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Analysis of adhesive behaviour of human skin in vivo by an indentation test
Tribology International 39 (2006) 12–21 www.elsevier.com/locate/triboint
Analysis of adhesive behaviour of human skin in vivo by an indentation test C. Pailler-Matte´i*, H. Zahouani Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syste`mes, UMR CNRS 5513, 36 Avenue Guy de Collongue, Ecully cedex 69134, France Received 25 March 2004; received in revised form 26 October 2004; accepted 8 November 2004 Available online 13 January 2005
Abstract Indentation testing is a widely used technique to quantify the elastoplastic properties of materials. However, it also allows the analysis of the adhesive force between a substrate and an indenter. In this paper, in order to contribute to the understanding of the human skin behaviour, an elastic adhesive theory has been applied to a steel/skin in vivo contact. The human skin adhesive behaviour is investigated by varying different parameters; namely the normal load, the indentation speed, the contact time and the indenter geometry. Under controlled experimental conditions, this in vivo skin study results in the characterisation of the skin adhesive behaviour. q 2004 Elsevier Ltd. All rights reserved. Keywords: Human skin; Adhesive force; Contact mechanics
1. Introduction The main goal of this paper is to understand the skin adhesive behaviour for the dermatological or cosmetic application and over all health application. Human skin may be modelled as an adhesive visco-elastic material [1,2] even though it is composed of three layers (stratum corneum, epidermis, derma), presenting different mechanical properties. However, under an exterior excitation the skin different layer behaviour is harmonized and the skin reacts like a monolayer material. This justifies, in first approximation, the study of the whole mechanical behaviour of the skin as if it was a homogeneous material [1]. The skin adhesive aspect is principally due to the presence of continuous thin lipidic film on the entire body surface. Its thickness varies with body zone and its biological function is to protect the body from external aggressions. In recent years, many non-invasive techniques have been developed to understand and characterise in vivo skin mechanical properties. The most-commonly used techniques are based on the measurements of torsion [3,4], suction [5] and extensibility [6] of the skin. However, the data are mainly * Corresponding author. Tel.: C33 4 72 18 62 91; fax: C33 4 78 43 33 83. E-mail address: [email protected] (C. Pailler-Matte´i). 0301-679X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2004.11.003
semi-quantitative and often distorted by the experimental conditions. In the past decades, a few authors have using indentation techniques in order to improve thin layer material property measurements and to minimize the disturbance due to the experimental conditions. Therefore, an indentation device has been developed in order to accurately evaluate the skin visco-elastic properties. It controls tribological parameters such as indentation speed and the applied normal load to the skin. Comparative experiments have been run where these parameters were varied. During all this study, we have tested the inner forearm skin of 10 30-year-old women. The average reduced Young’s modulus of the skin, estimated by indentation [7,8] was E*Z9.5G2 kPa. In the literature, the Young’s modulus of skin, in vivo, calculate by different method vary between 10 kPa (torsion) until 50 MPa (suction) in function of the authors [9]. Concerning the roughness, it decreases the adhesion effect, but there is no surface in the body without roughness to analyze its effect. The inner forearm skin is one of the less rough zone in the body (Ra (inner forearm skin)Z30 mm, Ra is the average roughness), so we will consider that inner forearm skin is fairly smooth zone compare to every body zone. Moreover, when normal load is applied on the surface skin, the skin relief unfolds oneself under the normal load effect [10].
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Skin mechanical properties are very dependent on the age [9], and we may consider that at 30-years-old, the viscous component of the skin is negligible compared to the elastic component. In order to avoid disturbance from any human movement, the forearm, chosen as testing zone, is put in an adjustable gutter independent of the rest of the indentation device. To analyse and understand the skin adhesive behaviour, we used different contact mechanical theories; namely those due to Hertz [11], and Johnson, Kendall and Roberts (JKR) [12,13]. The Derjaguin, Muller and Toporov theory (DMT) [14] is not considered in this study because it is not applicable to the considered soft solid [15]. These theories have allowed us examine the effect of many tribological conditions on adhesive skin behaviour. Adhesion forces are able to modify the contact area and pressure distribution between the indenter and the material [16] as compared to the non-adhesive contact. As a consequence, we have analysed normal load and indentation speed effects on mechanical and adhesive skin behaviour. Moreover, the effect of the nature of the indenter has been studied to investigate the role of material surface energy on adhesive properties. Finally, the effect of liquid treatment on adhesive skin behaviour has been investigated.
2. Contact mechanics, theory elements 2.1. Hertzian contact [11] We consider a contact between a smooth spherical steel indenter and a smooth elastic flat substrate (Fig. 1). The main assumptions with Hertz theory are the following: – The solids are submitted to small strain under elastic limit. – There is no sliding or adhesion between surfaces. – The contact dimensions are small compared to radii of curvature of both surface.
R is the radius of curvature of the spherical punch, E* is the reduced Young’s modulus, with: 1 1 K n21 1 K n22 1 K n22 C z Z E E1 E2 E2
(3)
since E1 [ E2 ; with n1 and n2 the Poisson ratio:
2.2. Johnson, Kendall and Roberts (JKR) theory [12,13] JKR theory considers only the surface forces inside the contact and neglects the surface forces outside. The action of adhesive forces is to increase the contact area between the indenter and the material. Adhesive forces produce infinite normal strains at the edge of the contact. These infinite strains appear naturally by superposition of compressive Hertzian strains under the action of the load FN1 and that of tensile stresses caused by the punch, under the effect of load (FNKFN1) applied to the same contact area. FN1 is the load which produces, in the absence of attraction forces, the same contact area as under the load applied FN (load applied to the system) when these forces interact. Consequently, the contact area includes two distinct areas; an adjacent annular zone at the edge, in which the normal strains are tensile (attractive zone) and a circular central zone inside which these strains are compressive (repulsive zone) (Fig. 2). For a JKR contact, there is a sudden separation of both surfaces when the normal force is equal to K(3/2)pRw, where w is the adhesion energy. For a sphere/flat contact, JKR theory gives the following results rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 R aJKR ¼ ðF þ 2Fad þ 2 Fad ðFN þ Fad ÞÞ (4) 4 E N a2 dJKR Z JKR K R
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 aJKR Fad a2JKR FN C Z 3 RE 3R 2aJKR E
For a Hertzian contact, the penetration depth, d, and contact radius, aH, are given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 a2H 9 FN2 Z dZ (1) 16 RE2 R rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 R aH Z F (2) 4 E N where FN is the normal load,
Fig. 1. Elastic contact between a soft substrate and undeformable indenter. d is the penetration depth of the indenter, and a represents the contact radius.
13
Fig. 2. Pressure distribution in JKR contact.
(5)
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where
and FS for untreated skin, since the thickness of cutaneous lipidic film and indentation speed are small. It has been shown for a spherical/flat contact with a thin liquid film at the interface that the adhesive force is given by [18]
aJKR is the JKR contact radius, dJKR is the JKR penetration depth. This relation is valid for a rigid spherical indenter. The adhesive force for a JKR’s contact is given by: 3 Fad Z pRw 2
(6)
It is noteworthy that Fad depends on w, and the adhesion energy depends on the nature of contact between the indenter, the material and the temperature. JKR theory is applied mainly to soft solid contacts with large adhesion energies and contact radii [15]. Moreover, the contact radius aJKR between the indenter and the material is different from zero [13] for a normal load equal to zero. This is due to the effect of adhesive forces and the contact radius in this case, a0JKR , is given by: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3R 0 aJKR Z F (7) E ad 2.3. Adhesive contact with a liquid meniscus for total wettability of surface If two solids are approached, they are subjected to an attractive force. When both solids are in contact, adhesive forces appear. They depend on solid geometry, surface energy and solid mechanical properties. If there is a liquid film between the indenter and the material, adhesive forces are mainly controlled by the properties of this liquid film. In general, a liquid film increases the adhesive force value above its value without liquid film [17], accept for the smooth elastomeric contact [12]. With a liquid meniscus, the total adhesive force may be expressed as: Fad Z FW C FH C FS
(8)
FW is the wettability force. FW is the short-range surface attraction through the liquid phase. If the liquid fully wets the solids, then its value will be less than JKR autoadhesion pullforce for the dry contact given by Eq. (6) [12]. FH is the hydrodynamic force or the viscous force. It will be small if the separation velocity is small, but if the liquid film is thin then this term could be large and not negligible. Fs is the capillary meniscus force. It depends on the geometry of the liquid bridge and the liquid surface tension. For a sphere in contact with a flat for contact angle of zero: FSZ4pRgLV, with gLV is the liquid surface energy. The nature of the thin liquid film, and especially its viscosity, is a major parameter to evaluate the adhesive force. In first approximation, we may consider that the hydrodynamic term, FH , is negligible in comparison to FW
jFad j Z npRg
(9)
with g is defined by gZgLV cos qCgSL, with gLV is the liquid surface energy, and gSL is the adhesion energy of the surfaces in presence of the liquid. By comparison with the Young’s equation for a drop on a solid surface, gZgSV where gSV is the surface energy of the solid surface in air. For total wettability cos qZ1 then gSVZgLVCgSL. If the liquid attenuates the autoadhesion, then gSL is small and hence gSVzgLV. By consequence, FSZ4pRgLV for a capillary meniscus and FWZ3pRgSV [19] for the dry contact solid contact between like bodies (i.e. wZ2gSV). Thus, it is to be expected for a wetting liquid that the maximum separation force in the absence of viscous force is similar to that obtained for the dry case [19]: 3 jFad j Z 3pRgSV Z pRw 2
(10)
The adhesion energy, w, directly depends on the surface energy gSV. In order to estimate the adhesion energy we have used Eq. (10) for analysing data recorded at low indentation speeds. This speed restriction allows the hydrodynamic term to be neglected.
3. Experimental details A specific indentation device has been developed in order to measure and understand the skin mechanical behaviour. The indentation device is controlled in displacement. It measures continuously the normal force variation, FN, as a function of the penetration depth d in the material. The indenter used to do these tests is a smooth spherical steel indenter. The radius of curvature of the steel indenter is RZ 6.35 mm. The indentation tests allow us to obtain many mechanical characteristics, like stiffness, reduced Young’s modulus, adhesive force, elastic, viscous and adhesive energies. During an indentation cycle, the normal displacement is controlled by an LVDT sensor. The maximum displacement during a loading–unloading cycle is 2000 mm with a resolution of 0.1 mm. The indentation system is able to measure very small forces like adhesion forces. Under controlled experimental conditions, it allows the evaluation of attractive forces between the indenter and human skin. The indentation system components are summarised below: – A LVDT sensor to measure displacement. – A motion controller to displace the indenter at constant velocity.
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Fig. 3. Indentation curves for both normal and dry skin. Tests were made with a spherical steel indenter with a radius of curvature RZ6.35 mm and indentation velocity VZ400 mm/s.
– A data acquisition card to collect the signals emitted by the various sensors. Indentation test characteristics and principle: – – – –
Range of normal load (FN) is about 1–100 mN. Penetration range d is about 1–2000 mm. Indentation speed is varying from 5 to 1500 mm/s. Possibility of multi-indentation with different speed and normal load (maximum 10).
4. Results and discussion Tests results are reported here for one 30-year-old female, well-representative of the tester population. The Young’s modulus of the skin measured by indentation test is about E*Z9.5G2 kPa. To understand the effect of surface lipidic film on skin adhesion behaviour, we made an indentation test on normal skin and dry skin (Fig. 3). To dry the human skin, we used ether solution. The indentation tests were made with a spherical steel indenter with a curvature radius equal to RZ 6.35 mm. The skin adhesion behaviour is mainly controlled by a thin skin surface film (Fig. 3). But adhesive aspects are experimentally difficult to study because of their dependence with experimental and biologic conditions. In fact, the temperature and the relative humidity are the key parameters to control. In our tests, the temperature is 295G3 K and the relative humidity is approximately 25%. First of all, in order to justify the approximation regarding Hertz theory, we have checked that for the same normal load, there is no significant difference between the Hertzian theoretical depth and measured depth (Fig. 4). The difference appears when the normal load increases. At high normal load, the viscosity parameter of the human skin increases and becomes less neglectable. For indentation depths of 1 mm there will be a considerable influence of the sub-cutaneous fat on the force. Since this will have a much lower elastic
modulus than the epidermis/dermis, this could explain the deviation from Hertzian behaviour. Moreover, at such a load, the small strain Hertzian assumption is not valid and the contact geometry (sphere/flat) is modified accordingly. Therefore, under some experimental conditions, the Hertzian theory is pertinent to determinate the penetration depth of the spherical punch into the human skin. 4.1. Influence of the experimental conditions 4.1.1. Normal load Fig. 5 depicts the evolution of the contact radius with an increasing normal load, calculated for an adhesive contact (JKR) and non-adhesive contact (Hertz). The JKR contact radius is calculated with Eq. (4) with the experimental pulloff force value, Fad, obtain in the normal skin (FadZ0.5 mN for normal load FNZ20 mN). It can be seen that adhesive forces increase the contact area between the indenter and
Fig. 4. Comparison between the Hertzian depth and the measured depth in human skin in vivo (Indentation speed VZ400 mm/s and radius of curvature RZ6.35 mm).
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Table 2 Values of adhesive forces and adhesion energies for different normal loads and different radius of curvature (indentation speed VZ400 mm/s) Radius of curvature R (mm)
Normal load (mN)
Adhesive force (mN)
Theoretical adhesion energy (mJ/m2)
Experimental adhesion energy (mJ/m2)
6.35
20 40 80 20 40 80 20 40 80
0.52 0.58 1.15 0.41 0.5 0.82 – 0.25 0.48
17.5 19.5 38 18 22 36 – 23.5 45
16G1 17G1 28G1 18G1 20G1 26G1 – 21G1 33G1
4.75
2.25
Fig. 5. Variation of the contact radius with the normal load (RZ6.35 mm) for human skin.
the material [20]. As a consequence, deformations are lower for non-adhesive contact than for adhesive contact. Because of the low value of the adhesives forces, it may be assumed that the skin deformation obeys the Hertzian theory. The average strain 3 for a Hertzian contact is given by: rffiffiffiffi a d 3 Z 0:4 Z 0:4 (11) R R This result is obtained from Eqs. (1) and (2). We observe from Table 1 that the strain increases as the radius of curvature decreases. From Eq. (6), it is noted that the adhesive force is a function of the radius of curvature, R, of the indenter and of the adhesion energy, w, between the indenter and the skin. The adhesion energy is independent of the normal load. However, Table 2 clearly shows that the adhesive force increases with the normal load, and the values of adhesion energy, calculated with Eq. (6), vary. For a small radius of curvature, the deformations are important and the sphere/flat contact geometry is not respected anymore. Eq. (6) may not be used to calculate the adhesion energy in this case. Consequently, Eq. (6) is pertinent to calculate adhesion energy only at low normal load, when the sphere/flat contact is respected. For small deformations we can calculate a good theoretical value of the adhesion energy (Table 2). The corresponding experimental value has been determinated from the adhesive work (defined as the negative area between the unloading curve and normal load axis) (Fig. 6). Table 1 Mean percentage strain versus normal load for indenters of different radii of curvature Radius of curvature R (mm)
FNZ20 mN (%)
FNZ40 mN (%)
FNZ80 mN (%)
2.25 4.75 6.35
28 17 14
36 22 18
46 31 23
To obtain a value of the experimental adhesion energy in mJ/m2, the adhesive work has been divided by the contact area corresponding to a normal load equal to zero (Eq. (7) where FNZ0). The average value of theoretical adhesion energy, w, is 18.5 mJ/m2 whereas the experimental method gives a wexp of about 16.5G1 mJ/m2 (for RZ6.35 mm and without the value corresponding to normal load FNZ80 mN). The theoretical adhesion energy value is in agreement with the experimental one. 4.1.2. Indentation velocity The literature highlights the fact that the adhesive force is sensitive to the contact time between the indenter and the material [21,22]. The indentation device does not control the contact time between the indenter and the skin. However, at constant normal load, the indentation speed is equivalent to this contact time. Therefore, the indentation speed is a key parameter to analyse adhesive force. For human skin, a viscous thin surface film is responsible for the adhesive behaviour (Fig. 3). Tests realised at different indentation speeds confirm that the adhesive force Fad is correlated to variations (Fig. 7). The adhesive force increases with the indentation speed. Eq. (8) gives the expression of the adhesive force with a fluid meniscus: Fad Z FW C FH C FS The hydrodynamic force FH is: FH Z
6phR2 dD Z hLD_ dt D
(12)
with h the viscosity of the thin film, L parameters geometric function [23], D the central film thickness, D_ the separation speed between solids. As previously seen, at high indentation speed, hydrodynamic force cannot be neglected. Therefore, the adhesive _ force becomes very dependent on the indentation speed D.
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Fig. 6. Adhesive work for an indentation speed VZ400 mm/s.
The faster the indentation speed, the more difficult is the separation between the indenter and the skin, since the adhesive force increases (Fig. 7, Table 3). This result was previously observed by Matthewson [23] for a sphere/flat contact with a thin liquid film at the interface. It is a specific characteristic of adhesive thin films. This observation leads to affirm that skin adhesive behaviour is mainly controlled by the viscous thin surface film at high pull-off velocities. The indentation speed range being limited, the speed effect on adhesive force has not clearly been observed experimentally. Probably, because a change of a factor 4 in indentation speed is insufficient to pick up any speed effect. At high indentation speeds, a value of the adhesion energy cannot be calculated accurately, because the hydrodynamic force is not negligible. During tests carried out under specific experimental conditions, the hydrodynamic force can be neglected. The variation with the speed (Eq. (12)) must be minimized. Therefore, the indentation tests have been done at slow indentation speeds. However, very small values of the indentation speed are unsuitable because of
the device sensitivity to unavoidable bodily movements. Consequently, the indentation speed has been chosen equal to VZ500 mm/s. 4.1.3. Effect of the radius of curvature For a JKR contact, the adhesive force depends on the radius of curvature of the indenter, R, and the adhesion energy, w (Eq. (6)). Therefore, three different radii of curvature have been tested at constant indentation speed but at normal loads varying from 20 to 80 mN (Table 1). We observe that, when the radius of curvature increases, the adhesive force increases independently of the normal load and the indentation speed. The adhesion energy remains constant as a function of the radius of curvature if V!500 mm/s and FN!50 mN. Then, the sphere/flat contact geometry is respected and the hydrodynamic term can be neglected. Experimentally, the adhesive force is sensitive to a combination of the indenter radius of curvature, the applied normal load, the indentation speed. It has not been possible to determine the predominant parameter since their relative influence on the adhesive force is coupled.
Fig. 7. Variation of adhesive force for different indentation speed (RZ6.35 mm).
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Table 3 Values of adhesion energy for different experimental conditions (radius of curvature RZ6.35 mm and applied normal load FNZ30 mN) Indentation speed (mm/s)
Adhesive force (mN)
Theoretical adhesion energy (mJ/m2)
200 400 800
0.51 0.51 0.65
17 17 22
We only know that the chemical nature of skin thin film is important and that experimental conditions are important to correctly calculate adhesive parameters. 4.2. Influence of the nature of the indenter An elastomeric spherical indenter has been used to analyse the material effect on adhesive force. The indenter has a radius of curvature equal to RZ6.35 mm, exactly the same radius of curvature as the steel spherical indenter. The elastomeric indenter is made of silicone and has a reduced Young’s modulus of E*Z2G0.1 MPa. It may be considered that the elastomeric indenter is not deformable in comparison to the human skin. With this approximation, JKR sphere/glass relations are still valid. 4.2.1. Comparison between elastomeric and steel spherical indenter Comparative indentation tests have been carried out for two kinds of indenters (steel and elastomer). The adhesive force can be plotted versus the normal load at constant indentation speed (Fig. 8a) or versus the indentation speed for constant normal load (Fig. 8b). These figures clearly demonstrate that the adhesive force increases with increasing normal load and indentation speed, for the two indenters. Therefore, it can be concluded that the adhesive force is sensitive to the contact area and contact time. The adhesive force, in the case of an elastomer/skin contact is greater to that of the steel/skin contact in the chosen experimental conditions. The experimental adhesion
energy may be estimated, wsteelZ17.5 mJ/m2, welastomerZ 31 mJ/m2, for the normal load of 20 mN and an indentation speed of 400 mm/s. Higher value of the adhesion energy is found for an elastomeric contact than for the steel contact, which is due to the difference of the surface energy of the two materials. From these experiments, the influence of the surface energy on adhesive force may be noted. The nature of the contact plays a major role in the adhesive phenomena. The adhesive force is not constant as a function of the normal load and the indentation speed. Therefore, for high normal load and high indentation speed the adhesive force measured is not the adhesive force defined by the adhesive contact theory, because the hypothesis of the elastic contact is not respected. Moreover, the viscoelastic energy losses at the ‘crack tip’ could be responsible for the increase in pulloff velocity. 4.3. Adhesive force for treated skin A liquid treatment, based on dermatologic water and called TA, has been sprayed on the tester skin. After chemical treatment the skin adhesive behaviour usually differs from the untreated skin behaviour. The adhesive force increases and its mechanical properties change. But with TA treatment we may consider that Young’s modulus stays constant, because the contact stiffness between the indenter and skin stays constant (Fig. 9). The indentation curves for the normal and the treated skin are practically the same, except for the adhesive force. In this study, we sprayed TA on the skin and have waited for 5 min before measuring the adhesive force. The test has been made with a spherical steel indenter, with a radius of curvature RZ6.35 mm, for a 30 mN normal load and 400 mm/s indentation speed. Fig. 10 shows the evolution of the adhesive force following TA application. The adhesive force increases after liquid treatment to a level eight times greater than that of normal skin. The high adhesion observed 5 min after
Fig. 8. (a) Variation of adhesive force with normal load for steel and elastomeric indenter, for an indentation speed VZ400 mm/s. (b) Variation of adhesive force with indentation speed for steel and elastomeric indenter, for normal load FNZ30 mN.
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Fig. 9. Indentation test on normal skin and skin treated with TA (5 min after application), and for indentation speed VZ400 mm/s.
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spraying with TA is due to the formation of capillary meniscus which would lead to an increase in the value of FS. After 33 min, skin surface seems to have absorbed all the liquid treatment and the adhesive behaviour reverses back to the initial state. As the TA is adsorbed/evaporates the size of this bridge will shrink and this could be responsible for the decrease in pull-off force with time after application. If the test was made with pure water we see the same evolution of adhesion force in function of time after liquid application. However, the value of the maximum adhesion force will bigger than TA. With treated skin, the indentation device is sensitive to the attractive force at the beginning of indentation cycle (Fig. 11). The jump-to-contact distance allows the evaluation of the thickness of the thin liquid film, e, on the skin [24]. The latter is measured using the distance between mechanical contact (abscissa 0 by convention) and the point of maximum attractive force. This distance h is equal to three times the thickness e of thin liquid film (Fig. 11), as described in detail in [24]. After 5 min the thickness is: e Z 20 mmG3 mm Attractive phenomena disappear after 7!t!9 min after application of treatment. The device is not sensitive enough to the thickness of the liquid thin film on skin when the latter is too small. Hertz theory gives a good approximation of the mechanical properties of the untreated skin, because the adhesive force is small, but for treated skin the adhesive force increases and JKR theory is necessary to estimate mechanical skin properties. For treated skin, 5 min after application penetration depth are estimated from (Fig. 11):
Fig. 10. Variation of adhesive force with time following TA application.
dmeasured Z 1:3 mm dHertz Z 0:92 mm dJKR Z 1:17 mm
Fig. 11. Indentation curve for treated skin 5 min after application of TA.
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Penetration depth dHertz, dJKR are calculated with Eqs. (1) and (5). JKR theory gives the best approximation, because the adhesive force is bigger. JKR theory is confined to elastic materials and the difference between dJKR and dmeasured is due to the viscous component of the skin which has not been taken into account for treated skin. The analysis of theoretical adhesion energy confirms the importance of surface forces on adhesive force with treated skin: wJKRZ107 mJ/m2 (5 min after treatment), wJKRZ17 mJ/m2 (33 min after treatment) To calculate the adhesion energy, w, if the capillary is constant with the applied normal load the DMT theory [25] can be more appropriate. In this case, the value of DMT’s adhesion energy, wDMT is: wDMT Z
daJKR dt
Time after TA application (min)
5
11
17
23
29
33
Crack propagation velocity (mm/s)
1.1
1.15
1.25
2.8
2.9
3
For an indentation speed VZ400 mm/s, the crack propagation velocity increases with time after treatment application. This is because the adhesive force diminishes with time after treatment application (Fig. 10). As a consequence, the crack propagation velocity is greater when the adhesive force and adhesion energy decrease.
5. Conclusion
Fad Z 82 mJ=m2 ð5 min after treatmentÞ 2pR
In order to further analyse the adhesive force effects on treated skin, we can measure crack propagation velocity [26] between the skin and the spherical indenter. Crack propagation velocity is defined as: vZ
Table 4 Values of crack propagation velocity versus time after treatment application
(13)
where aJKR is the JKR contact radius. The crack propagation velocity is the slope of curve aJKRZf(t) (Fig. 12) and is calculated between the beginning of the adhesive zone (az) and the maximum adhesive force (FNmax) (Fig. 11). Table 4 gives the results concerning crack propagation velocity versus time after treatment application.
Fig. 12. Crack propagation velocity versus time after chemical treatment application, for normal load FNZ30 mN and indentation speed VZ 400 mm/s.
The indentation device contributes to the understanding of skin adhesive behaviour. Generally, human skin is considered to be a visco-elastic adhesive material. But, in this study, we have compared skin to an elastic material since the range of normal loads used is the range of acceptable loads for the behaviour to be elastic. Since skin mechanical behaviour is a function of the age [7], the age of the testers was confined to the range in which skin mechanical behaviour is mainly elastic. In a first approximation of the skin mechanical properties, Hertz theory gives good results for normal skin but cannot be applied to treated skin. Measurements of the skin adhesive force are influenced by experimental conditions, such as normal load and indentation speed. In fact skin adhesive force increases if normal load or indentation speed increases. At high normal load the sphere/flat contact geometry between indenter and skin is not respected and JKR theory cannot be used to estimate theoretical adhesive force and adhesion energy. The augmentation of the adhesive force with indentation speed is attributed to the existence of a thin liquid film at the interface indenter/skin; the hydrodynamic component is not negligible anymore. Therefore, to accurately measure the adhesive skin properties, the tests have to be made under controlled experimental conditions. Skin strain must remain less than 20% to have a good estimation for adhesion energy. Moreover, indentation speed must be less than 500 mm/s to neglect the hydrodynamic term in the adhesive force expression with a liquid meniscus. For a spherical/flat contact, contact geometry is also an important parameter; when the radius of curvature increases, adhesive force increases. This observation is in agreement with the elastic theory of adhesion. Adhesive force is sensitive to the material’s nature in terms of surface energy and mechanical properties. Finally, the adhesive force is influenced by the nature of the interface between indenter and skin. The cosmetic treatments that people spray on skin
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modify the skin mechanical properties and skin adhesive forces. These treatments increase the adhesive force and Hertz theory is unsuitable to correctly evaluate skin mechanical properties. As a consequence, to estimate adhesive skin behaviour with cosmetic treatment, JKR theory has been applied. This theory is often used in the case of adhesive elastic contact. However, the application of this theory is limited since the skin viscous behaviour cannot be neglected when chemically treated. Quantifying skin adhesive force is a very difficult task, because of the measurement dependence on experimental and climatic conditions, and on skin age. Nevertheless, under controlled experimental conditions, the indentation of the skin in vivo allows to characterise and better understand the effect of cutaneous films on skin adhesive properties.
References [1] Agache P. Physiologie de la peau et exploitations fonctionnelles cutane´es. Editions Me´dicales Internationales 2000. [2] Meynadier J. Pre´cis de physiologie cutane´e. Editions de la Porte Verte 1980. [3] Sanders R. Torsional elasticity of human skin in vivo. Pfluger Arch 1973;342:255–60. [4] Agache P, Monneur C, Leveque JL, de Rigal J. Mechanical properties and Young’s modulus of human skin in vivo. Arch Dermatol Res 1980; 269:127–35. [5] Diridollou S, Berson M, Vabre V, Black D, Karlsson B, Auriol F, et al. An in vivo method for measuring the mechanical properties of the skin using ultrasound. Ultrasound Med Biol 1998;24:215–24. [6] Alexander H, Cook TH. Accounting for natural tension in the mechanical testing of human skin. J Invest Dermatol 1977;69:310–4. [7] Loubet JL, Bauer M, Tonck A, Bec S, Gauthier-Manuel B. Nanoindentation with a surface force apparatus. In: Naskasi M et al, editor. In Mechanical properties and deformation behavior of materials having ultra-fine microstructures. Dordrecht, MA: Kluwer; 1993, p. 429–47. [8] Sneddon IN. The relation between load and penetration in the axisymmetric boussinesq for a punch of arbitrary profile. Int J Eng Sci 1965;3:47–57.
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[9] Diridollou S, Vabre V, Berson L, Vaillant L, Black D, Lagarde JM, et al. Skin ageing: changes of physical properties of human skin in vivo. Int J Cosmet Sci 2001;23:353–62. [10] Koudine AA, Barquins M, Anthoine P, Aubert L, Leveque JL. Frictional properties of skin: proposal of a new approach. Int J Cosmet Sci 2000;22:11–20. [11] Hertz H. Uber die beruhung fester elastischer korper (on the contact of elastic solids). J Reine Angewandte Mathematik 1882;92. [12] Johnson KL, Kendall K, Roberts AD. Surface energy and the contact of elastic solids. Proc R Soc London; A 1971;324:301–13. [13] Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 2001. [14] Derjaguin BV, Muller VM, Toporov YP. Effect of contact deformations on the adhesion of particles. J Coll Interface Sci 1975;53(2): 314–26. [15] Maugis D. Adhesion of sphere: the JKR-DMT transition using a Dugale model. J Coll Interface Sci 1992;150(1):243–69. [16] Johnson KL. Mechanics of adhesion. Tribol Int 1998;31(8):413–8. [17] Bocquet L, Charlaix E, Restagno F. Physics of humid granular media. C.R. Physique 2002;3:207–15. [18] Barthel E, Yun Lin X, Loubet JC. Adhesion energy measurements in the presence of adsorbed liquid using a rigid surface force apparatus. J Coll Interface Sci 1996;177:401–6. [19] Christenson HK. Adhesion between surfaces in undersatured vapors, a reexamination of the influence of meniscus curvature and surface forces. J Coll Interface Sci 1987;121(1):170–8. [20] Maugis D. Contact, adhesion and rupture of elastic solids. Berlin: Springer; 2000. [21] Barquins M. Adherence, friction and wear of rubber-like materials. Wear 1992;158:87–117. [22] Robbe-Valloire F, Barquins M. Kinetics of adherence of a rigid flatended sphere in contact on a soft rubber-like material surface. Int J Adhes Adhes 1999;19:287–94. [23] Matthewson MJ. Adhesion of spheres by thin liquid films. Phil Mag A 1988;2:207–16. [24] Crassous J, Loubet JC, Charlaix E. Adhesion force between high energy surfaces in vapor atmosphere. Mat Res Soc Symp Proc 1995; 366:33–8. [25] Derjaguin BV, Muller VM, Toporov YP. Effect of contact deformations on the adhesion of particles. J Coll Interface Sci 1975;53: 314–26. [26] Barquins M, Shanahan ER. Effect of surface cavities on static and dynamic adhesion to an elastomeric. Int J Adhes Adhes 1997;17: 313–7.
Analysis of adhesive behaviour of human skin in vivo by an indentation test C. Pailler-Matte´i*, H. Zahouani Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syste`mes, UMR CNRS 5513, 36 Avenue Guy de Collongue, Ecully cedex 69134, France Received 25 March 2004; received in revised form 26 October 2004; accepted 8 November 2004 Available online 13 January 2005
Abstract Indentation testing is a widely used technique to quantify the elastoplastic properties of materials. However, it also allows the analysis of the adhesive force between a substrate and an indenter. In this paper, in order to contribute to the understanding of the human skin behaviour, an elastic adhesive theory has been applied to a steel/skin in vivo contact. The human skin adhesive behaviour is investigated by varying different parameters; namely the normal load, the indentation speed, the contact time and the indenter geometry. Under controlled experimental conditions, this in vivo skin study results in the characterisation of the skin adhesive behaviour. q 2004 Elsevier Ltd. All rights reserved. Keywords: Human skin; Adhesive force; Contact mechanics
1. Introduction The main goal of this paper is to understand the skin adhesive behaviour for the dermatological or cosmetic application and over all health application. Human skin may be modelled as an adhesive visco-elastic material [1,2] even though it is composed of three layers (stratum corneum, epidermis, derma), presenting different mechanical properties. However, under an exterior excitation the skin different layer behaviour is harmonized and the skin reacts like a monolayer material. This justifies, in first approximation, the study of the whole mechanical behaviour of the skin as if it was a homogeneous material [1]. The skin adhesive aspect is principally due to the presence of continuous thin lipidic film on the entire body surface. Its thickness varies with body zone and its biological function is to protect the body from external aggressions. In recent years, many non-invasive techniques have been developed to understand and characterise in vivo skin mechanical properties. The most-commonly used techniques are based on the measurements of torsion [3,4], suction [5] and extensibility [6] of the skin. However, the data are mainly * Corresponding author. Tel.: C33 4 72 18 62 91; fax: C33 4 78 43 33 83. E-mail address: [email protected] (C. Pailler-Matte´i). 0301-679X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2004.11.003
semi-quantitative and often distorted by the experimental conditions. In the past decades, a few authors have using indentation techniques in order to improve thin layer material property measurements and to minimize the disturbance due to the experimental conditions. Therefore, an indentation device has been developed in order to accurately evaluate the skin visco-elastic properties. It controls tribological parameters such as indentation speed and the applied normal load to the skin. Comparative experiments have been run where these parameters were varied. During all this study, we have tested the inner forearm skin of 10 30-year-old women. The average reduced Young’s modulus of the skin, estimated by indentation [7,8] was E*Z9.5G2 kPa. In the literature, the Young’s modulus of skin, in vivo, calculate by different method vary between 10 kPa (torsion) until 50 MPa (suction) in function of the authors [9]. Concerning the roughness, it decreases the adhesion effect, but there is no surface in the body without roughness to analyze its effect. The inner forearm skin is one of the less rough zone in the body (Ra (inner forearm skin)Z30 mm, Ra is the average roughness), so we will consider that inner forearm skin is fairly smooth zone compare to every body zone. Moreover, when normal load is applied on the surface skin, the skin relief unfolds oneself under the normal load effect [10].
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Skin mechanical properties are very dependent on the age [9], and we may consider that at 30-years-old, the viscous component of the skin is negligible compared to the elastic component. In order to avoid disturbance from any human movement, the forearm, chosen as testing zone, is put in an adjustable gutter independent of the rest of the indentation device. To analyse and understand the skin adhesive behaviour, we used different contact mechanical theories; namely those due to Hertz [11], and Johnson, Kendall and Roberts (JKR) [12,13]. The Derjaguin, Muller and Toporov theory (DMT) [14] is not considered in this study because it is not applicable to the considered soft solid [15]. These theories have allowed us examine the effect of many tribological conditions on adhesive skin behaviour. Adhesion forces are able to modify the contact area and pressure distribution between the indenter and the material [16] as compared to the non-adhesive contact. As a consequence, we have analysed normal load and indentation speed effects on mechanical and adhesive skin behaviour. Moreover, the effect of the nature of the indenter has been studied to investigate the role of material surface energy on adhesive properties. Finally, the effect of liquid treatment on adhesive skin behaviour has been investigated.
2. Contact mechanics, theory elements 2.1. Hertzian contact [11] We consider a contact between a smooth spherical steel indenter and a smooth elastic flat substrate (Fig. 1). The main assumptions with Hertz theory are the following: – The solids are submitted to small strain under elastic limit. – There is no sliding or adhesion between surfaces. – The contact dimensions are small compared to radii of curvature of both surface.
R is the radius of curvature of the spherical punch, E* is the reduced Young’s modulus, with: 1 1 K n21 1 K n22 1 K n22 C z Z E E1 E2 E2
(3)
since E1 [ E2 ; with n1 and n2 the Poisson ratio:
2.2. Johnson, Kendall and Roberts (JKR) theory [12,13] JKR theory considers only the surface forces inside the contact and neglects the surface forces outside. The action of adhesive forces is to increase the contact area between the indenter and the material. Adhesive forces produce infinite normal strains at the edge of the contact. These infinite strains appear naturally by superposition of compressive Hertzian strains under the action of the load FN1 and that of tensile stresses caused by the punch, under the effect of load (FNKFN1) applied to the same contact area. FN1 is the load which produces, in the absence of attraction forces, the same contact area as under the load applied FN (load applied to the system) when these forces interact. Consequently, the contact area includes two distinct areas; an adjacent annular zone at the edge, in which the normal strains are tensile (attractive zone) and a circular central zone inside which these strains are compressive (repulsive zone) (Fig. 2). For a JKR contact, there is a sudden separation of both surfaces when the normal force is equal to K(3/2)pRw, where w is the adhesion energy. For a sphere/flat contact, JKR theory gives the following results rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 R aJKR ¼ ðF þ 2Fad þ 2 Fad ðFN þ Fad ÞÞ (4) 4 E N a2 dJKR Z JKR K R
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 aJKR Fad a2JKR FN C Z 3 RE 3R 2aJKR E
For a Hertzian contact, the penetration depth, d, and contact radius, aH, are given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 a2H 9 FN2 Z dZ (1) 16 RE2 R rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 R aH Z F (2) 4 E N where FN is the normal load,
Fig. 1. Elastic contact between a soft substrate and undeformable indenter. d is the penetration depth of the indenter, and a represents the contact radius.
13
Fig. 2. Pressure distribution in JKR contact.
(5)
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14
where
and FS for untreated skin, since the thickness of cutaneous lipidic film and indentation speed are small. It has been shown for a spherical/flat contact with a thin liquid film at the interface that the adhesive force is given by [18]
aJKR is the JKR contact radius, dJKR is the JKR penetration depth. This relation is valid for a rigid spherical indenter. The adhesive force for a JKR’s contact is given by: 3 Fad Z pRw 2
(6)
It is noteworthy that Fad depends on w, and the adhesion energy depends on the nature of contact between the indenter, the material and the temperature. JKR theory is applied mainly to soft solid contacts with large adhesion energies and contact radii [15]. Moreover, the contact radius aJKR between the indenter and the material is different from zero [13] for a normal load equal to zero. This is due to the effect of adhesive forces and the contact radius in this case, a0JKR , is given by: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3R 0 aJKR Z F (7) E ad 2.3. Adhesive contact with a liquid meniscus for total wettability of surface If two solids are approached, they are subjected to an attractive force. When both solids are in contact, adhesive forces appear. They depend on solid geometry, surface energy and solid mechanical properties. If there is a liquid film between the indenter and the material, adhesive forces are mainly controlled by the properties of this liquid film. In general, a liquid film increases the adhesive force value above its value without liquid film [17], accept for the smooth elastomeric contact [12]. With a liquid meniscus, the total adhesive force may be expressed as: Fad Z FW C FH C FS
(8)
FW is the wettability force. FW is the short-range surface attraction through the liquid phase. If the liquid fully wets the solids, then its value will be less than JKR autoadhesion pullforce for the dry contact given by Eq. (6) [12]. FH is the hydrodynamic force or the viscous force. It will be small if the separation velocity is small, but if the liquid film is thin then this term could be large and not negligible. Fs is the capillary meniscus force. It depends on the geometry of the liquid bridge and the liquid surface tension. For a sphere in contact with a flat for contact angle of zero: FSZ4pRgLV, with gLV is the liquid surface energy. The nature of the thin liquid film, and especially its viscosity, is a major parameter to evaluate the adhesive force. In first approximation, we may consider that the hydrodynamic term, FH , is negligible in comparison to FW
jFad j Z npRg
(9)
with g is defined by gZgLV cos qCgSL, with gLV is the liquid surface energy, and gSL is the adhesion energy of the surfaces in presence of the liquid. By comparison with the Young’s equation for a drop on a solid surface, gZgSV where gSV is the surface energy of the solid surface in air. For total wettability cos qZ1 then gSVZgLVCgSL. If the liquid attenuates the autoadhesion, then gSL is small and hence gSVzgLV. By consequence, FSZ4pRgLV for a capillary meniscus and FWZ3pRgSV [19] for the dry contact solid contact between like bodies (i.e. wZ2gSV). Thus, it is to be expected for a wetting liquid that the maximum separation force in the absence of viscous force is similar to that obtained for the dry case [19]: 3 jFad j Z 3pRgSV Z pRw 2
(10)
The adhesion energy, w, directly depends on the surface energy gSV. In order to estimate the adhesion energy we have used Eq. (10) for analysing data recorded at low indentation speeds. This speed restriction allows the hydrodynamic term to be neglected.
3. Experimental details A specific indentation device has been developed in order to measure and understand the skin mechanical behaviour. The indentation device is controlled in displacement. It measures continuously the normal force variation, FN, as a function of the penetration depth d in the material. The indenter used to do these tests is a smooth spherical steel indenter. The radius of curvature of the steel indenter is RZ 6.35 mm. The indentation tests allow us to obtain many mechanical characteristics, like stiffness, reduced Young’s modulus, adhesive force, elastic, viscous and adhesive energies. During an indentation cycle, the normal displacement is controlled by an LVDT sensor. The maximum displacement during a loading–unloading cycle is 2000 mm with a resolution of 0.1 mm. The indentation system is able to measure very small forces like adhesion forces. Under controlled experimental conditions, it allows the evaluation of attractive forces between the indenter and human skin. The indentation system components are summarised below: – A LVDT sensor to measure displacement. – A motion controller to displace the indenter at constant velocity.
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Fig. 3. Indentation curves for both normal and dry skin. Tests were made with a spherical steel indenter with a radius of curvature RZ6.35 mm and indentation velocity VZ400 mm/s.
– A data acquisition card to collect the signals emitted by the various sensors. Indentation test characteristics and principle: – – – –
Range of normal load (FN) is about 1–100 mN. Penetration range d is about 1–2000 mm. Indentation speed is varying from 5 to 1500 mm/s. Possibility of multi-indentation with different speed and normal load (maximum 10).
4. Results and discussion Tests results are reported here for one 30-year-old female, well-representative of the tester population. The Young’s modulus of the skin measured by indentation test is about E*Z9.5G2 kPa. To understand the effect of surface lipidic film on skin adhesion behaviour, we made an indentation test on normal skin and dry skin (Fig. 3). To dry the human skin, we used ether solution. The indentation tests were made with a spherical steel indenter with a curvature radius equal to RZ 6.35 mm. The skin adhesion behaviour is mainly controlled by a thin skin surface film (Fig. 3). But adhesive aspects are experimentally difficult to study because of their dependence with experimental and biologic conditions. In fact, the temperature and the relative humidity are the key parameters to control. In our tests, the temperature is 295G3 K and the relative humidity is approximately 25%. First of all, in order to justify the approximation regarding Hertz theory, we have checked that for the same normal load, there is no significant difference between the Hertzian theoretical depth and measured depth (Fig. 4). The difference appears when the normal load increases. At high normal load, the viscosity parameter of the human skin increases and becomes less neglectable. For indentation depths of 1 mm there will be a considerable influence of the sub-cutaneous fat on the force. Since this will have a much lower elastic
modulus than the epidermis/dermis, this could explain the deviation from Hertzian behaviour. Moreover, at such a load, the small strain Hertzian assumption is not valid and the contact geometry (sphere/flat) is modified accordingly. Therefore, under some experimental conditions, the Hertzian theory is pertinent to determinate the penetration depth of the spherical punch into the human skin. 4.1. Influence of the experimental conditions 4.1.1. Normal load Fig. 5 depicts the evolution of the contact radius with an increasing normal load, calculated for an adhesive contact (JKR) and non-adhesive contact (Hertz). The JKR contact radius is calculated with Eq. (4) with the experimental pulloff force value, Fad, obtain in the normal skin (FadZ0.5 mN for normal load FNZ20 mN). It can be seen that adhesive forces increase the contact area between the indenter and
Fig. 4. Comparison between the Hertzian depth and the measured depth in human skin in vivo (Indentation speed VZ400 mm/s and radius of curvature RZ6.35 mm).
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Table 2 Values of adhesive forces and adhesion energies for different normal loads and different radius of curvature (indentation speed VZ400 mm/s) Radius of curvature R (mm)
Normal load (mN)
Adhesive force (mN)
Theoretical adhesion energy (mJ/m2)
Experimental adhesion energy (mJ/m2)
6.35
20 40 80 20 40 80 20 40 80
0.52 0.58 1.15 0.41 0.5 0.82 – 0.25 0.48
17.5 19.5 38 18 22 36 – 23.5 45
16G1 17G1 28G1 18G1 20G1 26G1 – 21G1 33G1
4.75
2.25
Fig. 5. Variation of the contact radius with the normal load (RZ6.35 mm) for human skin.
the material [20]. As a consequence, deformations are lower for non-adhesive contact than for adhesive contact. Because of the low value of the adhesives forces, it may be assumed that the skin deformation obeys the Hertzian theory. The average strain 3 for a Hertzian contact is given by: rffiffiffiffi a d 3 Z 0:4 Z 0:4 (11) R R This result is obtained from Eqs. (1) and (2). We observe from Table 1 that the strain increases as the radius of curvature decreases. From Eq. (6), it is noted that the adhesive force is a function of the radius of curvature, R, of the indenter and of the adhesion energy, w, between the indenter and the skin. The adhesion energy is independent of the normal load. However, Table 2 clearly shows that the adhesive force increases with the normal load, and the values of adhesion energy, calculated with Eq. (6), vary. For a small radius of curvature, the deformations are important and the sphere/flat contact geometry is not respected anymore. Eq. (6) may not be used to calculate the adhesion energy in this case. Consequently, Eq. (6) is pertinent to calculate adhesion energy only at low normal load, when the sphere/flat contact is respected. For small deformations we can calculate a good theoretical value of the adhesion energy (Table 2). The corresponding experimental value has been determinated from the adhesive work (defined as the negative area between the unloading curve and normal load axis) (Fig. 6). Table 1 Mean percentage strain versus normal load for indenters of different radii of curvature Radius of curvature R (mm)
FNZ20 mN (%)
FNZ40 mN (%)
FNZ80 mN (%)
2.25 4.75 6.35
28 17 14
36 22 18
46 31 23
To obtain a value of the experimental adhesion energy in mJ/m2, the adhesive work has been divided by the contact area corresponding to a normal load equal to zero (Eq. (7) where FNZ0). The average value of theoretical adhesion energy, w, is 18.5 mJ/m2 whereas the experimental method gives a wexp of about 16.5G1 mJ/m2 (for RZ6.35 mm and without the value corresponding to normal load FNZ80 mN). The theoretical adhesion energy value is in agreement with the experimental one. 4.1.2. Indentation velocity The literature highlights the fact that the adhesive force is sensitive to the contact time between the indenter and the material [21,22]. The indentation device does not control the contact time between the indenter and the skin. However, at constant normal load, the indentation speed is equivalent to this contact time. Therefore, the indentation speed is a key parameter to analyse adhesive force. For human skin, a viscous thin surface film is responsible for the adhesive behaviour (Fig. 3). Tests realised at different indentation speeds confirm that the adhesive force Fad is correlated to variations (Fig. 7). The adhesive force increases with the indentation speed. Eq. (8) gives the expression of the adhesive force with a fluid meniscus: Fad Z FW C FH C FS The hydrodynamic force FH is: FH Z
6phR2 dD Z hLD_ dt D
(12)
with h the viscosity of the thin film, L parameters geometric function [23], D the central film thickness, D_ the separation speed between solids. As previously seen, at high indentation speed, hydrodynamic force cannot be neglected. Therefore, the adhesive _ force becomes very dependent on the indentation speed D.
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Fig. 6. Adhesive work for an indentation speed VZ400 mm/s.
The faster the indentation speed, the more difficult is the separation between the indenter and the skin, since the adhesive force increases (Fig. 7, Table 3). This result was previously observed by Matthewson [23] for a sphere/flat contact with a thin liquid film at the interface. It is a specific characteristic of adhesive thin films. This observation leads to affirm that skin adhesive behaviour is mainly controlled by the viscous thin surface film at high pull-off velocities. The indentation speed range being limited, the speed effect on adhesive force has not clearly been observed experimentally. Probably, because a change of a factor 4 in indentation speed is insufficient to pick up any speed effect. At high indentation speeds, a value of the adhesion energy cannot be calculated accurately, because the hydrodynamic force is not negligible. During tests carried out under specific experimental conditions, the hydrodynamic force can be neglected. The variation with the speed (Eq. (12)) must be minimized. Therefore, the indentation tests have been done at slow indentation speeds. However, very small values of the indentation speed are unsuitable because of
the device sensitivity to unavoidable bodily movements. Consequently, the indentation speed has been chosen equal to VZ500 mm/s. 4.1.3. Effect of the radius of curvature For a JKR contact, the adhesive force depends on the radius of curvature of the indenter, R, and the adhesion energy, w (Eq. (6)). Therefore, three different radii of curvature have been tested at constant indentation speed but at normal loads varying from 20 to 80 mN (Table 1). We observe that, when the radius of curvature increases, the adhesive force increases independently of the normal load and the indentation speed. The adhesion energy remains constant as a function of the radius of curvature if V!500 mm/s and FN!50 mN. Then, the sphere/flat contact geometry is respected and the hydrodynamic term can be neglected. Experimentally, the adhesive force is sensitive to a combination of the indenter radius of curvature, the applied normal load, the indentation speed. It has not been possible to determine the predominant parameter since their relative influence on the adhesive force is coupled.
Fig. 7. Variation of adhesive force for different indentation speed (RZ6.35 mm).
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Table 3 Values of adhesion energy for different experimental conditions (radius of curvature RZ6.35 mm and applied normal load FNZ30 mN) Indentation speed (mm/s)
Adhesive force (mN)
Theoretical adhesion energy (mJ/m2)
200 400 800
0.51 0.51 0.65
17 17 22
We only know that the chemical nature of skin thin film is important and that experimental conditions are important to correctly calculate adhesive parameters. 4.2. Influence of the nature of the indenter An elastomeric spherical indenter has been used to analyse the material effect on adhesive force. The indenter has a radius of curvature equal to RZ6.35 mm, exactly the same radius of curvature as the steel spherical indenter. The elastomeric indenter is made of silicone and has a reduced Young’s modulus of E*Z2G0.1 MPa. It may be considered that the elastomeric indenter is not deformable in comparison to the human skin. With this approximation, JKR sphere/glass relations are still valid. 4.2.1. Comparison between elastomeric and steel spherical indenter Comparative indentation tests have been carried out for two kinds of indenters (steel and elastomer). The adhesive force can be plotted versus the normal load at constant indentation speed (Fig. 8a) or versus the indentation speed for constant normal load (Fig. 8b). These figures clearly demonstrate that the adhesive force increases with increasing normal load and indentation speed, for the two indenters. Therefore, it can be concluded that the adhesive force is sensitive to the contact area and contact time. The adhesive force, in the case of an elastomer/skin contact is greater to that of the steel/skin contact in the chosen experimental conditions. The experimental adhesion
energy may be estimated, wsteelZ17.5 mJ/m2, welastomerZ 31 mJ/m2, for the normal load of 20 mN and an indentation speed of 400 mm/s. Higher value of the adhesion energy is found for an elastomeric contact than for the steel contact, which is due to the difference of the surface energy of the two materials. From these experiments, the influence of the surface energy on adhesive force may be noted. The nature of the contact plays a major role in the adhesive phenomena. The adhesive force is not constant as a function of the normal load and the indentation speed. Therefore, for high normal load and high indentation speed the adhesive force measured is not the adhesive force defined by the adhesive contact theory, because the hypothesis of the elastic contact is not respected. Moreover, the viscoelastic energy losses at the ‘crack tip’ could be responsible for the increase in pulloff velocity. 4.3. Adhesive force for treated skin A liquid treatment, based on dermatologic water and called TA, has been sprayed on the tester skin. After chemical treatment the skin adhesive behaviour usually differs from the untreated skin behaviour. The adhesive force increases and its mechanical properties change. But with TA treatment we may consider that Young’s modulus stays constant, because the contact stiffness between the indenter and skin stays constant (Fig. 9). The indentation curves for the normal and the treated skin are practically the same, except for the adhesive force. In this study, we sprayed TA on the skin and have waited for 5 min before measuring the adhesive force. The test has been made with a spherical steel indenter, with a radius of curvature RZ6.35 mm, for a 30 mN normal load and 400 mm/s indentation speed. Fig. 10 shows the evolution of the adhesive force following TA application. The adhesive force increases after liquid treatment to a level eight times greater than that of normal skin. The high adhesion observed 5 min after
Fig. 8. (a) Variation of adhesive force with normal load for steel and elastomeric indenter, for an indentation speed VZ400 mm/s. (b) Variation of adhesive force with indentation speed for steel and elastomeric indenter, for normal load FNZ30 mN.
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Fig. 9. Indentation test on normal skin and skin treated with TA (5 min after application), and for indentation speed VZ400 mm/s.
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spraying with TA is due to the formation of capillary meniscus which would lead to an increase in the value of FS. After 33 min, skin surface seems to have absorbed all the liquid treatment and the adhesive behaviour reverses back to the initial state. As the TA is adsorbed/evaporates the size of this bridge will shrink and this could be responsible for the decrease in pull-off force with time after application. If the test was made with pure water we see the same evolution of adhesion force in function of time after liquid application. However, the value of the maximum adhesion force will bigger than TA. With treated skin, the indentation device is sensitive to the attractive force at the beginning of indentation cycle (Fig. 11). The jump-to-contact distance allows the evaluation of the thickness of the thin liquid film, e, on the skin [24]. The latter is measured using the distance between mechanical contact (abscissa 0 by convention) and the point of maximum attractive force. This distance h is equal to three times the thickness e of thin liquid film (Fig. 11), as described in detail in [24]. After 5 min the thickness is: e Z 20 mmG3 mm Attractive phenomena disappear after 7!t!9 min after application of treatment. The device is not sensitive enough to the thickness of the liquid thin film on skin when the latter is too small. Hertz theory gives a good approximation of the mechanical properties of the untreated skin, because the adhesive force is small, but for treated skin the adhesive force increases and JKR theory is necessary to estimate mechanical skin properties. For treated skin, 5 min after application penetration depth are estimated from (Fig. 11):
Fig. 10. Variation of adhesive force with time following TA application.
dmeasured Z 1:3 mm dHertz Z 0:92 mm dJKR Z 1:17 mm
Fig. 11. Indentation curve for treated skin 5 min after application of TA.
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Penetration depth dHertz, dJKR are calculated with Eqs. (1) and (5). JKR theory gives the best approximation, because the adhesive force is bigger. JKR theory is confined to elastic materials and the difference between dJKR and dmeasured is due to the viscous component of the skin which has not been taken into account for treated skin. The analysis of theoretical adhesion energy confirms the importance of surface forces on adhesive force with treated skin: wJKRZ107 mJ/m2 (5 min after treatment), wJKRZ17 mJ/m2 (33 min after treatment) To calculate the adhesion energy, w, if the capillary is constant with the applied normal load the DMT theory [25] can be more appropriate. In this case, the value of DMT’s adhesion energy, wDMT is: wDMT Z
daJKR dt
Time after TA application (min)
5
11
17
23
29
33
Crack propagation velocity (mm/s)
1.1
1.15
1.25
2.8
2.9
3
For an indentation speed VZ400 mm/s, the crack propagation velocity increases with time after treatment application. This is because the adhesive force diminishes with time after treatment application (Fig. 10). As a consequence, the crack propagation velocity is greater when the adhesive force and adhesion energy decrease.
5. Conclusion
Fad Z 82 mJ=m2 ð5 min after treatmentÞ 2pR
In order to further analyse the adhesive force effects on treated skin, we can measure crack propagation velocity [26] between the skin and the spherical indenter. Crack propagation velocity is defined as: vZ
Table 4 Values of crack propagation velocity versus time after treatment application
(13)
where aJKR is the JKR contact radius. The crack propagation velocity is the slope of curve aJKRZf(t) (Fig. 12) and is calculated between the beginning of the adhesive zone (az) and the maximum adhesive force (FNmax) (Fig. 11). Table 4 gives the results concerning crack propagation velocity versus time after treatment application.
Fig. 12. Crack propagation velocity versus time after chemical treatment application, for normal load FNZ30 mN and indentation speed VZ 400 mm/s.
The indentation device contributes to the understanding of skin adhesive behaviour. Generally, human skin is considered to be a visco-elastic adhesive material. But, in this study, we have compared skin to an elastic material since the range of normal loads used is the range of acceptable loads for the behaviour to be elastic. Since skin mechanical behaviour is a function of the age [7], the age of the testers was confined to the range in which skin mechanical behaviour is mainly elastic. In a first approximation of the skin mechanical properties, Hertz theory gives good results for normal skin but cannot be applied to treated skin. Measurements of the skin adhesive force are influenced by experimental conditions, such as normal load and indentation speed. In fact skin adhesive force increases if normal load or indentation speed increases. At high normal load the sphere/flat contact geometry between indenter and skin is not respected and JKR theory cannot be used to estimate theoretical adhesive force and adhesion energy. The augmentation of the adhesive force with indentation speed is attributed to the existence of a thin liquid film at the interface indenter/skin; the hydrodynamic component is not negligible anymore. Therefore, to accurately measure the adhesive skin properties, the tests have to be made under controlled experimental conditions. Skin strain must remain less than 20% to have a good estimation for adhesion energy. Moreover, indentation speed must be less than 500 mm/s to neglect the hydrodynamic term in the adhesive force expression with a liquid meniscus. For a spherical/flat contact, contact geometry is also an important parameter; when the radius of curvature increases, adhesive force increases. This observation is in agreement with the elastic theory of adhesion. Adhesive force is sensitive to the material’s nature in terms of surface energy and mechanical properties. Finally, the adhesive force is influenced by the nature of the interface between indenter and skin. The cosmetic treatments that people spray on skin
C. Pailler-Matte´i, H. Zahouani / Tribology International 39 (2006) 12–21
modify the skin mechanical properties and skin adhesive forces. These treatments increase the adhesive force and Hertz theory is unsuitable to correctly evaluate skin mechanical properties. As a consequence, to estimate adhesive skin behaviour with cosmetic treatment, JKR theory has been applied. This theory is often used in the case of adhesive elastic contact. However, the application of this theory is limited since the skin viscous behaviour cannot be neglected when chemically treated. Quantifying skin adhesive force is a very difficult task, because of the measurement dependence on experimental and climatic conditions, and on skin age. Nevertheless, under controlled experimental conditions, the indentation of the skin in vivo allows to characterise and better understand the effect of cutaneous films on skin adhesive properties.
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