626 M. Stockdale where J = water transfer rate (TEWL) (mg cm -•' h -x) Di = diffusion constant at point i (cm a h -x) Ci = water activity at point i (mg cm -a) x = distance from the edge of the stratum corneum (cm) Scheuplein and Blank (7) have shown that the water diffusion coefficient of the stratum corneum is the dominant factor in determining the permeability of whole skin and thus the great majority of the water activity differential across the skin will take place across the stratum corneum. For the purpose of this discussion, it will be assumed that any other water activity differential is negligible in comparison. The definition of Ci needs further amplification. The concentration of water vapour in air in equilibrium with the water at point i is a useful concept, but since the diffusion process in vivo is generally non-isothermal, it is necessary to define Cx, in relation to a standard state. This is normally saturated vapour at the temperature of point i. The following definition of Ci will be used in this correlation, 4.39 x 10 -a x R.H.i Ci = (mg cm -a) 100 where R.H.i = relative humidity in air, at the temperature of point i, which would be in equilibrium with the water at point i. (4.39 x 10 -a mg cm -a is the saturated water vapour concentration at body temperature (8), i.e. Cint,rna•). Several investigators have reported values of TEWL at different external relative humidities, either in vivo (9-11), or in vitro (4, 12). Diffusion coefficients are obtainable from these reports. (This requires an assumption to be made about stratum corneum thickness, but since the values used finally are relative to a standard state, the accuracy of that assumption does not affect the correlation.) These diffusion coefficients can then be plotted against the average water activity of the stratum corneum samples. In all cases the internal relative humidity was approxi- mately 100•o. If the initial assumption is made that the water activity profile is close to linearity, the average water activity is derived from the average of the internal and external humidities (a correction for the non-linearity of the water activity profile will be applied later). C = 4.39 x 10-a(R.H.interna! q-R.H.ext•rn• ) (mg cm -a) 200 In addition, E1-Shimi and Princen (13) have determined diffusion coefficients at different humidities from kinetic sorption, desorption experiments. In these the relative humidity was the same on both sides of the stratum corneum samples, and thus 4.39 x 10 -a x R.H. Ci = 100 (mg cm -a) The data from the above references were obtained using different sources of stratum corneum and under different experimental conditions. In order to attempt a correlation, it is necessary to convert the results to relative diffusion coefficients (relative to a standard water activity state). The reference state chosen for convenience was the common experimental conditions of R.H.interna! • 100•o, R.H.ext,rnal = 0•o (i.e. C= 0.5 x 4.39 x 10 -a mg cm-a). The diffusion coefficient for this condition is denoted by Do.

Water diffusion coefficients and activity 627 Jt where D -- AC D R = relative diffusion coefficient = m Do hC • Cinternal-- Cexternal t = stratum corneum thickness (cm), assumed to be 15 x 10 4 cm, a typical value for human stratum corneum (14) Cintcrna• = C o = 4'39 X 10 -3 mg cm -a CORRELATION The data used in the correlation is given in Table L It was found that there was generally a linear relationship between D and Col(Co - C). In those cases where the data does not include a value for Do, this was obtained by extrapolation of D against Col(Co - C) using linear regression. The extrapolated value of Do was then used to obtain values of R. Table I. Water activity of stratum corneum versus water diffusion coefficients from literature sources Source R.H.ex•mal C x l0 s Co D x 10 * (Reference) (•) (mg cm 4) Co-C (cm * h -•) R 12 0 2.195 2.00 28'5 1.00 29 2.83 2-81 31.2 1'09 55 3 '40 4'43 43 '7 1 '53 80 3.95 9.98 91.2 3'20 88 4.13 16.88 125.0 4'39 15 2.52 2.34 12.5 1.02 31 2.88 2'91 13-4 1-09 51 3'31 4'07 16.05 1'31 75 3'84 7'94 25.95 2'11 89 4-15 18-20 43'5 3'55 1.5 2.23 2-04 17'3 26 2'77 2'69 20-25 28 2.81 2'75 19'95 28 2'81 2'75 20'4 32 2-90 2'94 22'05 33 2.92 2'99 19'95 33 2'92 2'99 21 '9 34 2'94 3-03 22'8 45 3'18 3'64 23'55 49 3'27 3'92 25'5 53 3'36 4'26 29'85 56 3'42 4'55 27-15 59 3'49 4'88 32'55 2.6 2'25 2'05 12'6 25-0 2'74 2-67 26'4 49-0 3•27 3'92 31 '5 76'0 3'86 8'33 42-75 1.00 1'17 1'15 1'18 1'27 1'15 1-27 1'32 1-36 1 '47 i .73 1'57 1'88 1'00 2'10 2-50 3'40 Continued on next page