Theoretical Part of the Problem

The equation of diffusion taking into account the radial and the longitudinal transport is  

An analytical solution is found when the values of the diffusivity are the same in the polymer and in the food [3, 4], but it seems that no solution exists when the diffusivity of a diffusing substance in the food is different from that in the polymer. 

The initial conditions in the polymer bottle and in the solid food are  

At the food-bottle interface, where the concentrations are equal in the polymer and the food  

Moreover, Equation (4.33) holds either for the polymer bottle or for the food located in it. 

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Half the theoretical part of the problem is therefore solved. It is now necessary to determine the other half, the energy dissipated by actual column sway. Consider that columns have only length, diameter and thickness and assume that the energy dissipated by column sway tends to be proportional to the stress in the column material caused by sway and the volume of the material stressed. Because the stress distribution over the length of the column for columns swaying laterally in a specific mode will be similar, the energy dissipated per cycle of sway is... 

The purpose of Step I is to define the appropriate function to be used in Step II. Gibbs introduced this function, the chemical potential m, and provided a very simple answer for Step II the chemical potential of each component of the equilibrium mixture in the one phase equals that in the other. He provided, thus, the solution to the theoretical part of the problem. 

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