measurements of the skin contact area as a function of the normal load (Section 3.1). An interesting direction of future work would be to investigate whether possible changes in the material behaviour of strongly deformed soft tissue has an influence on the friction behaviour of skin. Recently, Ramalho et al. [5] reported on different friction regimes when palmar skin was investigated at varying normal loads.
5. Conclusions Friction measurements using a tri-axial force plate and contact area measurements using a pressure sensitive film were conducted in order to study the friction behaviour of skin in contact with smooth and rough glass under dry and wet conditions as a function of the contact pressure. The investigation of different skin areas and contrasting cases of sliding friction gave insights in the complex friction mechanisms of skin which were determined from the pressure dependence of measured friction coefficients on the basis of theoretical concepts for the friction of elastomers. Adhesion was observed as a friction mechanism in all investigated cases. If adhesion mechanisms predominated, the friction coefficients were generally high and their pressure dependence was characterised by exponents n1 of typically 0.5 to 0.2. Contributions to the friction coefficient due to viscoelastic skin deformations were relatively small. When the deformation component of friction was important in combination with adhesion, the pressure dependence of the friction coefficients showed weak trends characterised by exponents between 0.1 and +0.2. If hydrodynamic lubrication came into play under wet sliding conditions on smooth glass, the friction coefficients of skin were strongly reduced compared to dry friction, and their decrease with increasing contact pressures was characterised by exponents of o0.7.
Acknowledgements We thank Hanspeter Feuz and Roman Huber for the measurement and analysis of profilometric and topographical data of the glass surfaces and skin replicas.
4.4. Limitations of the study and further research questions References The friction behaviour of human skin sliding on different glass surfaces was investigated for different subjects and skin areas under dry and wet conditions. For each experimental configuration, the pressure dependence of the friction coefficients was assumed to follow a power law according to mðpÞ ¼ k pn1 , from which the exponent n1 was determined and used to identify the involved friction mechanisms. This method is expected to be reliable in cases where one specific friction mechanism is predominant. If different mechanisms are superposed and contribute similarly to the friction coefficient, a refined version of the data analysis would improve the interpretation of measurement results. In the present study, however, the applied method allowed the consistent interpretation of friction measurement data for different subjects and skin areas in plausible agreement with commonly applied theoretical concepts. In this study, no measurements were carried out concerning the elastic properties of skin. As no specific experimental data for finger pads and the edge of the hand were available from the
[1] Dowson D. Tribology and the skin surface. In: Wilhelm K-P, et al., editors. Bioengineering of the skin: skin surface imaging and analysis. Boca Raton: CRC Press; 1997. p. 159–79. [2] Johnson SA, Gorman, DM, Adams MJ, Briscoe BJ. The friction and lubrication of human stratum corneum. In: Thin films in tribology. Leeds–Lyon symposium on tribology, Amsterdam: Elsevier Science Publishers; 1993. p. 663–72. [3] Sivamani RK, Goodman J, Gitis NV, Maibach HI. Coefficient of friction: tribological studies in man — an overview. Skin Research and Technology 2003;9(3):227–34. [4] Egawa M, Takahashi M. Skin friction evaluation by unidirectional stress using a friction tester. In: Serup J, Jemec GBE, Grove GL, editors. Non-invasive methods and the skin. Boca Raton: CRC Press, Taylor & Francis; 2006. p. 225–32. [5] Ramalho A, Silva CL, Pais AACC, Sousa JJS. In vivo friction study of human skin: influence of moisturizers on different anatomical sites. Wear 2007;263(7–12):1044–9. [6] Sivamani RK, Maibach HI. Tribology of skin. Proceedings of the Institution of Mechanical Engineers Part J — Journal of Engineering Tribology 2006;20(J8): 729–37. [7] Sivamani RK, Wu GC, Gitis NV, Maibach HI. Tribological testing of skin products: gender, age, and ethnicity on the volar forearm. Skin Research and Technology 2003;9(4):299–305.
ARTICLE IN PRESS 1574
S. Derler et al. / Tribology International 42 (2009) 1565–1574
[8] Gee MG, Tomlins P, Calver A, Darling RH, Rides M. A new friction measurement system for the frictional component of touch. Wear 2005; 259(7–12):1437–42. [9] Lewis R, Menardi C, Yoxall A, Langley J. Finger friction: grip and opening packaging. Wear 2007;263(7–12):1124–32. [10] Tomlinson SE, Lewis R, Carre MJ. Review of the frictional properties of fingerobject contact when gripping. Proceedings of the Institution of Mechanical Engineers Part J — Journal of Engineering Tribology 2007;221(J8):841–50. [11] Derler S, Schrade U, Gerhardt L-C. Tribology of human skin and mechanical skin equivalents in contact with textiles. Wear 2007;263(7–12):1112–6. [12] Gerhardt L-C, Lenz A, Spencer ND, Mu¨nzer T, Derler S. Skin-textile friction and skin elasticity in young and aged persons. Skin Research and Technology, submitted. [13] Gitis N, Sivamani R. Tribometrology of skin. Tribology Transactions 2004; 47(4):461–9. [14] Sivamani R, Wu G, Maibach HI, Gitis N. Tribological studies on skin: measurement of the coefficient of friction. In: Serup J, Jemec GBE, Grove GL, editors. Non-invasive methods and the skin. Boca Raton: CRC Press, Taylor & Francis; 2006. p. 215–24. [15] Li W, Kong M, Liu XD, Zhou ZR. Tribological behavior of scar skin and prosthetic skin in vivo. Tribology International 2008;41(7):640–7. [16] Tang W, Ge S-r, Zhu H, Cao X-c, Li N. The influence of normal load and sliding speed on frictional properties of skin. Journal of Bionic Engineering 2008; 5(1):33–8. [17] Pailler-Mattei C, Pavan S, Vargiolu R, Pirot F, Falson F, Zahouani H. Contribution of stratum corneum in determining bio-tribological properties of the human skin. Wear 2007;263(7–12):1038–43. [18] Meyers MA, Chen P-Y, Lin AY-M, Seki Y. Biological materials: structure and mechanical properties. Progress in Materials Science 2008;53(1):1–206. [19] Pailler-Mattei C, Zahouani H. Study of adhesion forces and mechanical properties of human skin in vivo. Journal of Adhesion Science and Technology 2004;18(15–16):1739–58. [20] Moore DF. The friction and lubrication of elastomers. Oxford: Pergamon Press; 1972. [21] Myshkin NK, Petrokovets MI, Kovalev AV. Tribology of polymers: adhesion, friction, wear, and mass-transfer. Tribology International 2005;38(11–12):910–21.
[22] Adams MJ, Briscoe BJ, Johnson SA. Friction and lubrication of human skin. Tribology Letters 2007;26(3):239–53. [23] Wolfram LJ. Friction of skin. Journal of the Society of Cosmetic Chemists 1983;34(8):465–76. [24] Landau LD, Lifschitz EM. Elastizita¨tstheorie. 7th ed. Berlin: Akademie Verlag; 1991. [25] Comaish S, Bottoms E. The skin and friction: deviations from Amontons laws, and the effects of hydration and lubrication. British Journal of Dermatology 1971;84(1):37–43. [26] Koudine AA, Barquins M, Anthoine P, Aubert L, Leveque J-L. Frictional properties of skin: proposal of a new approach. International Journal of Cosmetic Science 2000; 22(1): 11–20. [27] Sivamani RK, Goodman J, Gitis NV, Maibach HI. Friction coefficient of skin in real-time. Skin Research and Technology 2003;9(3):235–9. [28] Greenwood JA, Tabor D. The friction of hard sliders on lubricated rubber — the importance of deformation losses. Proceedings of the Physical Society of London 1958;71(462):989–1001. [29] Gerhardt L-C, Stra¨ssle V, Lenz A, Spencer ND, Derler S. Influence of epidermal hydration on the friction of human skin against textiles. Journal of The Royal Society Interface 2008;5(28):1317–28. [30] Greenwood JA, Williamson JBP. Contact of nominally flat surfaces. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) 1966;295(1442):300–19. [31] Pailler-Mattei C, Bec S, Zahouani H. In vivo measurements of the elastic mechanical properties of human skin by indentation tests. Medical Engineering & Physics 2008;30(5):599–606. [32] Hamrock BJ, Dowson D. Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication. In: Proceedings of the fifth Leeds–Lyon symposium on tribology. Bury St. Edmunds, Suffolk: Mechanical Engineering Publikation; 1979. p. 22–27. [33] Esfahanian M, Hamrock BJ. Fluid-film lubrication regimes revisited. Tribology Transactions 1991;34(4):628–32. [34] Roberts AD, Tabor D. The extrusion of liquids between highly elastic solids. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) 1971;325(1562):323–45.
Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Friction of human skin against smooth and rough glass as a function of the contact pressure S. Derler a,, L.-C. Gerhardt a, A. Lenz a, E. Bertaux a, M. Hadad b a
Laboratory for Protection and Physiology, Swiss Federal Laboratories for Materials Testing and Research (Empa), Lerchenfeldstrasse 5, CH-9014 St. Gallen, Switzerland Laboratory for Materials Processing and Characterization, Swiss Federal Laboratories for Materials Testing and Research (Empa), Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland b
a r t i c l e in fo
abstract
Article history: Received 21 July 2008 Received in revised form 22 November 2008 Accepted 28 November 2008 Available online 9 December 2008
The friction behaviour of human skin was studied by combining friction measurements using a tri-axial force plate with skin contact area measurements using a pressure sensitive film. Four subjects carried out friction measurement series, in which they rubbed the index finger pad and the edge of the hand against a smooth and a rough glass surface under dry and wet conditions. The normal loads were varied up to values of 50 N, leading to skin contact pressures of up to 120 kPa. The analysis of the pressure dependence of friction coefficients of skin for contrasting sliding conditions allowed to determine the involved friction mechanisms on the basis of theoretical concepts for the friction of elastomers. Adhesion was found to be involved in all investigated cases of friction between skin and glass. If adhesion mechanisms predominated (skin against smooth glass in the dry condition and skin against rough glass in the wet condition), the friction coefficients were generally high (typically 41) and decreased with increasing contact pressure according to power laws with typical exponents between 0.5 and 0.2. Contributions to the friction coefficient due to viscoelastic skin deformations were estimated to be relatively small (o0.2). In those cases where the deformation component of friction played an important role in connection with adhesion (skin against rough glass in the dry condition), the friction coefficients of skin were typically around 0.5 and their pressure dependence showed weak trends characterised by exponents ranging from 0.1 to +0.2. If hydrodynamic lubrication came into play (skin sliding on smooth glass in the wet condition), the friction coefficients were strongly reduced compared to dry friction (o1), and their decrease with increasing contact pressures was characterised by exponents of o0.7. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Skin tribology Sliding friction coefficient Contact area Adhesion Deformation Hydrodynamic lubrication
1. Introduction The friction behaviour of human skin is determined by the complex interplay of material and surface properties of the skin as well as the contacting material, and strongly depends on the contact parameters (e.g. pressure and sliding velocity) and the presence of substances such as water, sweat or skin surface lipids at the interface [1–3]. To a large extent, the current knowledge on the tribology of skin resulted from dermatological studies on the effects of skin care products [4–7]. However, the frictional properties of skin are of general importance in connection with mechanical contacts of the human body with external materials, e.g. when touching and handling objects or when wearing clothes and accessories. In several recent studies on skin tribology, specific practical cases such as friction contacts between hand and object [8–10] or
Corresponding author.
E-mail address: [email protected] (S. Derler). 0301-679X/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2008.11.009
between skin and textiles [11,12] were analysed by in vivo measurements. The typical experimental set-up in these studies was to rub the skin against objects and surface samples attached to a multi-axial force plate or a force transducer in order to measure normal and friction forces and to determine friction coefficients. An alternative approach consists in the use of a tribometer with which (mostly spherical) probes made of different materials are slid over the skin of subjects [13,14]. This measurement technique was applied to characterise the general friction properties of skin [15,16] and to study the contribution of the stratum corneum to the friction of skin [17]. Human skin shows viscoelastic material properties similar to those of a soft elastomer [2,18,19]. Therefore, theoretical concepts for the friction of elastomers [20,21] were applied to interpret experimental data for the friction of skin. Under dry conditions, adhesion at the skin/material interface as well as deformation of the skin and the soft sub-surface tissue contribute to the coefficient of friction (two-term model of friction) [1]:
m ¼ madhesion þ mdeformation
(1)
ARTICLE IN PRESS 1566
S. Derler et al. / Tribology International 42 (2009) 1565–1574
The friction of skin is considered to be mainly determined by adhesion, while deformation is normally believed to be unimportant [2,22,23]. Applying the contact theory of Hertz [24], Wolfram derived the following expression for the adhesion component of friction
madhesion / N 1=3 E2=3
(2)
where N denotes the normal load and E the elastic modulus of skin [23]. A decrease of friction coefficients with increasing normal load according to m / N1=3 is consistent with experimental studies in which the friction of dry skin was investigated using solid probe materials [25–27]. Friction coefficients that decreased with increasing load were also observed in experiments, in which spherical probes were slid on wet skin [22]. In order to estimate the contribution of viscoelastic skin deformations to friction (hysteresis), Johnson et al. [2] applied the approach of Greenwood and Tabor [28]. In contrast to the adhesion component of friction (Eq. (2)), the contribution due to hysteresis is expected to increase with normal load:
mhysteresis / N
þ1=3
1=3
E
(3)
It is usually experienced in everyday life that the friction of skin increases with hydration, e.g. due to sweating. This was explained by the fact that moist skin becomes softer and is characterised by a lower elastic modulus so that adhesion is increased (Eq. (2)) [23]. In addition, human skin swells due to water uptake, leading to a smoothing of the skin surface and an increased microscopic contact area in friction contacts [22]. In a recent study, Gerhardt et al. systematically varied the hydration state of the skin of the volar forearm in 22 subjects and found a highly positive linear correlation between skin moisture and friction coefficients against textiles [29]. When the skin is saturated and excess water accumulates in the interface, capillary bridges between the skin and the countersurface might be relevant to a certain degree, but with further increasing amounts of water lubrication phenomena will become more and more important. Dowson [1] described various types of lubrication that are relevant in connection with human skin. Hydrodynamic lubrication is characterised by the complete separation of the sliding surfaces by a liquid film. Under these conditions, the adhesion component of friction is replaced by a contribution due to viscous friction 1 V V mviscous ¼ Z (4) A¼Z p1 N h h where N denotes the normal load, Z the viscosity of the fluid, h the film thickness, V the sliding velocity, A the apparent contact area and p the contact pressure [1]. Depending on contact conditions as well as fluid film thickness in relation to the surface roughness of the skin and the contacting material, mixed lubrication or boundary lubrication can take place. The former lubrication regime is characterised by the coexistence of dry and wet contact zones, the latter by molecular surface films influencing the friction behaviour. It is a common empirical approach to express measurement data for the friction force F in the form F ¼ k Nn , where k corresponds to the conventional friction coefficient at unit normal load, N denotes the normal load and n is termed the load index [22]. The friction coefficient as a function of the normal load is then given by
mðNÞ ¼ k N n1
(5)
In the logarithmic form logðmÞ ¼ logðkÞ þ ðn 1Þ logðNÞ, this equation can be used to determine the exponent n1 (and the load index n) by linear regression and to test if the friction measurement data can be attributed to a predominant friction
mechanism. According to Eqs. (2)–(4), friction mechanisms such as adhesion, deformation or hydrodynamic lubrication should be indicated by distinctive exponents of 13, þ13 and 1, respectively. In this study, the friction behaviour of human skin was studied as a function of the contact pressure by combining friction measurements using a tri-axial force plate with contact area measurements using a pressure sensitive film. Four subjects carried out compression tests and friction measurement series, in which they rubbed the skin of two different anatomical sites against a smooth and a rough glass surface under dry and wet conditions. The objectives were (1) to analyse the pressure dependence of the friction of skin for contrasting cases (dry/wet, smooth/rough) and to determine the involved friction mechanisms and lubrication regimes and (2) to test how far theoretical concepts developed for the friction of elastomers are applicable to describe the experimental data found for human skin.
2. Experimental 2.1. Friction measurements The friction behaviour of the human skin was investigated for two anatomical sites, namely the pad of the index finger and the edge of the dominant hand. Two females and two males with ages between 23 and 45 y (four of the authors) carried out friction measurement series, in which they repeatedly rubbed their skin against a smooth and a rough glass surface using normal loads of up to 50 N. The skin slid over distances between 5 and 8 cm within periods of 0.5–1.5 s, leading to sliding velocities between 5 and 10 cm/s. Two subjects carried out the experiments with a pulling motion and the other two with a pushing motion, holding the finger and the hand in a stretched position (Fig. 1). When measuring friction coefficients for the skin of the finger pad, the index finger was inclined at angles between 301 and 451 to the counterface. The glass plates were attached to a quartz 3-component dynamometer Kistler, type 9254 (dimensions 15 cm 10 cm). The normal and the friction force were measured using charge amplifiers (Kistler, type 5011), and Dynoware software (Kistler, type 2825A-02) was used to acquire the friction and normal force with a resolution of approximately 25 mN at a sampling rate of 125 Hz. Measurements were carried out over periods of 20 s, allowing a subject to conduct a sequence of friction movements at varied normal loads. In the process, the subjects controlled the applied normal load by means of an analogue voltage meter. Figs. 2a and b show typical results measured in one friction experiment. Individual friction coefficients were determined for each single friction movement by analysing the peaks of the normal and friction force signals over intervals of 0.1 s. The variation of friction coefficients within these time intervals was characterised by typical (median) standard deviations of 0.02. For each glass surface and each anatomical site, the subjects carried out at least 10 friction measurements under dry and wet conditions. In the wet condition, the glass surfaces were covered by a film of deionised water with a thickness of approximately 1 mm. All friction experiments took place at a temperature of (2371) 1C and a relative humidity of (5075)%. The subjects were acclimatised to the laboratory climate for at least 10 min prior to the measurements. The skin of the subjects was cleaned with ethanol before each measurement series. In addition, the dry glass surfaces were cleaned with ethanol before each friction experiment. 2.2. Contact area measurements In order to measure the apparent contact area between the skin and a flat surface as a function of the normal load, a pressure
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
1567
surface profile was 0.0570.01 mm for the smooth glass and 45.075.6 mm for the rough glass. The surface topography of the skin was analysed by an optical profilometer based on white-light (Cotec, AltiSurf 500), using silicone replicas (negatives) of the anatomical sites investigated. Surface scans were carried out for samples of size 5 mm 5 mm, using a lateral resolution of 10 mm and a vertical resolution of 10 nm. Fig. 3 shows examples of the skin surface structure at two anatomical sites for two subjects. 3. Results 3.1. Apparent contact area of skin as a function of the normal load
Pushing motion
Pulling motion
Fig. 1. Measurement of sliding friction coefficients for the skin of the index finger pad (a) and the edge of the hand (b) against glass. The sliding directions corresponded to pushing and pulling motions of the arm.
sensitive film (Tekscan, model 5051; sensor density: 62 elements per cm2) was combined with the force plate. The subjects placed the index finger and the edge of the hand on the pressure sensitive film (using the same stretched position as in the friction tests) and gradually increased the normal load (Fig. 2c). The subjects checked the applied normal load by means of an analogue voltage meter. The pressure distribution of the skin and the normal force acting on the force plate were simultaneously recorded using a sampling rate of 125 Hz. From the measured pressure distributions, the apparent contact area of the skin could be determined with an estimated uncertainty of 70.2 cm2. For each anatomical site investigated, the four subjects carried out series of six experiments over periods of 20 s, in which the applied normal forces ranged up to 50 N. A typical result of a contact area measurement is shown in Fig. 2d.
2.3. Surface characterisation Glass surface samples were cut from a plate of technical glass. An untreated sample represented the smooth glass surface, and a sample with random surface roughness was produced by means of sandblasting. A mechanical profilometer (Mahr, Perthometer M1) was used to measure standard roughness parameters for the two glass surfaces. The parameter Rz, characterizing the average height difference between highest peaks and lowest valleys in a
Results of the compression tests for the finger pad and the edge of the hand are shown in Fig. 4. For both anatomical sites, the measurements of the contact area as a function of the normal force showed a satisfying reproducibility for the same subject (4a). The averaged results revealed differences between the four subjects, but showed the same qualitative behaviour (4c), characterised by a steep initial increase of the contact area with normal load (in the force range of up to 1 N in the case of the finger and within about 10 N in the case of the edge of the hand). At normal loads between 45 and 50 N, maximum skin contact areas of about 15 cm2 were observed for the edge of the hand and of about 4 cm2 for the index finger pad, leading to maximum mean contact pressures of about 40 and 120 kPa, respectively. For all subjects and skin sites, the averaged curves were fitted with empirical functions of the form AðNÞ ¼ a þ b N1=4 þ c N with adjusted R2-values between 0.94 and 0.99 (Fig. 4b and d). The resulting fit functions (4d) were used to relate normal forces to skin contact areas and to calculate mean contact pressures for the subsequent analysis of the friction behaviour of skin (Sections 3.2 and 3.3). The mean contact pressure of the skin linearly depended on the normal load in most cases (Fig. 4e). The deviations from the linear relationship observed in some cases (Figs. 4e and f) were probably due to slight positional changes of the hand during the compression tests. 3.2. Friction coefficients of skin for different subjects and anatomical sites More than 4500 single sliding friction coefficients ranging from about 0.05 to 5 were determined from the friction measurements performed by all subjects. The highest friction coefficients of skin were found against dry, smooth glass (2.1871.09; range: 0.39–5). On the wet, smooth glass surface, the friction coefficients were considerably lower (0.6170.37; range: 0.07–2.12). When rubbed against the rough glass surface, the investigated skin sites showed relatively low friction coefficients of 0.5370.22 (0.03–1.42) under dry conditions and values of 1.4370.57 (0.32–4.56) under wet conditions, respectively. The skin of the edge of the hand showed systematically lower friction coefficients than the skin of the finger pad (Fig. 5). For contact pressures in the range from 10 to 30 kPa, the average differences were between 0.3 and 0.7, depending on the glass surface and the presence of water. In the case of the edge of the hand, the measurement results of the four subjects were comparable for all glass surfaces and test conditions. In contrast, the friction behaviour of finger pads seemed to depend on the direction of the sliding motion. For pulling motions of the finger, the pressure dependence of the friction coefficients was more pronounced. Comparisons between the results of the different subjects are shown in Fig. 6 for the example of the rough glass surface in the wet condition.
ARTICLE IN PRESS 1568
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Friction coefficient
Force (N)
20 Normal Force Friction Force
15 10 5 0
2.0 1.5 1.0 0.5 0.0
0
5
10
15
20
0
5
10
15
20
Normal force (N)
35 30 25 20 15 10 5 0
Contact area (cm2)
Force (N)
Time (s)
4 3 2 1
1 cm
0 0
5
10
15
20
0
5
10
Time (s)
15
20
25
30
Time (s)
Fig. 2. (a) Normal force and friction force as a function of time, measured in a friction experiment on smooth glass in the wet condition. The subject (#, 31 y) rubbed the right index finger on the substrate, using different normal loads for the individual sliding movements. (b) The resulting friction coefficients (m) varied with the applied normal force. The plots c and d show results of the simultaneous measurement of the applied normal force (force plate) and the contact area (pressure sensitive film) for the index finger of the same subject. An example of the pressure distribution at a certain time is illustrated in the insert of plot d. The independent force and contact area measurements were synchronised via initial peaks resulting from a short touch.
mm 0
1
2
mm 3
4
5
0
0
0.5
0.5
1
1
1.5
1.5
1
2
0
1
2
2.5 3
3 3.5
4
4
4.5
4.5
5
5
3
4
5
5 mm 1
2
mm 3
4
5
mm
0
mm
4
2.5
3.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
3
2 mm
mm
2
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Fig. 3. Surface structure of the skin at the finger tip (left) and the edge of the hand (right) for two subjects (pictures above: #, 45 y; pictures below: ~, 23 y). Concentric ridges are characteristic for finger pads while first and second order furrows are visible for the skin of the edge of the hand.
ARTICLE IN PRESS
15
Contact area (cm2)
Contact area (cm2)
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Hand
10 5
Finger 0 0
10
20
30
40
15 Hand
10 5
Finger 0 0
50
10
15 Hand
5 Finger 0
30
40
50
15 Hand
10 5
Finger 0
0
10
20 30 40 Normal force (N)
0
50
100
10
20 30 40 Normal force (N)
50
100
80
Pressure (kPa)
Pressure (kPa)
20
Normal force (N)
Contact area (cm2)
Contact area (cm2)
Normal force (N)
10
1569
Finger
60 40 20
Hand
0
80 Finger
60 40 20
Hand
0 0
10
20 30 40 Normal force (N)
50
0
10
20 30 40 Normal force (N)
50
Fig. 4. Apparent contact area measured as a function of the normal load: (a) measurement results for the pad of the index finger and the edge of the hand for one subject (#, 31 y), (b) average curves for the finger and the edge of the hand, calculated from the six measurements shown in plot a, (c) comparison between the average curves of the four subjects (pink curve: ~, 23 y; red curve: ~, 27 y; blue curve: #, 31 y; green curve #, 45 y), (d) fits of the average curves for the four subjects. Relationship between normal force and mean contact pressure: (e) average curves for the four subjects and (f) linear fits of the pressure-force curves.
Fig. 5. Comparison between the friction coefficients of the skin for the finger and the edge of the hand when rubbed against smooth glass in the wet condition. Normal (a) and logarithmic plot (b) of the pressure dependence. The measurement results of all subjects are plotted.
The uncertainty of the friction measurement results was estimated on the basis of differences between successive data points in plots of friction coefficients versus contact pressure
(Figs. 5–7) for the same subject, skin site, glass surface and test condition. The statistical analysis indicated that the measured friction coefficients were typically scattered around the fitted
ARTICLE IN PRESS 1570
S. Derler et al. / Tribology International 42 (2009) 1565–1574
Fig. 6. Friction coefficients of the skin of four subjects on rough glass in the wet condition. In the case of the index finger pad (a, b) the friction behaviour depended on the sliding direction ( and J: pulling motion; ’ and &: pushing motion). The skin of the edge of the hand (c, d) showed comparable results for all subjects.
trends with average standard deviations of about 0.1 for skin against dry, rough glass and against wet, smooth glass, of about 0.2 for skin in contact with wet, rough glass and of about 0.5 for skin against dry, smooth glass. 3.3. Pressure dependence of the friction of skin In most cases, the measured friction coefficients of skin strongly depended on the contact pressure. Fig. 7 exemplarily shows the measurement results for one subject. In the experiments on the dry, rough glass surface, the friction coefficients of skin were practically constant or depended slightly on the contact pressure. In contrast, the friction coefficients systematically decreased with increasing contact pressure in the experiments on dry, smooth glass as well as in all experiments carried out under wet conditions. In order to characterise the load-dependence of the friction of skin, the experimental data was assumed to follow a power law mðpÞ ¼ k pn1 , analogous to Eq. (5). The exponent n1 was determined by linear regression of the logarithmic data (as shown in the Figs. 5b, 6b and d and 7b and d). Results for the exponent n1 are given in Table 1. On the basis of the previous literature on the friction of skin (Section 1), the obtained exponents can be associated with different predominant friction mechanisms (see Section 4). 3.4. Skin surface characteristics The topographical measurement data of the skin replicas were analysed concerning the surface roughness parameters Ra and Rz
(Table 2). For all subjects, the skin surface on the index finger pad was found to be rougher (mean Rz values between 62 and 99 mm) than that on the edge of the hand (mean Rz values ranging from 33 to 73 mm).
4. Discussion 4.1. General The friction coefficients between skin and glass measured for two skin sites in four subjects ranged from about 0.05 to values greater than five and strongly depended on the glass surface roughness, test conditions and skin area. In this study, the skin was rubbed against two different flat glass surfaces attached to a tri-axial force plate, while in previous investigations glass lenses or spheres (radii of curvature in the range of centimetres) with smooth surfaces were slid over the skin of the volar forearm [2,22,26]. Direct comparisons between measurement results are further complicated by differences in the sliding velocities and the applied normal loads. We measured friction coefficients of skin over a wide range of contact pressures up to 120 kPa, covering practical cases of mechanical contacts of the skin, e.g. when touching or gripping hard objects or assessing the roughness of surfaces [11]. The analysis of the friction behaviour of skin on different glass surfaces (smooth and rough) and contrasting conditions (dry and wet) indicated various friction mechanisms which are combined in different ways. The measured friction coefficients systematically depended on the mean contact pressure (determined from the apparent contact area as a function of the normal load), so that a classification became possible on the basis of the load index
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
1571
Fig. 7. Sliding friction coefficients of the skin of one subject (#, 31 y) against smooth and rough glass under dry (a, b) and wet conditions (c, d).
Table 1 Exponents n1 determined from linear fits to the logarithmic data mðpÞ ¼ k pn1 for the skin of all subjects and anatomical sites when rubbed against smooth and rough glass under dry and wet conditions. Exponent n1
Skin site
Subject
Smooth glass
Rough glass
Dry condition
Finger
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.96 –0.79 –0.26 –0.15
+0.15 +0.10 –0.03 –0.09
Hand
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.56 –0.48 –0.19 –0.32
(–0.21) +0.04 +0.04 +0.17
Finger
~, 23 y ~, 27 y #, 31 y #, 45 y
–1.42 –1.05 –0.70 –0.74
–0.80 –0.63 –0.34 –0.36
~, 23 y ~, 27 y #, 31 y #, 45 y
–0.87 –1.44 –0.73 –0.79
–0.26 –0.48 –0.45 –0.37
Wet condition
Hand
The value given in brackets is based on a small range of applied contact forces.
(Eq. (5)) as described in the following. For a common treatment of the two investigated skin areas, the pressure dependence of the friction coefficient (characterised by the exponent n1) is studied instead of the relationship between friction force and normal force (characterised by the load index n).
4.2. Friction mechanisms of skin under dry sliding conditions 4.2.1. Dry friction of skin against smooth glass For contact pressures of 2072 kPa, the mean friction coefficients of finger pads in contact with the smooth glass surface were
2.2570.82. For the edge of the hand, the corresponding friction coefficients were 1.2170.34. The exponents n1 for the edge of the hand ranged from 0.56 to 0.19, indicating the importance of adhesion in the friction mechanism, for which an exponent of 13 would be expected (Eq. (2)). In the case of the two subjects who rubbed the skin of their finger pads using a pushing motion, the exponents n1 of 0.26 and 0.15 were close to the results for the edge of the hand. For the subjects pulling their fingers over smooth glass, however, the exponents were 0.96 and 0.79, respectively. Different deformation of the skin and the finger pad in pulling and pushing motions probably contributed to the differences in the friction behaviour. Effects of moisture (sweat) in the skin/glass interface could not be excluded during the experiments.
4.2.2. Dry friction of skin against rough glass In dry sliding friction contacts with the rough glass surface, the investigated skin areas showed mean friction coefficients of 0.6370.22 (finger) and 0.3870.03 (edge of the hand) for contact pressures of 2072 kPa. Typically, the measured friction coefficients slightly increased with the contact pressure and were characterised by exponents n1 between 0.09 and +0.17 (the result for the edge of the hand of one subject was not taken into account, because the small range of applied normal loads did not allow a reliable regression analysis). The case of pressureindependent friction coefficients was physically explained by a linear increase of the real contact area between the asperities of rough surfaces in contact with increasing pressure [20,30]. As the microscopic contact areas between surface asperities grow and more and more new surface asperities come in contact with increasing pressure, the mean pressure at the contact zones remains constant. Friction coefficients increasing with the contact pressure, on the other hand, can be associated with a mechanism that involves skin deformation (Eq. (3)). Tang et al. [16] attributed the contribution of skin deformations to friction to the penetration and ploughing of surface asperities of a hard material into the skin surface. In our experiments, however, we neither observed
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
damages to the skin nor visible modifications of the skin surface, even though each subject on average carried out more than 550 individual friction measurements per investigated skin area. Therefore, we assume that ploughing and abrasion of the skin surface were less important as friction mechanisms than viscoelastic skin deformations (hysteresis), resulting from cyclic deformations of the skin due to glass surface asperities sliding over the skin surface. Adams et al. [22] who investigated the skin of the volar forearm, estimated an order of magnitude of 0.05 for the hysteresis component of skin friction. Among the four subjects and investigated skin areas, the most pronounced increase in dry friction on rough glass was found in the case of an edge of the hand (#, 45 years; reflected by n1 ¼ +0.17, Table 1). In the pressure range of up to 35 kPa, the total friction coefficient increased from 0.32 to 0.45, from which a maximum contribution of mhysteresis 0:13 can be estimated. Based on the two-term model of friction (Eq. (1)), the adhesive component of the friction coefficient can then be assumed to lie around 0.3. Thus, even if measurable contributions due to viscoelastic skin deformations are evident, adhesion remains an essential friction mechanism. Compared to dry friction contacts against smooth glass, the adhesion of skin is significantly reduced when in contact with the rough glass surface, indicating a smaller real contact area between the skin and glass surface asperities. 4.3. Friction mechanisms of skin under wet sliding conditions 4.3.1. Wet friction of skin against smooth glass The mean friction coefficients at contact pressures of 2072 kPa on smooth glass in the wet condition were 0.6670.32 for finger pads and 0.2170.05 for skin on the edge of the hand. The exponents n1 ranged from 1.44 to 0.70 and indicated an influence of the sliding direction of the skin. Pushing motions showed exponents between 0.79 and 0.70 and pulling motions values from 1.44 to 0.87. The relatively low friction coefficients, especially those found for the edge of the hand, as well as the high absolute values of the exponents n1 indicated aqueous lubrication effects (Eq. (4)). On the other hand, stick–slip phenomena occurring in some of the friction experiments with finger pads indicated that the lubricating water films can be penetrated by the surface elevations of the skin during the sliding processes. The maximum friction coefficient due to hydrodynamic lubrication of the skin can be estimated by Eq. (4), using the minimum fluid film thickness derived from the theory of soft EHL (or isoviscous-elastic hydrodynamic lubrication) [22,32]. The regime of soft EHL is characterised by significant elastic deformaTable 2 Skin surface roughness parameters determined from skin replicas (negatives) of the anatomical sites for the four subjects investigated.
tion of the solids, but relatively low contact pressure, so that the viscosity of the fluid film is not increased [33]. Johnson et al. [2] discussed the lubrication of skin by water films on the basis of an expression which was used to estimate the minimum film thickness for a smooth elastomer sphere sliding in a fluid on a rigid flat surface [34]. Fig. 8 shows the results of an analogous calculation which was adopted to the case of finger pads and the edge of the hand, in comparison with calculations using the formulae for soft EHL. For parameters representing the experimental conditions, the minimum water film thickness ranged from 1 to 3 mm. The calculated results for mviscous strongly decrease with increasing contact pressure, showing values around 0.005 for a pressure of 20 kPa. For contact pressures up to 30 kPa, fingertips show slightly higher values of mviscous than the edge of the hand. Linear regression analysis of the logarithmic version of the data shown in Fig. 8 indicates that the pressure dependence of mviscous is characterised by exponents in the order of 1. Even though considerations based on soft EHL provide a general picture that is qualitatively consistent with the trends of the measured friction coefficients, the contributions due to hydrodynamic lubrication alone are too small to explain the friction behaviour of wet skin on smooth glass quantitatively. Because the surface roughness of the skin (Rz between 30 and 100 mm) is much greater than the thickness of hydrodynamic films as estimated above, it can be assumed that water films between skin and smooth glass are only formed locally, while dry contact zones coexist in other regions (mixed lubrication). In the dry contact zones, adhesion is expected to be important for the sliding friction behaviour while stick–slip effects indicated that skin deformations are an essential factor at the same time. At the highest contact pressures applied by the individual subjects when rubbing different skin areas against the smooth wet glass surface, the average friction coefficients were 0.1470.03 (range: 0.07–0.18), which is in the range of the maximum hysteresis component estimated from the measurement data of one subject for the edge of the hand in contact with dry rough glass (Section 4.2). The skin of finger pads and the edge of the hand showed similar friction coefficients against smooth wet glass at maximum contact pressures, being 2–3 times higher in the case of the fingers. For comparable contact pressures, the skin of the finger pads showed greater total friction coefficients, and
0.04
0.03 viscous
1572
0.02
Subject
Skin site
Ra (mm)
Rz (mm)
~, 23 y
Index finger Edge of hand
27.074.7 18.573.0
94.1717.1 73.0712.7
0.01
~, 27 y
Index finger Edge of hand
32.7710.3 8.671.8
98.6720.2 32.776.0
0.00
#, 31 y
Index finger Edge of hand
26.673.6 22.474.0
94.5714.4 71.6714.7
#, 45 y
Index finger Edge of hand
18.973.7 10.072.0
61.8712.6 39.177.2
The given mean values and standard deviations are based on the analysis of 40 surface profiles in different directions.
0
20
40 60 Contact pressure (kPa)
80
Fig. 8. Calculated values of mviscous for fingertips and the skin of the edge of the hand when sliding with a velocity of 7.5 cm/s in a water film on wet smooth glass, assuming an elastic modulus of 15 kPa for both skin areas [31]. The effective radii of curvature were assumed to be 13 mm for fingertips and 30 mm for the edge of the hand. Calculations according to [2,34] (m: fingertips; : edge of the hand) are compared to the results for soft EHL (D: fingertips; J: edge of the hand). Data for the radius of the contact area as a function of the normal force were determined from the experimental results shown in Fig. 4.
ARTICLE IN PRESS S. Derler et al. / Tribology International 42 (2009) 1565–1574
higher deformation contributions are plausible due to the rougher skin surface. 4.3.2. Wet friction of skin against rough glass When rubbed against the wet rough glass surface at contact pressures of 2072 kPa, the skin of finger pads showed a mean friction coefficient of 1.0870.40 and the edge of the hand a slightly lower mean value of 0.8870.08. In the case of fingers, the exponents n1 were 0.80 and 0.63 for pulling motions and 0.36 and 0.34 for pushing motions, respectively. For the edge of the hand the exponents ranged from 0.48 to 0.26. Both the magnitudes and the trends of the friction coefficients point to adhesion as the predominant friction mechanism, although lubrication effects might have influenced the measurement results for finger pads pulled over the wet rough glass surface. The deformation component of friction is considered to be similar as in the friction experiments performed on dry rough glass (Section 4.2), i.e., small compared to the adhesion component. In order to compare the friction between skin and a rough glass surface under dry and wet conditions, it is useful to express the friction force as F ¼ A S, where A denotes the contact area and S the shear strength of the adhesive contact. As skin swells and becomes softer with water uptake (Section 1), a decrease rather than an increase of the shear strength is normally expected in adhesive contacts of wet skin. An increase in the adhesion and friction of wet skin therefore must necessarily be associated with an increase of the real contact area. One mechanism increasing the real contact area between wet skin and a rough surface is the softening of the hydrated skin and the stratum corneum in particular, making the skin surface more compliant and conforming to penetrating hard asperities. Another mechanism leading to an increased effective contact area is provided by the interfacial water, e.g. by filling tiny surface cavities and bridging microscopic gaps between the skin and glass asperities. Compared to the case of dry friction of skin on rough glass, the presence of water in the interface increased the sliding friction coefficients by a factor of ca. 2 for both the finger pads and the edge of the hand. It is interesting to note that the discussed mechanisms to increase the real contact area of wet skin only worked on the rough glass surface. In contrast, on smooth glass the presence of water seems to cause a reduction of the shear strength due to skin softening and the local development of lubricating films, so that the friction coefficients are strongly decreased compared to the dry situation.
1573
literature, we assumed equal and constant elastic properties for the two skin areas and used an elastic modulus of 15 kPa, which lies in the range of recently published data for the skin of the volar forearm [31]. The skin and the sub-surface soft tissue show nonlinear material behaviour [10] as was also evident from the measurements of the skin contact area as a function of the normal load (Section 3.1). An interesting direction of future work would be to investigate whether possible changes in the material behaviour of strongly deformed soft tissue has an influence on the friction behaviour of skin. Recently, Ramalho et al. [5] reported on different friction regimes when palmar skin was investigated at varying normal loads.
5. Conclusions Friction measurements using a tri-axial force plate and contact area measurements using a pressure sensitive film were conducted in order to study the friction behaviour of skin in contact with smooth and rough glass under dry and wet conditions as a function of the contact pressure. The investigation of different skin areas and contrasting cases of sliding friction gave insights in the complex friction mechanisms of skin which were determined from the pressure dependence of measured friction coefficients on the basis of theoretical concepts for the friction of elastomers. Adhesion was observed as a friction mechanism in all investigated cases. If adhesion mechanisms predominated, the friction coefficients were generally high and their pressure dependence was characterised by exponents n1 of typically 0.5 to 0.2. Contributions to the friction coefficient due to viscoelastic skin deformations were relatively small. When the deformation component of friction was important in combination with adhesion, the pressure dependence of the friction coefficients showed weak trends characterised by exponents between 0.1 and +0.2. If hydrodynamic lubrication came into play under wet sliding conditions on smooth glass, the friction coefficients of skin were strongly reduced compared to dry friction, and their decrease with increasing contact pressures was characterised by exponents of o0.7.
Acknowledgements We thank Hanspeter Feuz and Roman Huber for the measurement and analysis of profilometric and topographical data of the glass surfaces and skin replicas.
4.4. Limitations of the study and further research questions References The friction behaviour of human skin sliding on different glass surfaces was investigated for different subjects and skin areas under dry and wet conditions. For each experimental configuration, the pressure dependence of the friction coefficients was assumed to follow a power law according to mðpÞ ¼ k pn1 , from which the exponent n1 was determined and used to identify the involved friction mechanisms. This method is expected to be reliable in cases where one specific friction mechanism is predominant. If different mechanisms are superposed and contribute similarly to the friction coefficient, a refined version of the data analysis would improve the interpretation of measurement results. In the present study, however, the applied method allowed the consistent interpretation of friction measurement data for different subjects and skin areas in plausible agreement with commonly applied theoretical concepts. In this study, no measurements were carried out concerning the elastic properties of skin. As no specific experimental data for finger pads and the edge of the hand were available from the
[1] Dowson D. Tribology and the skin surface. In: Wilhelm K-P, et al., editors. Bioengineering of the skin: skin surface imaging and analysis. Boca Raton: CRC Press; 1997. p. 159–79. [2] Johnson SA, Gorman, DM, Adams MJ, Briscoe BJ. The friction and lubrication of human stratum corneum. In: Thin films in tribology. Leeds–Lyon symposium on tribology, Amsterdam: Elsevier Science Publishers; 1993. p. 663–72. [3] Sivamani RK, Goodman J, Gitis NV, Maibach HI. Coefficient of friction: tribological studies in man — an overview. Skin Research and Technology 2003;9(3):227–34. [4] Egawa M, Takahashi M. Skin friction evaluation by unidirectional stress using a friction tester. In: Serup J, Jemec GBE, Grove GL, editors. Non-invasive methods and the skin. Boca Raton: CRC Press, Taylor & Francis; 2006. p. 225–32. [5] Ramalho A, Silva CL, Pais AACC, Sousa JJS. In vivo friction study of human skin: influence of moisturizers on different anatomical sites. Wear 2007;263(7–12):1044–9. [6] Sivamani RK, Maibach HI. Tribology of skin. Proceedings of the Institution of Mechanical Engineers Part J — Journal of Engineering Tribology 2006;20(J8): 729–37. [7] Sivamani RK, Wu GC, Gitis NV, Maibach HI. Tribological testing of skin products: gender, age, and ethnicity on the volar forearm. Skin Research and Technology 2003;9(4):299–305.
ARTICLE IN PRESS 1574
S. Derler et al. / Tribology International 42 (2009) 1565–1574
[8] Gee MG, Tomlins P, Calver A, Darling RH, Rides M. A new friction measurement system for the frictional component of touch. Wear 2005; 259(7–12):1437–42. [9] Lewis R, Menardi C, Yoxall A, Langley J. Finger friction: grip and opening packaging. Wear 2007;263(7–12):1124–32. [10] Tomlinson SE, Lewis R, Carre MJ. Review of the frictional properties of fingerobject contact when gripping. Proceedings of the Institution of Mechanical Engineers Part J — Journal of Engineering Tribology 2007;221(J8):841–50. [11] Derler S, Schrade U, Gerhardt L-C. Tribology of human skin and mechanical skin equivalents in contact with textiles. Wear 2007;263(7–12):1112–6. [12] Gerhardt L-C, Lenz A, Spencer ND, Mu¨nzer T, Derler S. Skin-textile friction and skin elasticity in young and aged persons. Skin Research and Technology, submitted. [13] Gitis N, Sivamani R. Tribometrology of skin. Tribology Transactions 2004; 47(4):461–9. [14] Sivamani R, Wu G, Maibach HI, Gitis N. Tribological studies on skin: measurement of the coefficient of friction. In: Serup J, Jemec GBE, Grove GL, editors. Non-invasive methods and the skin. Boca Raton: CRC Press, Taylor & Francis; 2006. p. 215–24. [15] Li W, Kong M, Liu XD, Zhou ZR. Tribological behavior of scar skin and prosthetic skin in vivo. Tribology International 2008;41(7):640–7. [16] Tang W, Ge S-r, Zhu H, Cao X-c, Li N. The influence of normal load and sliding speed on frictional properties of skin. Journal of Bionic Engineering 2008; 5(1):33–8. [17] Pailler-Mattei C, Pavan S, Vargiolu R, Pirot F, Falson F, Zahouani H. Contribution of stratum corneum in determining bio-tribological properties of the human skin. Wear 2007;263(7–12):1038–43. [18] Meyers MA, Chen P-Y, Lin AY-M, Seki Y. Biological materials: structure and mechanical properties. Progress in Materials Science 2008;53(1):1–206. [19] Pailler-Mattei C, Zahouani H. Study of adhesion forces and mechanical properties of human skin in vivo. Journal of Adhesion Science and Technology 2004;18(15–16):1739–58. [20] Moore DF. The friction and lubrication of elastomers. Oxford: Pergamon Press; 1972. [21] Myshkin NK, Petrokovets MI, Kovalev AV. Tribology of polymers: adhesion, friction, wear, and mass-transfer. Tribology International 2005;38(11–12):910–21.
[22] Adams MJ, Briscoe BJ, Johnson SA. Friction and lubrication of human skin. Tribology Letters 2007;26(3):239–53. [23] Wolfram LJ. Friction of skin. Journal of the Society of Cosmetic Chemists 1983;34(8):465–76. [24] Landau LD, Lifschitz EM. Elastizita¨tstheorie. 7th ed. Berlin: Akademie Verlag; 1991. [25] Comaish S, Bottoms E. The skin and friction: deviations from Amontons laws, and the effects of hydration and lubrication. British Journal of Dermatology 1971;84(1):37–43. [26] Koudine AA, Barquins M, Anthoine P, Aubert L, Leveque J-L. Frictional properties of skin: proposal of a new approach. International Journal of Cosmetic Science 2000; 22(1): 11–20. [27] Sivamani RK, Goodman J, Gitis NV, Maibach HI. Friction coefficient of skin in real-time. Skin Research and Technology 2003;9(3):235–9. [28] Greenwood JA, Tabor D. The friction of hard sliders on lubricated rubber — the importance of deformation losses. Proceedings of the Physical Society of London 1958;71(462):989–1001. [29] Gerhardt L-C, Stra¨ssle V, Lenz A, Spencer ND, Derler S. Influence of epidermal hydration on the friction of human skin against textiles. Journal of The Royal Society Interface 2008;5(28):1317–28. [30] Greenwood JA, Williamson JBP. Contact of nominally flat surfaces. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) 1966;295(1442):300–19. [31] Pailler-Mattei C, Bec S, Zahouani H. In vivo measurements of the elastic mechanical properties of human skin by indentation tests. Medical Engineering & Physics 2008;30(5):599–606. [32] Hamrock BJ, Dowson D. Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication. In: Proceedings of the fifth Leeds–Lyon symposium on tribology. Bury St. Edmunds, Suffolk: Mechanical Engineering Publikation; 1979. p. 22–27. [33] Esfahanian M, Hamrock BJ. Fluid-film lubrication regimes revisited. Tribology Transactions 1991;34(4):628–32. [34] Roberts AD, Tabor D. The extrusion of liquids between highly elastic solids. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990) 1971;325(1562):323–45.