Abstract Many aspects of both grip function and tactile perception depend on complex frictional interactions occurring in the contact zone of the finger pad, which is the subject of the current review. While it is well established that friction plays a crucial role in grip function, its exact contribution for discriminatory touch involving the sliding of a finger pad is more elusive. For texture discrimination, it is clear that vibrotaction plays an important role in the discriminatory mechanisms. Among other factors, friction impacts the nature of the vibrations generated by the relative movement of the fingertip skin against a probed object. Friction also has a major influence on the perceived tactile pleasantness of a surface. The contact mechanics of a finger pad is governed by the fingerprint ridges and the sweat that is exuded from pores located on these ridges. Counterintuitively, the coefficient of friction can increase by an order of magnitude in a period of tens of seconds when in contact with an impermeably smooth surface, such as glass. In contrast, the value will decrease for a porous surface, such as paper. The increase in friction is attributed to an occlusion mechanism and can be described by first-order kinetics. Surprisingly, the sensitivity of the coefficient of friction to the normal load and sliding velocity is comparatively of second order, yet these dependencies provide the main basis of theoretical models which, to-date, largely ignore the time evolution of the frictional dynamics. One well-known effect on taction is the possibility of inducing stick -slip if the friction decreases with increasing sliding velocity. Moreover, the initial slip of a finger pad occurs by the propagation of an annulus of failure from the perimeter of the contact zone and this phenomenon could be important in tactile perception and grip function. Many aspects of both grip function and tactile perception depend on complex frictional interactions occurring in the contact zone of the finger pad, which is the subject of the current review. While it is well established that friction plays a crucial role in grip function, its exact contribution for discriminatory touch involving the sliding of a finger pad is more elusive. For texture discrimination, it is clear that vibrotaction plays an important role in the discriminatory mechanisms. Among other factors, friction impacts the nature of the vibrations generated by the relative movement of the fingertip skin against a probed object. Friction also has a major influence on the perceived tactile pleasantness of a surface. The contact mechanics of a finger pad is governed by the fingerprint ridges and the sweat that is exuded from pores located on these ridges. Counterintuitively, the coefficient of friction can increase by an order of magnitude in a period of tens of seconds when in contact with an impermeably smooth surface, such as glass. In contrast, the value will decrease for a porous surface, such as paper. The increase in friction is attributed to an occlusion mechanism and can be described by first-order kinetics. Surprisingly, the sensitivity of the coefficient of friction to the normal load and sliding velocity is comparatively of second order, yet these dependencies provide the main basis of theoretical models which, to-date, largely ignore the time evolution of the frictional dynamics. One well-known effect on taction is the possibility of inducing stick -slip if the friction decreases with increasing sliding velocity. Moreover, the initial slip of a finger pad occurs by the propagation of an annulus of failure from the perimeter of the contact zone and this phenomenon could be important in tactile perception and grip function. Introduction Grasping an object between the pads of the thumb and the index finger is the prototype grip used for precision-handling studies. Precision grip must be controlled in order to achieve the optimal minimum force necessary to prevent the slip of an object. In perceptual tasks such as surface discrimination, the normal loading must be modulated to provoke a controlled slip. The precise control of finger pressure derives from the responses of strain-sensitive cutaneous mechanoreceptors at the tips of the digits, as well as from motor control systems that sense muscle length and power based on sensory input from both cutaneous and muscle mechanoreceptors [1, 2] . The dynamic tactile signals from the cutaneous mechanoreceptors reliably encode various aspects of contact events around which most object manipulation tasks are organized [3, 4] . In 1984, Westling & Johansson [5] published the results of an ingenious paradigm to study the control of grip force during the grasping and lifting of objects. They reported that the normal component of the grip force is influenced by three important factors: (i) the weight of the object, (ii) the friction between the object and the skin, and (iii) the safety margin set by the individual based on prior experience. Moreover, data from studies involving healthy participants with experimentally induced sensory deficits and from patients with sensory loss, because of peripheral nerve damage or central brain lesions, clearly demonstrate the central role of somatosensory feedback for dexterous manipulation. Several methods have been used to transiently interrupt sensory information from the hands of healthy subjects: the use of gloves [6] , cooling with sprays or gels [7] and injections of local anaesthetics [8, 9] . An almost invariable effect of these manipulations was an increase in the grip force applied against the grasped object. One logical primary reason for the increases in the motor output is a strategic response of the nervous system to ensure against slippage of the object despite a deficit of sensory information. Excessive grip forces have also been observed for the paretic hands of both children with hemiplegic cerebral palsy [10] and stroke patients [11] , and also for patients with strong compression of the median nerve [12] . The excessive grip forces were generally attributed to the perturbed feedback of sensory information. Introduction Tactile exploration involves the movement of a finger pad across a counter body, typically at smaller normal loads than those used in grip. The subjective assessment of the roughness of fine but not coarse textures is greatly enhanced by sliding [13] . This was considered as evidence for the duplex theory of texture perception, which was originally proposed by Katz [14] . He argued that coarse textures involve spatial coding as a result of the response of the low-threshold cutaneous mechanoreceptors in the finger pad while fine texture perception relies on a temporal coding, which has been termed vibrotaction. Essentially, the movement of the finger pad over such surfaces causes vibrations that have been measured directly by proximity sensing [15] . A similar mechanism applies to indirect touch in which a probe is moved across a surface causing vibrations to be propagated along the probe to the fingers [16, 17] . These studies suggest that the friction of the finger pad may not play a primary role in assessing the surface roughness. However, the analysis of oscillations in the frictional force has shown that there is some correlation with roughness [18] , and that the oscillation amplitude depends on both the orientation of the fingerprint ridges and any load dependence of the coefficient of friction [19, 20] . Moreover, lubrication can reduce the perceived magnitude of the roughness [18, 21] . Introduction In texture perception, the frictional and normal forces are adjusted optimally in a way that depends on the topography of the surface [22] , which supports the contention that friction is a significant factor in tactile appraisal. Data from such active touch studies on rough surfaces, which involve the subject stroking the surface rather than by an imposed sliding of the surface against the finger pad ( passive touch), are difficult to interpret because of this tendency to optimize the friction by changing the normal load in a way that is probably governed by pleasantness. There is not compelling evidence to support a feedback mechanism based on pleasantness. However, Skedung et al. [23] found that, for test papers having different roughnesses, the subjects reduced the normal force as the coefficient of friction increased. Correlations with perceived roughness have been found with both the measured roughness and the coefficient of friction, which is further evidence of the importance of friction [24] . Introduction The ranking of roughness is a relatively restricted attribute of a tactile response and is an example of discriminatory touch. For example, Gwosdow et al. [25] investigated the influence of perspiration on fabrics and found that the resulting increase in skin friction enhanced the perception of roughness. The increase in friction correlated with a reduction in comfort, which is arguably more important. Gerhardt et al. [26] also observed an increase in the friction of skin against fabrics as a function of increasing epidermal moisture. They pointed out the relevance of this work on textiles to skin damage such as blisters, abrasion and decubitus ulcers. Similar types of damage can result from sports activities that involve, for example, sliding contacts with equipment, grass or artificial playing surfaces. Introduction Simultaneous measurements of vibration and friction would establish whether tribological interactions play a significant role in modifying the vibratory response, which is currently regarded as the primary sensory cue in assessing fine surface texture. However, it is clear from a recent work [27] that subjects are capable of ranking friction quite accurately. It was found that the Weber index for the coefficient of friction of a glass surface is 0.18. That is, subjects could distinguish a difference of about an 18 per cent reduction in the coefficient of friction, which was achieved by increasing the amplitude of ultrasonic vibrations applied to the glass; this method of reducing the friction is well established in metal forming, for example [28] . These results are consistent with earlier work by Smith & Scott [29] , who showed that subjects can scale the friction of smooth surfaces, for which vibrotaction is not applicable. Introduction Thus, it is reasonable to conclude that friction is a significant factor in discriminatory touch. It is also an important factor in affective and hedonic touch, and in associated emotional attributes such as pleasantness and comfort. Although affective touch is commonly connected with the unmyelinated mechanoreceptive afferents that innervate hairy skin (the C tactile or CT-afferent system) [30] , it is clearly an important aspect in the context of the finger pads where such afferents are not thought to exist. It is also obvious that a lubricated surface is felt quite differently to one that is unlubricated even if the presence of a lubricant, owing to sensory compensation mechanisms, has a minor effect on the discrimination of the roughness. On the other hand, in the case of relatively smooth surfaces, friction must be a major source of sensory information. For example, Guest et al. [31] investigated the sensory attributes of a wide range of lubricants on a slightly textured polypropylene (PP) sheet and found that there were correlations between the measured friction and sensory dimensions such as watery. Even for unlubricated surfaces, the perception of dryness for a wide range of materials was found to increase as the friction decreased [32] . It has also been observed for dry surfaces that unpleasant tactile sensations increased with the extent of stick-slip motion [33] . Introduction Nakano et al. [34] simulated the application of cosmetic foundations by measuring the sliding friction between silicone elastomer surfaces in the presence of such products. They processed the data using artificial neural networks and were able to predict the emotional tactile comfort with relatively high accuracy based on the frictional data. However, despite such observations and that intuitively it might be expected that friction is a major factor in touch, attempts to objectively deconvolve the unique role of friction have proved to be difficult. For example, in one study, the human tactile evaluation of a range of surfaces was dominated by the rough/smooth and soft/hard dimensions with the stick/slippery dimension being ranked as a much weaker contribution [35] . More recently, Chen et al. [36] explored a wider range of dimensions and only a strong correlation between the coefficient of friction and the wet/dry dimension was observed. The interactions between the various dimensions, e.g. with the surface topography, will have a considerable effect on the friction, which is one complicating factor that was clearly recognized in this study and others [37] . Another is the sensitivity of the coefficient of friction to variables such as normal load, sliding velocity and occlusion, which will be discussed in the current review. As a further indication of the role of friction, virtual reality studies have shown that subjects can readily identify complex textured surfaces on the basis of vibrations alone [38] . While both low-and highfrequency components of the finger-surface interaction were due to friction, subjective reports indicated that absence of the low-frequency components in the simulation, i.e. the absence of net friction, decreased the level of realism. Introduction The detection of slip on the surface of the skin and sudden changes in the load force during object manipulation have been attributed to the fast-adapting low-threshold mechanoreceptors [39 -41] . The extremely high densities of these units in the fingertips, together with their small receptive fields, certainly provide a high spatial acuity to the fingertips [3] . The early adjustment to a new frictional condition, which may appear soon after the object is initially touched (approx. 0.1-0.2 s), depends on the vigorous responses of the mechanoreceptors during the initial phase of lifting an object [39] . In order to prevent slip, the grip/ load force ratio must exceed a minimal value determined by the coefficient of friction between the skin and the object, i.e. the critical ratio at which slips occurs will increase with the slipperiness of the object. Moreover, the responsiveness of especially the fast-adapting units to localized slips, which are not accompanied by acceleration events, suggests that they are also sensitive to other aspects of the mechanical changes reported by Johansson & Westling [39] . These include 'local redistributions of the strain/stress pattern of the field related to the sliding of the surface structure over the skin' [39, p. 151] . These authors also note that 'one important factor contributing to the low frequency of localised slip responses actually observed . . . might have been the spotty appearance of the slip zones' that portends widespread slip. Introduction In seminal work, Phillips & Johnson [42] applied a simple analytical model to estimate the compressive strains that were developed at the locations of the slow-adapting mechanoreceptors as a result of a grating being indented into a finger pad. Linear expressions were derived in order to relate these values to the discharge rates of the afferents. This concept of neuromechanical coupling has since been adopted by a number of researchers using more complex finite-element models of the finger pad, e.g. Maeno et al. [43] and Shao et al. [44] or closed-form solutions [45] . Such work should lead to a more quantitative understanding of tactile perception and grip function based on the principles of contact mechanics and the critical neurophysiological factors. However, the formulation of the stress boundary conditions to prescribe the frictional interactions in such models is simplistic compared with the actual behaviour of the finger pads. An aim of the current paper is to critically review the current knowledge about the friction of the finger pad. This will provide a basis for developing more realistic stress boundary conditions in order to improved simulations of touch and grip and, hence, more accurately predict the response of the low-threshold mechanoreceptors located just beneath the skin surface. Introduction The fingerprint ridges and the large number density of sweat pores that are located in the ridges [46, 47] are the main physiological characteristics that explain the tribological complexity of a finger pad (figure 1). In particular, the continuous eccrine sweat secretion causes an accumulation of moisture at the sliding interface for a finger pad in an enduring contact with an extended impermeable surface. This phenomenon is termed occlusion in the present paper. The dominant mechanism is the reduction in the evaporation of the secreted sweat because of the large decrease in the free surface area when such a contact is made. The kinetics of occlusion will be reviewed as will be the influence of the nature of the countersurface and the addition of excess water, when the contact is defined as being in the wet state. The contact mechanics of the finger pad, which is dominated by the fingerprint ridges, will be considered in terms of the influence of the load dependence of the contact area and friction. The mechanoreceptors respond to dynamic as well as static perturbations. Consequently, the evolution of a finger pad contact, when subjected to tangential loading, will be Figure 1 . A microstructural cross-section of a human finger pad (middle finger) obtained using Optical Coherence Tomography (Spectral Radar OCT -OCP930SR, ex Thorlabs). Typical fingerprint height and spacing are shown with four (spiral) sweat ducts (filled circles) and a drop of sweat (open circle) emerging from a pore on a ridge surface. The sweat ducts are visible within the stratum corneum layer which is relatively dark. The thickness of the stratum corneum is estimated to be approximately 300 mm. This is based on the difference of 400 mm in the optical depth between the light skin surface and the upper boundary of the intermediate light layer, which is the remainder of the epidermis [48, 49] , and using an assumed value of the refractive index for skin of 1.4. The inset photograph shows the same skin region from above, bounded top and bottom by the edges of the OCT contact probe. (Online version in colour.) rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 discussed in addition to the changes in the friction that occur when the sliding velocity is varied. Contact area Friction can be described by the two-term model that assumes an additive decomposition of an adhesion and a deformation term [50] . The deformation component is mainly important for the sliding or rolling of hard lubricated probes on planar softer materials such as elastomers, i.e. polymers at temperatures that are greater than their glass transition value [51, 52] . It arises from mechanical hysteresis (e.g. viscoelasticity) during the deformation of a subsurface region at the front of a contact and the subsequent inelastic recovery. A characteristic of this mechanism is that the velocity sensitivity arises from that of the bulk deformation behaviour of the substrate. However, it has been shown that this contribution is negligible for unlubricated skin on the basis of measurements on the inner forearm [53] . Contact area Invariably the friction of organic polymers in the glassy [54] and also the rubbery states [55] may be described by the adhesion mechanism with the frictional force, F, being given by the following expression: Contact area ð2:1Þ Contact area where t is the interfacial shear strength and A is the real area of contact. The parameter t arises from the energy dissipated by the rupture of intermolecular junctions formed intermittently at the sliding interface and the coupled viscoelastic deformation in a thin subsurface layer adjacent to this interface. For glassy organic polymers t increases linearly with the mean contact pressure, p, thus [56] t ¼ t 0 þ ap; ð2:2Þ where t 0 is the intrinsic value of t at zero contact pressure, a a pressure coefficient and p is given by W/A, where W is the applied normal force. The relationship between the contact area and the normal force for a sphere in contact with a flat surface may be written in the following form: Contact area where the areal load index, m, is unity when at least one of the contacting bodies is surface topographically rough [57] . That is, the real area of contact is linearly proportional to the applied normal load. For a contact between a smooth sphere of radius, R, and a smooth flat solid, with one of the contacting bodies being rigid, equation (2.3) corresponds to the Hertz equation [58] such that m ¼ 2/3: Contact area where E and n are Young's modulus and Poisson's ratio of the deformable body, respectively. The advantage of this form is that it can be applied to a spherically tipped rigid probe and a planar area of skin or to the finger pad and a rigid planar surface. This assumes that the finger pad may be approximated by the cap of an elastic sphere or an elliptical cap with R ¼ (R 0 R 00 ) 1/2 such that R 0 and R 00 are the major and minor radii of curvature. Contact area It is difficult to accurately measure the real area of contact for any system not involving perfectly smooth surfaces except for very compliant materials such as elastomers, for which it is usually assumed that the asperities are compressed to form an intimate interface. In the case of the finger pad, it is common to measure two parameters to characterize the contact area. The gross value, A gross , is defined as the total area contained within the overall contact boundary, including non-contacting regions such as the valleys between the fingerprint ridges. The apparent contact area of the fingerprint ridges, A ridge , ignores the potential influence of any topographical features on the surfaces of the ridges, viz. A gross . A ridge ! A. Skin is complicated by having a layered structure so that the bulk deformation depends mainly on the underlying tissue with a Young's modulus that is considerably less than that of the outermost epidermal layer, viz. the stratum corneum. Thus, it has been found that the indentation of a rigid spherical probe on the forearm may be described by the Hertz equation in a way that is not strongly affected by the hydration behaviour of the skin [59] . However, the contact area for dry skin calculated from the Hertzian form of equation (2.4) would be significantly greater than the real area of contact because of the surface topography. Contact area In the nominal dry state under ambient conditions, the surface layers of stratum corneum behave as a typical glassy organic hydrophilic polymer, e.g. nylon and keratin [53] , provided that there has been no occlusion. A characteristic of such polymers is that invariably the friction increases with the absorption of moisture and, hence, with increasing relative humidity [60] , despite a reduction in the value of t [61] . This is because plasticization by the moisture causes a reduction in Young's modulus. If the configuration involves a smooth sphere sliding on a smooth flat surface, there will be an increase in A that may be calculated using equation (2.4) . In addition, if either of the sliding bodies is surface topographically rough, the softening of the asperities may also lead to an increase in A under an applied normal load since the roughness in the dry state prevents an intimate contact being formed. Contact area The plasticization mechanism leads to an increase in the friction by a factor of two for nylon, from the dry to the saturated wet states [60] , whereas the comparable increase for the inner forearm is about an order of magnitude [53] . The enormous increase for the forearm was attributed to the extreme sensitivity of the elastic modulus of stratum corneum to moisture that leads to a large increase in the contact area due to the flattening of the asperities under an applied normal force. A large increase in the friction in the wet state has also been observed for the finger pad. It was argued that this was associated with an increase in A towards A ridge as a result of fingerprint ridge asperity plasticization [62] . Contact area The elastic modulus of stratum corneum decreases by about three orders of magnitude from the dry to the wet state [63] . This corresponds to a glass-rubber transition since the Young's modulus of stratum corneum in the wet state is comparable with that of an elastomer. Consequently, the tribological properties are similar in terms of the relatively large values of the coefficient of friction compared with glassy organic polymers. Similarly, as described in §4 and §5, also in terms of the initiation of slip and the velocity dependence of the coefficient of friction. Another important similarity is that both materials are hydrophobic; the advancing contact angles with water are about 1008 for both stratum corneum [64, 65] and elastomers [66] . The common use of elastomers as artificial skin materials may be attributed to these similarities with the properties of skin. rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 It has been commonly observed that the coefficient of friction of the finger pad can increase with decreasing normal load for the relatively small normal loads associated with taction. For example, André et al. [67] observed that this was the case for normal loads of less than 3.5 N. It is possible to account for such observations by considering equations (2.1), (2.2) and (2.4), which provide a relationship between the frictional and normal forces: rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 It has been shown that equation (2.5) may be approximated by the following expression [68] : rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 where n is termed the frictional load index and k 2 is a loaddependent coefficient of friction, m, thus rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 For such contacts, it has been shown that 2/3 n 1 [68] but by inspection of equation (2.5) it is evident that this is the case since the friction depends on two terms involving W having indices of 2/3 and unity, with the actual value depending on the relative magnitudes of the coefficients of the two terms. rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 The above approach has been applied to frictional data for the skin of the inner forearm using smooth rigid spherical probes and flooded with water [53] . Since water plasticizes skin, which leads to an intimate contact for such probes, it is reasonable to assume that equation (2.5) for the Hertzian case is then valid. For the inner forearm, the values of t 0 , a, k 2 and n are given in table 1 for both glass and PP probes. The frictional load indices are in the expected range and the values of t 0 are similar for both probes. It was speculated that the smaller value of a for the glass probe could have been associated with a pressure-dependent ultrathin layer of water molecules formed on the glass surface. As has been pointed out, wet stratum corneum is in a rubbery state; however, the load index for elastomers is 2/3 [55] . This suggests that the interfacial shear stress for elastomers is independent of the contact pressure, which has been confirmed by the direct measurement of the distribution of shear stresses for the sliding contact of an elastomer and a rigid spherical probe [69] . The pressure dependence for glassy polymers arises from a free volume mechanism. The transition to the rubbery state causes an increase in the free volume but, because Poisson's ratios of elastomers approach 0.5, they are considered to be incompressible, i.e. the bulk modulus is very much greater than the tensile value. rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 For dry skin, it was observed in the above work on the inner forearm [53] that the load index is unity. Consequently, Amontons' law of friction applies such that the coefficient of friction is independent of the normal force. This is because of the pronounced surface topography of forearm skin that forms an extended multiple asperity contact in the unplasticized state. That the coefficient of friction is a constant equal to (k 1 t 0 þ a) may be shown from equations (2.1) -(2.3) with m ¼ 1. rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 The deformation behaviour of the finger pad is more complex than that of the inner forearm. For compression against a rigid flat plate, Derler et al. [70] found that A gross increased by only a small extent for increasing normal loads greater than 1 N. Similarly, Childs & Henson [71] reported that the transition to an approximately constant value of A gross occurred in the range 1-2 N. A load of about 2 N seems to typically characterize the upper bound of the deformation limit due to the underlying tissue being compressed against the distal phalanx of the finger. That is, at high normal forces a finger pad would behave as an extended multiple asperity contact with m ¼ 1 in equation (2.3) and it would be expected that n ¼ 1 in equation (2.6). Tomlinson et al. [72] found that this was the case, albeit with a small negative intercept on the normal load axis in some cases. In general, such an intercept may be ascribed to the pull-off or adhesive force, W A , by a generalization of equation (2.6) [55] : rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 That is, the adhesive force effectively augments the applied normal force. In practice, it is difficult to distinguish the fit of equation (2.8) with n ¼ 1, W A . 0 and W A ¼ 0, n = 1 unless accurate data are available at small normal loads. This is evident with the data of Tomlinson et al. [72] even at small normal loads, but it is clear that virtually all of their data correspond to a small value of the adhesive force. rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 The relatively large normal force range of greater than 2 N is generally relevant to grip but precision grip and tactile exploration invariably occur at smaller forces. Warman & Ennos [73] measured A ridge and the friction of the finger pad in this smaller force range (0 -1.7 N) as shown in figure 2 ; these measurements were carried out with ink so that it is reasonable to presume that the fingerprint ridges were fully plasticized, i.e. A ridge ¼ A. They found that A ridge increased with the load to a power in the range 0.68-0.95, depending on the finger. The value would be 0.67 on the basis of equation (2.4) if it is assumed that the finger pad approximates to a Hertzian contact and that A ridge scales Table 1 . The interfacial shear strength, t 0 , and the pressure coefficient, a, of wet forearm skin for glass and PP spherical contacts, obtained for the best fits of equation (2.2) to shear strength and pressure data derived from experimental friction force data as a function of normal load using equations (2.1) and (2.4). The power-law parameters k 2 and n are derived from t 0 and a by approximating equation (2.5) using equation (2.6) [53] . linearly with A gross . They also observed that the ratio of A ridge to A gross was approximately 70 per cent. However, in more recent work using an optical method, it was reported that this ratio was about 30 per cent for a normal force of 1 N and that A ridge increased with load according to the Hertz equation but A gross was associated with a smaller index of 0.52 [74] . Despite the approximate applicability of the Hertz equation, Warman & Ennos [73] found that the load indices for different fingers were generally in the range expected from equation (2.5) . Their data for the dynamic frictional force as a function of the normal load are also shown in figure 2 and the deviation from linearity is evident. Like Adams et al. [53] , Warman & Ennos [73] also argued that Wolfram's [75] suggestion that the friction of skin could be described by a pressure independent coefficient of friction is incorrect since it predicts a load index of two-thirds, i.e. equation (2.5) with a ¼ 0. On the basis of their friction data they computed values of t 0 and a that were similar to those obtained for the inner forearm [53] . As mentioned above, a common complicating feature is that if the data are sparse, particularly at small normal forces, or if there are significant errors in the data, it is difficult to distinguish between equations (2.8) and (2.6) in terms of the quality of the fit. Tomlinson et al. [76] argued that this problem applied to some of the published data of the friction of the finger pad. Occlusion Smith & Scott [29] measured the coefficient of friction of a finger pad against a range of surfaces using a repetitive unidirectional stroking procedure. It was found that the values increased with the number of strokes; in one example it increased from 0.36 to 0.79 after seven strokes. They concluded that it was the result of increased sweat secretion, which possibly was triggered mechanically by the stroking action although they stated that physiological evidence was not available to support this contention. Occlusion is an alternative mechanism. The importance of sweat in determining the friction of the finger pad has been observed in a number of studies. Smith et al. [77] described the results of applying scopolamine patches to subjects in order to suppress palmar sweating by blocking the muscarinic receptors of the eccrine sweat glands. On the basis of grip experiments it was found that, for some of the surfaces examined, there was an increase in the peak and static grip forces, which was interpreted as a response to an increase in the slipperiness of the skin. Johansson & Westling [78] carried out precision manipulation studies and observed that the friction of the hand was reduced significantly after washing and drying, which was considered to arise from the removal of accumulated moisture. Occlusion More systematic studies were carried out by André et al. [67] , who reported values of the coefficient of friction measured during grip studies as a function of the moisture content at the skin surface of a finger pad using a device that had been developed previously [79] . The subjects exhibited moisture levels that ranged from dry to very wet and it was found that there was a maximum value of the coefficient of friction at intermediate moisture levels. Subsequently, it was observed that the measured moisture values either increased, remained unchanged or decreased after prolonged contact depending on the inherent wetness exhibited by the subject at the initial contact [80] . They argued that this was evidence for a natural mechanism, which resulted in an optimal moisture content for achieving a maximum friction between the finger pad and an object. An example for one subject is shown in figure 3 . The measured grip forces as a function of the moisture level for all subjects are given in figure 4 . The majority of the trials resulted in moisture values that were in the range required to minimize the grip force by maximizing the coefficient of friction, which corresponded to a moisture level of 7.75 arbitrary units. Moreover, it is clear that the grip force increases for levels of the moisture outside of this optimal range. Occlusion Pasumarty et al. . The corresponding mean values of m 0 are 0.23 and 0.37 and for m 1 they are 3.1 and 3.6. Equation (3.1) was derived on the basis that the coefficient of friction is proportional to the quantity of moisture at the sliding interface and that the excretion of sweat can be described by first-order kinetics. This was consistent with the moisture level measured instrumentally as a function of time, which could also be described by an analogous relationship with a characteristic time of about 16 s. In summary, there is strong evidence that the increase in friction is due to an occlusive mechanism in which the rate of sweat excretion is not influenced by sliding. This is because there was not a systematic trend in the characteristic times associated with the coefficients of friction when the sliding velocities were varied. Moreover, similar data were obtained when a finger pad was held statically in contact for various time periods before measuring the friction. It is possible that there is some active mechanism of sweat secretion associated with the contact pressure, which may also have some neurophysiological basis, but experimental evidence does not currently exist to support this contention. Occlusion The above work shows that the coefficient of friction of a finger pad in an occluded contact increases by about an order of magnitude over tens of seconds. The increase is comparable to that observed for the inner forearm when water is introduced in the contact region [53] . The latter work was carried out using spherical probes with sliding distances of many contact diameters so that it was not possible to determine the influence of occlusion in the dry state. It is reasonable to assume that the plasticization mechanism for the wet state also applies in the case of the finger pad in the occluded state. When a contact in the forearm study was allowed to dry from the wet state, it was found that the coefficient of friction increased to a maximum value before decreasing to that for the dry state [53] . When excess water was added to a fully occluded finger pad contact, the coefficient of friction was reduced by a factor of about 3, as shown in figure 6 [62] . This is analogous to the results reported by André et al. [80] , who showed that the coefficient of friction decreased when the moisture level was greater than the optimal value as described above. Similar data have been reported by Tomlinson et al. [81] , who also observed a maximum in the coefficient of friction for intermediate levels of moisture in the contact region. Occlusion Thus, the fully occluded state for a finger pad must correspond approximately to the maximum possible coefficient of friction, although the actual value will depend on the subject. This suggests that there is some mechanism that limits the maximum accumulated level of moisture in the contact region to a value that is less than in the wet state. The simplest mechanism could involve the hydrostatic pressure developed in the sweat pores being effectively blocked figure 3 , which is for one of the subjects. The line is the best fit to the data and exhibits a minimum at approximately 7.75 arbitrary units corresponding to the optimal moisture level for grip. Adapted from André et al. [80] . Occlusion rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 Occlusion by contact with the countersurface. Evaporation and twodimensional Darcy flow of water vapour through the valleys of the fingerprint ridges could also contribute. Finally, it is possible that excess moisture could be deposited on the counter body by leakage flows. This is known to occur for elastomers/glass contacts under certain conditions; the residual films with thicknesses of less than 600 nm were not visible to the naked eye [82] . Occlusion Since the coefficient of friction of the finger pad in the fully occluded state is comparable to the maximum value observed when forearm skin is allowed to dry, it suggests that the mechanism involved is similar. Adams et al. [53] argued that the behaviour of the forearm is analogous to that of nylon in a sphere/flat configuration, which also shows such a maximum in the friction [83] . Nylon is plasticized by moisture so that the steady-state friction in the wet state is greater than that in the dry state since the real area of contact increases more than the interfacial shear stress is reduced as discussed in §2. When the surface of nylon was allowed to dry, there was an initial further increase in the friction because the interfacial shear strength increased while the contact area was unchanged. The contact area is controlled by the deformation characteristics of a subsurface region with a length scale of the order of the contact radius while the corresponding length scale for the interfacial shear strength is of the order of nm. Thus, the diffusion time associated with drying will be much shorter for the interfacial layer, which results in the initial increase in the interfacial shear strength without a significant reduction in the real area of contact. Both forearm and finger pad skin are somewhat different since the thickness of the stratum corneum may be less than the nominal contact radius and it is topographically much rougher than the nylon studied. Consequently, it was argued by Adams et al. [53] that the increase in contact area arose from the plasticization of the surface asperities, which also have a length scale that is large compared with that governing the interfacial shear strength. Occlusion It has also been proposed that the increase of the friction in the presence of moisture is due to capillary forces [33] . It was explained in §2 that the friction depends on the sum of the applied and adhesive forces (see equation (2.8) ). The capillary forces arise from the surface tension and the reduced Laplace pressure in a liquid junction having a concave meniscus [84] . For poorly wetted surfaces, such as skin, the large contact angle may result in a convex meniscus with the Laplace pressure being positive so that this component of the capillary forces could be repulsive. For some systems not involving skin, it has been shown that the capillary forces can make a major contribution to the measured friction [85] . However, this is only the case if they are of a similar order to the applied normal forces. The adhesive force for wet forearm skin, which was measured using a rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 spherical steel probe of radius 6.35 mm in direct pull-off experiments, is only about 5 mN [86] , which is a small fraction of the normal forces that are typically applied in tactile exploration. Correspondingly small values were also obtained by extrapolation of the measured frictional force to a zero applied force [53] . However, these data were for a dry forearm and consequently any adhesion could only arise from molecular interactions rather than capillary forces. Tomlinson et al. [81] recently analysed friction data for the finger pad following immersion in water and could not unequivocally estimate the role of capillary bridges. Their analysis was based on a model developed by Persson [87] for a hard rough surface in contact with a more deformable body, who considered individual asperity contacts with condensed liquid bridges. Thus, currently, there is not evidence to support the contention that the capillary forces are a significant factor in increasing the friction of skin except possibly at small applied normal forces. Occlusion The smaller value of the friction of forearm skin in the wet state compared with the partially dried or damp state was attributed by Adams et al. [53] to the formation of a boundary film of water on the counter body. This was again based on the study of nylon friction by Cohen & Tabor [83] , who showed that the friction in the wet state was increased by initially subjecting the contact to a normal force for an extended period, which would be consistent with disrupting a bound water film. More recently, the formation of water films has been measured directly in elastomer/glass contacts by Deleau et al. [82] and, as discussed in §2, elastomers are a useful model material for moisture plasticized skin. At low sliding velocities (less than 10 mm s 21 ), it was found that water caused a reduction in the friction by about a factor of two. The surface mean roughness of the elastomer was 1 mm and the contact area of the asperities was unaffected by the presence of water; the reduction in friction was considered to arise from an attenuation of the autoadhesion. It is well established that such interactions are attenuated by wetting [85] and they were large for the elastomer studied by Deleau et al. [82] compared with skin. Elastomers are also different from skin because they are not plasticized by water and hence the friction does not increase in the wet state. However, these results show that sliding can operate in a boundary regime (i.e. a solid -solid interaction regime where the term 'solid' may include a thin molecular layer of bound water molecules) at low sliding velocities; this is important in the context of the velocity dependence of the friction (see §5). More importantly, in the current context, this may provide an alternative explanation for the reduction in skin friction in the wet compared with the fully occluded or damp states. That the adhesive forces for skin are small in terms of the pull-off values is common for topographically rough surfaces because the stored elastic strains in the asperities effectively act to create elastic repulsive forces [88] . However, adhesive interactions must operate when the asperities are deformed under an applied normal force in order to account for the friction. It is possible that these interfacial shear interactions are attenuated by the presence of moisture, which could also be the case for the elastomer/ glass contacts since the contact area was unaffected by the presence of water. This will be discussed further in §5 where a fracture mechanics treatment is considered. Adhesive pull-off involves mode I fracture (tensile crack propagation), whereas sliding involves mixed-mode II and III fracture corresponding to a combination of in-plane and out-ofplane shear fracture [89] . Occlusion Skedung et al. [90] observed that the friction of paper decreases as a function of sliding time as shown in figure 7 . It was ascribed to the deposition of a lubricating layer of lipid from the surface of the skin although Gee et al. [91] had proposed that similar data could be explained by the absorption in the paper of secreted sweat. This is consistent with the data being described by equation (3.1) ; the best fit is also shown in figure 7. Paper is an example of a rough surface and Skedung et al. [90] found that the friction decreased with increasing surface roughness as shown in figure 8 . Pasumarty et al. [62] measured the influence of occlusion on the friction of rough glass and reported that the steady-state value of the coefficient of friction decreased to approximately one-third of that for smooth glass. This is a result of the smaller real area of contact for the rough compared with the smooth glass. Dinç et al. [33] found that the friction of the finger pad decreases with increasing roughness of the countersurface but they believed that this was due to a rsif.royalsocietypublishing.org J R Soc Interface 10: 20120467 reduction in the capillary forces. It is an unlikely explanation since the normal forces were in the range 0.1-20 N, which is very much greater than those arising by a capillary mechanism as discussed above. In summary, the occlusive frictional behaviour of paper could arise from a combination of competing factors possibly involving the permeability and topography of the paper, and lubrication by moisture and lipids. The behaviour of porous surfaces is in marked contrast to those that are impermeable and will contribute to the considerable different feel and grip of materials such as paper and glass. However, permeable surfaces tend not to be smooth so that any comparisons would have to account for any differences in surface topography. Evolution of slip in the contact region The evolution of slip is extremely important in both tactile perception and grip (see §1). In particular, it has been shown that increments in the grip force when holding an object stationary against gravity are triggered by incipient slips [5] . For small tangential stresses, relative slip does not occur and the effectiveness of the human mechanoreceptor tactile system to estimate the magnitude and direction of such stresses has been demonstrated in a number of studies [92 -94] . At some critical tangential stress, Westling & Johansson [40] first reported that localized slip occurred at the periphery of the contact zone before the onset for sustained sliding. André et al. [95] employed an optical technique to measure the contact region of a finger pad in the static state and with increasing tangential force for normal loads of approximately 0.5 and 5 N, which is particularly relevant to tactile exploration and grip, respectively. Some typical images are shown in figure 9 . As the tangential force, F, is increased, the stick area in the centre of contact region gradually decreases in size until gross sliding occurs when F ¼ mW. The data are shown in figure 10 in terms of the stick ratio, w, as a function of the tangential force where w ¼ C/A gross and C is the gross contact area in the no slip region. It was observed that A gross is approximately independent of F, although in some cases there was a small reduction when the contact was first loaded tangentially. Similar trends were reported by Tada et al. [96] . In addition, Terekhov & Hayward [97] showed that, frequently, the decreasing stick area apparently vanished at some critical tangential load rather than
{'paper_id': '17226967', 'title': 'Finger pad friction and its role in grip and touch', 's2_url': 'https://api.semanticscholar.org/CorpusID:17226967', 'source': 'S2ORC'}