RECENT DEVELOPMENTS IN SURFACE PHYSICS OF INTEREST TO COSMETIC SCIENCE Bv ANTHONY M. Scuw^•rz and Cu^•I•WS A. RADE• Presented November 2o ø , 1961, New York City THE two topics to be discussed in this paper have a mutual meeting ground in the application of cleansing materials and other topical treat- ments to skin and hair. The first is a novel approach to the problems of capillarity, and especially to the flow of two-phase liquid systems in capillary channels or networks. This has been worked out extensively in our own laboratory over the past several years as part of a fundamental study of the migration of liquids in fabrics. The second topic concerns some new but well-evidenced theories on the interaction of surfactant solutions with oils and oily solid surfaces. These have been developed in England and have been presented in most explicit form by Lawrence and by Stevenson (1, 2). Capillarity is the term applied to the motion of a liquid that is caused primarily by the surface forces of the liquid and of the solid with which it is in contact, rather than by externally applied pressures or by gravity. More specifically, it applies to movements of the three-phase liquid-solid- air boundary line over the solid surface. The rise of a liquid in a narrow tube and the wicking of a liquid through a mass of fibers such as paper or fabric or hair are familiar examples of capillarity. So is the spreading of a small droplet of liquid along a smooth surface which it wets or in the grooves of a wrinkled surface. In any situation where the mass of liquid is small compared to the areas of the phase interfaces, capillarity becomes the factor determining the liquid motion. The classical laws of capillarity are based on two concepts, each of which is associated with a familiar experimental construct. The first concept is that of surface tension or surface-free energy, which is a measure of the tendency of the interface to contract or minimize its area. A completely fluid interface can minimize its area by changing its shape, and when free will assume the shape of minimum surface-to-mass ratio, a sphere or spherical zone. The solid-liquid or solid-air interfaces can only change area if the liquid flows to cover more or less of the solid surface, leaving less * Harris Research I.aboratories, Washington 11, D.C. 245

246 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS or more in contact with air. The fundamental relationship of the three surface tensions at the liquid-solid-air (L-S-A) boundary are given by Young's equation: '•sA = '•sL -+- '•LA cos 0 (1) where 0 is the equilibrium contact angle, and the gammas are the interfacial free energies or surface tensions. The subscripts SAt, $L and LAt refer to the solid-air, solid-liquid and liquid-air interfaces, respectively. The second fundamental concept is that of capillary pressure, i.e., that the hydrostatic pressure on the concave side of a curved liquid-air or liquid- liquid interface is greater than the pressure on the convex side. The pres- sure difference (P• - P2) is given by Laplace's equation P•- P,=• (• + •..,) (2) where R• and R2 are the two principal radii of curvature of the surface. This is the equation that has until recently been the only one available to calculate the driving forces in capillary motion. In applying the Laplace equation it is necessary to determine the shape of the liquid front very precisely and describe it in terms of R• and R2. This is not difficult in a cylindrical tube, where a measurement of the contact angle (and a knowl- edge that the liquid-air surface must be spherical) immediately gives the total curvature. In a practical system, however, for example a liquid wicking in a yarn or even a column of liquid moving between two parallel rods, the liquid front usually has too complex a curvature to measure or calculate. We have found that this problem can be effectively solved by using the equation: d dF _ d (Area I_.4).T•.• q- ds (Area SL). (Ts• - •/SA) (3) ds ds where F is the free energy of the total system and s is forward distance moved by the liquid front along the solid surface. This equation can be derived by straightforward thermodynamic meth- ods (3). From the geometrical shape of the system we calculate the change in the liquid-air area and the liquid-solid area as the liquid front moves forward a unit distance. These area changes, multiplied by the respective free energy values per unit area, give the total free energy change per unit advance of the liquid front. This quantity, reduced to a differential in the usual manner, is identical with the force moving the liquid front forward. The free energy of the liquid-air interface is simply the surface tension. To get the free energy change associated with the covering of solid surface by liquid (7sL -- 7SA), we apply Young's equation 1 and find that it is equal to --"YLA COS 0