94 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS C^sEs WI•ERE TI• R^'r• CO•TROLL•G Swap Is • wI• AppL•E•) Pw^s• In the preceding section it was assumed that the thermodynamic activity of the species being absorbed was essentially uniform in all parts of the applied material at all times. If the concentration of the absorbed ma- terial changed in the applied cream or ointment, the assumption was made that only negligible concentration gradient developed in the direction normal to the skin surface that is, any decrease in concentration occurred uniformly. This is never quite the case since some concentration gradient must exist to promote the necessary diffusional flow. Because of the great resistance to penetration of intact skin, however, such gradients are usually very small and may normally be ignored. There are important instances, nevertheless, such as cases involving absorption by injured skin or where highly insoluble, suspension-type ointments are used where large concentration gradients may develop in the applied phase. Mathematical relationships governing such situations are considered in the following section. In all cases to be considered it will be assumed that all the concentration gradient occurs in the applied material, a situation shown diagrammatically in Fig. 7. This is equivalent to assuming that the skin surface is a perfect RECEPTOR PHASE O 7.--Schematic diagram ooe di•u$iona] •ow from homogeneous so|ution of •nit½ thickness into a pcroe½ct receptor. sink and will maintain essentially zero concentration of the penetrating material by rapidly dissipating it to deeper tissues. This simplication is necessary since any attempt to distribute the activity gradient between the skin phase and the applied phase would lead to extremely complex mathe-

PHYSICAL CHEMICAL ANALYSIS OF PERCUTANEOUS ABSORPTION PROCESS 95 matics. If essentially all ot the gradient is in the skin, it is evident the mathematics of the preceding section will apply. .4bsorptionfrom Solutions. For the simplest system of this type, where the penetrating substance is initially uniformly dissolved in a homogeneous base as shown in Fig. 7, it can be shown rigorously that the amount of material absorbed from the applied phase, 6•. = hCo 1 8 23 1 -D(2md-1)2•r2t'• •'2.m =0 (2m d- 1) • e • J where h = thickness of the applied phase, Co = initial concentration of me penetrating solute, D = diffusion ccnstant of the solute in the base, and t = elapsed time of application. It is evident that if an instantaneous rate is desired it is necessary only to differentiate the above with respect. to time. These relationships are extensively treated by Barter in his book on dif}hsion. dbsorptionfrom Suspensions. The case discussed above probably will rarely apply to percutaneous absorption through intact skin since the dif}hsion coefiqcient of any chemical readily taken in through such a barrier will be so great as to maintain a uniform concentration in the applied phase. A more important case is the absorption of a drug, for example, which is used as an extremely fine solid dispersion in a homogeneous base. This can be, for example, an ointment consisting of pencillin in petrolatum base. Receptor ß o 4, ß o ß ß ß Diffusion from ointment base of suspension type L = h a + Ah 2 %D 2CsD Figure 8. For such a system, shown schematically in Fig. 8, we are able to derive rather simple relationships among the several variables. Thus • Dt E = (2.4- c,) '] + 2(.4 - c.,5/c,