DIFFUSION ANALYSIS THROUGH OCCLUSIVE FILMS 557 where aj = 1j%. A measure of the hydration (water content) per unit area D.i of stratum corneum during steady-state diffusion can be obtained by inte- grating the concentration across the stratum corneum. This amount (Q) of water per unit area of stratum eorneum is given by a, 1 1 Q = dx Cs l) (X) = ai -- 0 yx ao 2(1 + ae/a•) (3) where csO) (x) is the steady-state concentration in the stratum corneum and is given by ¾•cs(. (x) = L[-• + -,(1- x/h)] + ao (4) Let us suppose that the diffusion coefficient for stratum corneum is de- pendent upon hydration. According to Scheuplein and Ross (6), this varia- tion can be greater than an order of magnitude for zero and 100 per cent relative humidity outside the skin. Grice et al. (7) also give evidence (TWL measurements ) that diffusion is dependent on hydrahon. We can now use equations (2) and (3) to predict the effect of a film on the hydration of the stratum corneum and flux (TWL). We assume that ao is near zero, and thus, have "dry" diffusion when the film is absent (as = 0). Thus js a _ ai -- ao ad (5) and Q• =_•(at+ a,,) 1 1• a• • ~• •- (6) where the superscript d corresponds to the nonoccluded case. For perfect occlusion (o•2- • ), we have J•0 (7) and •1 ai y• (8) where Qm is the mmximum hydration. If a2 is not all that different from we have an intermediate case. For a viscous hydroc•bon, we can •sume • De • 10 -s cm=/sec, 1• • 40•m, and y2/% • 10, •d for the stra•m cor- neum (8), let D•w• 10 -• cm=/sec, and 1• • 10•m. Thus, we have a=/a• w *The diffusion coefficient for a viscous hydrocarbon is approximated from the Stokes- Einstein equation, D=kT/6•rvr where k is Bo]tzmann's constant, T is temperature (30øC), is the hydrocarbon viscosity (taken to be 5aP as for castor oil), and r is the radius of water (taken to be 3A). The ratio %/% is bit uncertain, but since skin hy- drates well and water is not very soluble in hydrocarbons, a ratio of ten is not unreason- able.

558 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ~ 4, where a• w corresponds to the "wet" diffusion situation, i.e., D• ~ 10 -'• cm2/sec. If we assume that al a = 10 al 'v, we have and j2 v _ ai -a•o _ 2Ja (9) 50•1 w ai+¾o ~0.9 (10) Hence, we see that for a film that is sufficiently oeelusive such that a2= 4al, we can hydrate the skin to within 90 per cent of maximum hydration. This increased hydration can then give rise to an increase in flux or TWL, which is consistent with •e observed rise in TWL upon application of petrolatum to skin. In fact, from this analysis, a rise in TWL with an oeelusive film is good evidence that the stratum comeurn is being hydrated. CONCLUSION It has been obse•ed •ha• •he insensible water loss o• skin can increase when •reated wi•h occlusive agents. This increase is a logical consequence o• the increase in dieusion coe•cien• o• s•ra•um comeurn when it becomes hydrated. These resuks sugges• tha• evaluation o• cosmetic •ormulations on the bask o• •heir e•ec• on in vivo insensible wa•er loss could easily be mis- leading wi•h respect •o skin conditioning. That is, a material which gives an increase in TWL may indeed be hydrating •he skin •o within a •ew percent o• maximum hydrafion, •nd should not be eliminated as a poor conditioner on •hese grounds. ACKNOWLEDGMENT We wish to thank J. S. Berry of The Procter & Gamble Company for pro- viding the TWL data on skin treated with petrola•m. (Received June 10, 1975) REFEREN•S (1) I. H. Blank, Proc. Sci. Sect. Toilet Goods Ass., 23, 19 (1955). (2) P. Flesch, Amer. Per. Cosmet., 77, 77 (1962). (3) I. H. Blank, J. Amer. Med. Ass., 164, 412 (1957). (4) G. E. Osborne and R. J. Gerraughty, J. Soc. Cosmet. Chem., 12, 271 (1961). (5) J. Crank, The Mathematics o[ Diffusion, O•ford U. Press, London, 1957. (6) R. J. Scheuplein and L. W. Ross, J. Inve•. Dermatol., 62, 353 (1974). (7) K. Gri•, H. Sattar and H. Baker, J. Inve•. Dermtol., 58, 343. (1972). (8) R. J. Scheuplein, U.S. Department of Cornmere, Repo• AD 822 665.