Permeation through a laminate

Diffusion through a barrier layer is a special case of diffusion through a laminate film composed of several layers with different thicknesses and diffusion coefficients. The mathematical treatment of the non-steady state case is complicated. The steady state permeation case allows the overall transport to be simply treated. Let n films with thicknesses dpi, dp2. dpn with corresponding diffusion coefficients DP1, Dp2. Dpn be bound together in a laminate. Because in steady state, the flux J of the diffusing substance i is the same through every individual component of the laminate, one obtains an expression for the concentration gradient  

The total resistance related to the diffusion is then the sum of the individual resistances and the total flux is practically determined by the layer with the smallest diffusion coefficient. 

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