Diffusion through a liquid boundary layer

With large K values, that is low solubility of component i in a liquid food, the material transport through A can also be determined from the contribution of diffusion in L under conditions of thorough mixing. Van der Waals attractive forces between the package surface and the molecules of L in intimate contact with P lead to the formation of a thin but immobile layer in which the diffusion coefficient of i in L, DL, controls mass transport (the Nernst diffusion layer). 

If diffusion through the stagnant boundary layer determines the rate of transport through A for the system, then one can assume a constant, location-independent concentration cP in P. The partition equilibrium is assumed to be reached on the boundary area between P and L at x = 0 and consequently K = cP/cL(0). If one lets the thickness of the diffusion layer in L next to the surface of P be 1L and if L assumes a constant concentration of cL then one can assume a constant material transport flux through the boundary layer for short time intervals that follows Fick s first law and the contribution of the flux to time t is expressed according to Eq. (7-16)  

For short times if a t 1 the following equation can be used as a good approximate solution  

If diffusion in the packaging determines the rate of migration, there is a deviation from linearity in the plot (Fig.7-12). 

---