J. Chem. SOC., Faraday Trans. I , 1989, 85(11), 3853-3860

Droplet Formation and Contact Angles of Liquids on Mammalian Hair Fibres

Brendan Joseph Carroll Unilever Research Laboratory, Quarry Road East, Bebington, Merseyside, L63 3J W

The wetting by a liquid drop of a model mammalian hair fibre is compared with that of a smooth cylindrical fibre. (B. J . Carroll, J. Colloid Interface Sci., 1976,57,488). The model considered has a series of axially symmetrical serrations regularly spaced along the fibre length and these are shown to play an important role in the wetting behaviour of the system, principally through their ability to act as points of ‘hingeing’ for the three-phase contact lines at the two ends of the liquid drop. It is shown that the apparent contact angles in the system can in certain cases be related to the true contact angle and to the geometry of the fibre asperities. It should thus be possible to estimate empirically the true system contact angle and experimental results are presented in support of this conclusion.

The contact angle of a liquid on a solid provides a basis for the study of interactions between the two phases. Changes in this angle reflect changes in net interactions across interfaces and so also of composition close to interfaces. The accurate measurement of contact angles is therefore important.

The contact angle is most readily determined when the solid is available in the form of a smooth, flat plate when several methods can be used.’ When, as is often the case with textile materials, the solid is only available in fibrous form, techniques still exist which are reliable when the fibre has a smooth surface. These include the wetting balance,2 drop-~n-f ibre ,~ tilted fibre4 and reflected beam5 techniques. When, however, the fibre surface is irregular, the results obtained by these methods require careful interpretation.6,7 In what follows, the case of mammalian hair is considered. The expected wetting behaviour of such fibres is discussed in terms of a recently proposed model for the human hair and particular emphasis is placed on the application on the drop-on-fibre techniques to these systems. The drop-on-fibre technique has the advantage over the other techniques mentioned in that no unusual apparatus is required to make the measurement and it is furthermore capable (which the other techniques are not) of being applied to any fibre in situ, e.g. on a growing hair. The application of the wetting balance technique to such systems has already been discussed by

Theoretical The Drop-on-fibre Technique

When a liquid drop is placed on a fibre it will, provided that the contact angle is not too high, assume the conformation of which the profile is given in fig. 1 . The drop-on-fibre technique3 uses two dimensionless combinations of the three parameters x,, x, and L (fig. 1) to obtain the contact angle 9 = F(x, /x , , Llx , ) = F(n, E), using theoretically derived tabulations of the function F. The three parameters are conveniently obtained by direct measurements on a photomicrograph of the system.

When a liquid drop is placed on a mammalian hair fibre on which it has a sufficiently low contact angle, it adopts a conformation superficially the same as that in fig. 1, in that it is approximately symmetrical about the fibre axis and also about the meridonal plane

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3854 Liquids on Mammalian Hair Fibres

I I \

I I Y L M

- n = x 2 / x , 1 = L / x ,

Fig. 1. Parameters for the drop-on-fibre cylinder system.

I- CQ. 7 0 ~ m ----------ti

Fig. 2. Model for human hair fibre [ref. (12)].

through the drop which passes perpendicularly through the fibre axis (cf. plate 2, later). The apparent angles of contact at the two ends of the drop are thus approximately the same. However, it will be obvious from the discussion which follows that the apparent angle is not the true contact angle for the system. It will be shown, nevertheless, that this apparent and the true contact angle are related under certain conditions.

Model for the Animal Hair-Liquid System The model recently proposed for the human (head) hair fibre by Swift is taken.12 This is given in fig. 2. On this model, the cuticular scales which form the outer layer of the hair are symmetrical about the fibre axis. The fibre has the form of a stack of conical frustra, each frustrum having a height of ca. 5 pm, a radius (the fibre radius) of ca. 35 pm and a semi-angle of ca. 5". Seen in profile, the fibre appears to have a serrated edge, like a saw. This model is, of course, an idealisation. In all actual cases the scaley cuticle shows irregular edges and for non-human fibres (the various types of wool), the structure

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B. J . Carroll 3855

Fig. 3. Drop on model fibre, with both ends in contact with curved surfaces of cuticle.

apparent . . A

aLg le X Y z = e e~ x y z g go+ e = e

edge included angle = 90’

Fig. 4. The effect of a sharp edge on possible orientations of a liquid meniscus and a solid (a) before the edge, (b) at the edge (‘hingeing’) and (c) after the edge.

of the cuticular layer may be much less ordered than is suggested in fig. 2. The model is, however, quite closely approached by freshly emergent human hair; those undamaged specimens of this fibre which are found close to the scalp. Such specimens are completely enveloped by a thin layer of a highly cross-linked protein, which is known as the A layer.12 In the model adopted, it is assumed that this layer makes the whole of the hair fibre surface compositionally uniform, even though it is found in practice that the A layer is readily broken by mechanical means (e .g . by combing), especially towards the base end of the cuticular frustrum.

Wetting Properties of the Model This model has two noteworthy features. First, the curved surfaces of the cuticular frustra (scales) are inclined at an angle to the fibre axis. (These frustra have a semi-angle a of ca. 5”.) Thus, an axially symmetrical liquid meniscus making a true angle of contact 0 with the curved surface is, at the point of contact, inclined to the fibre axis at an angle of either (0+a) or (0-a) depending upon the orientation of the liquid meniscus with respect to the fibre axis (fig. 3) . It is therefore not possible for a liquid drop to have both ends equally inclined to the fibre axis when both are in contact with the curved surfaces of the cuticle, Since it is observed experimentally that the two ends of the drop do, in fact, tend to have similar angles of inclination to the fibre axis, it follows that a conformation such as has just been described is not at equilibrium.

The second feature is the existence of a series of axially symmetrical, more or less sharp edges (serrations) spaced along the length of the fibre. These correspond to the external ends of the cuticular scales of the real hair fibre. The presence of these edges profoundly influences the behaviour of the liquid drop on the fibre and is the key to understanding how at equilibrium the two ends of a drop tend to be equally inclined to the fibre. This is because any sharp edge has the ability to act as a ‘hinge’ for a liquid meniscus in contact with it. That is, the meniscus XYZ (fig. 4), instead of being

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3856 Liquids on Mammalian Hair Fibres

Fig. 5. Hingeing of the menisci at the two ends of the drop in contact with the fibre.

constrained to lie at an angle 0 to the solid (as it is when far away from the edge), may adopt any orientation in the range 8 up to (180-/3+0) while still satisfying microscopically the condition that the solid-liquid contact angle is 8. Thus, the sharper the edge (i.e. the lower the value of /?), the wider is the range of angles through which the liquid meniscus can ‘hinge’ whilst not (macroscopically) changing its point of contact. This phenomenon is discussed in more detail by Bayramli and Mason13 and by Oliver et al.14

In the present case, the description of the hingeing effect depends upon which end of the drop is being considered. Referring to fig. 5, at the left-hand end of the drop, the angle of the meniscus with the fibre axis may vary between (0-u) and (0+90). At the other end of the fibre, the range is formally from (90 - 8) up to (0 +a), although for the present case the lower limit is, in fact, zero. This asymmetry in behaviour at the two ends of the drop is important because of its role in determining stable conformations of a drop freshly placed upon the fibre, as is referred to again later.

The Approach to a Stable Conformation When a liquid drop is placed at random on the fibre, there is in general a tendency for it to move in a direction parallel to the fibre axis until it attains a stable conformation. This movement occurs as a result of differences in the local angle of contact of the liquid with the surface and on the fibre radius at the ends of the nascent drop which together, by their influence on the local drop shape, affect the local value of the Laplace excess Dressure :

AP = y(net curvature) = y -+- ($, d,) where y is the interfacial tension and R, and R, are orthogonal radii of curvature of the meniscus. A pressure gradient along the drop length is thus established which induces liquid flow and hence bodily movement of the drop.

This situation can be discussed more quantitatively using the results established for a drop on a smooth fibre. It was shown3 that the excess pressure inside such a drop is:

where n has already been defined (fig. 1). This expression follows from the requirement that the excess pressure over all of the drop’s surface is constant (n and 0 constant). It is reasonable to expect that in the case of the nascent drop, this condition applies locally in the region of the two three-phase contact lines, but that the constant value is different at the two ends. The expression (3) can then be applied to each end separately to evaluate the effect of changes in n (caused by changes in the fibre radius) and 0 (in the present

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B. J . CarroII 3857

$ = 8-a + = 8 + a

Fig. 6. Possible equilibrium conformations of a drop on the fibre. (A third possibility involves contact of both ends with hingeing edges.)

case, the angle made by a meniscus with a fibre axis). Note, however, that the effects of these changes must be evaluated at constant drop volume : differentiation of eqn (3) with respect to n (at constant 8) or 8 (at constant n) does not give the correct behaviour. Instead, the use of numerical tables giving the reduced excess pressure AF = APx, /y and the reduced drop volume v = V / x I 3 as a function of n and 8 is necessary. These have been calculated from the theory in ref. (3) and are available from the author. Using these tables, the way in which AP varies at constant volume when either n or 8 is varied can be readily ascertained.

The variations of n and 8 likely to be encountered in the present system are 6n = n(6xl /x , ) z 0.01 n and 68 z 10". The value of 6n is a maximum, based on a change in x, of one cuticular scale's thickness (0.5 pm): usually, it will be considerably lower. Inspection of the tables then shows that for all values of n the change in AP due to 6n is always outweighed by that due to 68. It is thus reasonable in the present case to consider only changes due to the latter. When this is done, the result is that the pressure gradient is always from the right to the left end of the fibre in fig. 5, that is, motion of the nascent drop tends always to be from left to right in this diagram. The drop thus tends to climb up the hair scales.

Stable Conformations

Motion of the drop along the length of the fibre means that one end or the other soon encounters a cuticular scale edge. It has been shown how, when this happens, the angle made by the liquid meniscus with the fibre axis can hinge through a range of values. Provided that the only significant contribution to the pressure gradient along the drop comes from the disparity between the angles of contact at the two ends, the drop motion will cease when the effect of this hingeing is to equalise the two angles. Inspection of fig. 6, in which the two possible cases are presented, shows that this equalisation always happens. A conformation in which one of the drop ends is in contact with the edge of a cuticular scale will thus be a stable one.

As fig. 6 shows, two distinct equilibrium conformations are possible, characterised, respectively, by making angles q5 = (e+a) or (8-a) with the fibre axis. Provided that a is fairly small with respect to 8, the two states will not have very different free energies and which one is the more favoured will depend upon the mode of formation of the drop on the fibre. So far, it has been assumed that a single 'equilibrium' contact angle 8 is obtained immediately between the drop end menisci and the cuticular scale which is away from the edge; i.e. that there is no hysteresis. If the cuticle surface is heterogeneous or rough, this will not be the case and the angle 8 will assume different advancing and receding values OA and OR, depending upon the direction of movement of the three-phase contact line. When, as is frequently the case, droplets are formed via the dis- proportionation of a coating film of the liquid, the receding angle 8, is relevant; when

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3858 Liquids on Mammalian Hair Fibres

the drop is placed directly on the fibre, the advancing angle 8, is involved. The likely behaviour when a drop is formed on the fibre by the respective techniques is readily seen. When both ends of the drop are receding along the fibre surface (that is, are approaching one another), then, referring to fig. 6 once more and replacing S by 8, or S,, the first stable conformation to be reached will involve hingeing at the left-hand end of the drop, the menisci at both ends being at an angle q5 = (8, - a) with the fibre axis. When the drop menisci are both advancing, on the other hand, the first stable conformation involves hingeing at the opposite (right-hand) end, with the menisci angles with the fibre axis now being (8, + a). One result of this is that the apparent advancing and receding angles in the present systems will differ by (8, - eR + 2a), rather than simply by (0, - S,), as would be the case in the absence of cuticle edges.

Contact Angle Measurement It can be seen from the foregoing that when a drop reaches static equilibrium, it is usually because one of its ends is ‘hingeing’. The apparent angle of contact (that is, the angle made with the fibre axis by the liquid meniscus at the three-phase contact line) is approximately the same at both ends of the drop and has a value of (0 fa), determined by the mode of drop formation (fig. 6). There exists also the possibility that both ends hinge. The likelihood of this will increase with decreasing cuticular scale length and with increasing vibration level. When this does occur, the two angles will still be equal, but will not have a predictable value if the vibration level is such that considerable movement of the drop ends becomes possible. If vibration levels are sufficiently low, the apparent angles will depend upon the wetting history, just as in the case where only one end of the drop hinges.

It is therefore possible, if the history of the drop’s formation is known, to estimate the true contact angle 8, given prior knowledge of the angle of scale inclination, a. The apparent contact angle is found by the usual drop-on-fibre analysis (the macroscopic drop shape is, of course, determined by the apparent, not the true contact angle). The true contact angle for the system follows at once.

Experimental Electron Micrography

Electron microscopy of the present systems is made difficult by the fact that the liquid drops volatilise under the high vacuum conditions the technique demands. However, Robinson,15 using a modified SEM technique in which the sample environmental vapour pressure was controllable, obtained photographs of oil droplets on wool fibres which clearly show that one end of the drop is hingeing at a cuticular scale edge, whilst the other is not (plate 1). The conformation is that expected for a drop formed by a receding meniscus technique but no details of the technique used to deposit the drop are given in ref. (15).

Receding Angles by Drop-on-fibre Technique

A partial check on the accuracy of the foregoing is provided by measuring the apparent contact angle as a function of surfactant concentration in a suitable system, when it is expected that the contact angle should vary smoothly and in a theoretically reasonable way. To this end, apparent contact angles have been measured, using the drop-on-fibre technique, in the system : human hair-squalane + cholesterol-water. The concentration of cholesterol in the oil was varied in the range (0-1.4) x mol dm-3 (the solubility limit) at 25 “C. The hair (the same section of a single fibre was used throughout) was from a switch of virgin Italian hair and was washed in ethanol vapour between runs. Drops

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J . Chem. SOC., Faraday Trans. I , 1989, Vol. 85, part I I

Plate 1. Oil on wool fibre under the SEM [ref. (15)].

Plate 2. Squalane-cholesterol drop on human hair in water.

B. J. Carroll

Plate 1

(Facing p . 3858)

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B. J. Carroll 3859

0

0

O O

0 0

0 ~

0 5 10 15 cholesterol concentration/ I 0-6 mol dm-3

Fig. 7. Contact angles in the system squalane-cholesterol/water/hair at 25 "C.

were formed in such a way that receding menisci were involved in all cases. A typical photograph is shown in plate 2. Apparent contact angles were calculated in the usual way.3

The results are given in fig. 7. The apparent contact angle decreases smoothly with the cholesterol concentration from a value of 75" at zero concentration to one of ca. 8" at the solubility limit. If the tilt angle a is taken to be 5", then the true contact angle must be varying from 80" down to ca. 13". Although no quantitative predictions can be made as to the expected variation, the sign of the variation is consistent with a picture of cholesterol adsorbing at the oil/water and (perhaps) at the oil/hair, but not at the water/hair, interfaces. This is reasonable, given that cholesterol is highly insoluble in water.

Conclusions A theoretical description has been given of the behaviour of a liquid droplet placed on a cylinder which has a series of axially symmetrical serrations along its length. Droplets are not in general stable with respect to lateral movement along the fibre unless one end is in contact with the edge of one of the serrations. There are then two (out of possibly three) stable conformations, which are characterised by (different) definite apparent angles of contact, the difference between the angles being determined by the serration geometry. When there is also a difference in the receding and advancing contact angles for the system, the two conformations just considered tend to be associated one with the receding process and one with the advancing. When (as is true for the case of human hair) the perturbations in the local Laplace excess pressure are due more to variation in the local apparent contact angle than to variations in the local fibre diameter, the two ends of the drop tend to assume equal apparent contact angles with the fibre axis and the drop shape is similar to that found for smooth fibres. The drop-on-fibre technique can then be used to establish true contact angles from knowledge of the measured (apparent) angles and of the geometry of the surface serrations on the fibre.

Experimental evidence in support of these theoretical conclusions has been adduced from SEM work14 and from a study of a system in which the contact angle could be varied in a predictable way. The results are in agreement with expectation.

Implications

A number of assumptions have been made in formulating the model system. The hair fibre is assumed to be of circular cross-section and to be straight, while the scales are

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3860 Liquids on Mammalian Hair Fibres

taken to be axially symmetrical and to be regularly spaced along the fibre length. The scale thickness is also regarded as being much smaller than the fibre diameter.

Human hair comes close to these criteria in many respects, more so than most of the mammalian wool fibres. The latter tend to have less regular scale patterns and to be convoluted in structure. Freshly emergent human hair tends to be roughly circular in cross-section and to have a fairly regularly spaced scale structure. If of Caucasian origin, it will usually be reasonably straight.

There is, therefore, scope for the technique which has been outlined to be applied to the study of contact angles on human hair. The inherent variations in the substrate fibre's fine structure possibly means that the contact angles so measured may not be regarded as absolute values, but rather should be used in a relative way whenever possible. Nevertheless, it would be of considerable interest to compare the contact angles so obtained with values which can sometimes be obtained from wetting balance techniques.*-'' In this way it might be possible to establish a likely range of variation of a particular measurement.

The author is grateful to Dr J. A. Swift of this laboratory for discussions on the structure of hair and its electron microscopy and for permission to reproduce fig. 2. Dr F. X. Carion Fite (Polytechnic University of Catalonia, Spain) is also thanked for discussions of his work on wool fibres.

References 1 A. W. Neumann and R. J. Good in Surface and Colloid Science, ed. R. J. Good and R. R. Stromberg

2 See e.g. H. L. Rossano, W. Gerbacia, M. E. Feinstein and J. W. Swaine, J . Colloid Interface Sci., 1971,

3 B. J. Carroll, J . Colloid Interface Sci., 1976, 57, 488. 4 T. H. Grindstaff, Text. Res. J . , 1969, 39, 958. 5 W. C. Jones and M. C. Porter, J . Colloid Interface Sci., 1967, 24, 1 . 6 K. Bayramli, T. G. M. van de Ven and S. G. Mason, Can. J . Chem., 1981, 59, 1954. 7 K. Bayramli and S. G. Mason, Can. J . Chem., 1981, 59, 1962. 8 Y . K. Kamath, C. J. Dansizer and H. D. Weigmann, J . Appl. Polym. Sci., 1978, 22, 2295. 9 Y. K. Kamath, C. J. Dansizer and H. D. Weigmann, J . Appl. Polym. Sci., 1984, 29, 101 1 .

(Plenum Press, New York, 1979), vol. 11, chap. 2.

36, 298.

10 Y . K. Kamath, C. J. Dansizer and H. D. Weigmann, J . Appl. Polym. Sci., 1984, 30, 925. 1 1 Y. K. Kamath, C. J. Dansizer and H. D. Weigmann, J . Appl. Polym. Sci., 1985, 30, 937. 12 J. A. Swift, in Hair Research, ed. C . E. Orfanos, W. Montague and G. Stuttgen (Springer-Verlag,

13 E. Bayramli and S. G. Mason, J. Colloid Interface Sci., 1977, 66, 200. 14 J. F. Oliver, C. Huh and S. G. Mason, J . Colloid Interface Sci., 1977, 59, 568. 15 V. N . Robinson, Proc. Elec. Micros. Symp., ed. Johani, Illinois Inst. Tech. Res. Inst., 1976, 1, 91.

Berlin Heidelberg, 198 1).

Paper 9/01263J; Received 23rd March, 1989

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