Diffusion in multi-phase systems

In this section the important cases for food packaging are treated. These cases differ from the previous examples in that mass transfer takes place across an interface between two different media with different characteristics, e.g. with different diffusion coefficients. If the value of a quantity is desired, for example the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium. 

For the sake of conformity, in the following every quantity related to the packaging is designated with the index P and the quantities related to the food are labeled with the index L. 

A component i in the liquid phase with an initial concentration cl.o is sorbed onto the contact surface area A between the liquid and packaging and subsequently diffuses into the matrix of the packaging. In so doing there is a decrease in concentration in the region of the contact surface which leads to further transport of i from the matrix of the liquid to the contact surface. 

A constant distribution of i between L and P takes place that is independent of concentration of i and time. For relatively small concentrations of i ( 1 %) this approximate assumption is fulfilled and one defines the partition coefficient K as a constant ratio of the concentration i in the packaging material at time t on the contact surface cPt (dP) to the concentration of i in the liquid independent of location at the same time, cL 

Where K is the ratio at t = oc of the equilibrium concentrations of i in P, cPoc to that in L, cUx.This concentration ratio is also sometimes referred to as the relative solubility constant, Sr, of i in P (relative to cL,t). 

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