TABLE OF CONTENTS As already stated in Chapter 1, the matter transfers taking place between a polymer package and a liquid are controlled either by diffusion through the polymer or by convection at the liquid-solid interface.
The mathematical theory of diffusion in isotropic materials is thus based on the hypothesis that the rate of transfer of diffusing substance through unit area of a section of the material is proportional to the concentration gradient measured normal to the section, as shown in Equation (4.1):
F being the rate of diffusing substance transferred per unit area of section,
C is the concentration of the diffusing substance,
x is the space coordinate normal to the section along which the diffusion takes place, and D is the diffusion coefficient, also called diffusivity.
The negative sign arises because diffusion occurs in the direction opposite to that of increasing concentration.
At the packaging-liquid interface, the rate at which the substance is transferred into the liquid is constantly equal to the rate at which this substance is brought to the surface by internal diffusion through the polymer packaging, leading to the following relationship:
where: h is the coefficient of transfer by convection in the liquid next to the surface,
CL, t is the concentration of the diffusing substance on the surface of the solid,
C eq is the concentration of the...
