Study of release and consumption of agents from active polymer packaging into food using dimensionless numbers

In protecting food, packagings are shifting from passive protection to taking an active role in improving food quality. The active packaging, consisting of a polymer liner with an active agent in it, is able to produce a desired effect on the food. A wide variety of active agents exist, such as antimicrobials, which can improve the quality of the food. This packaging comprises at least two layers, one with the usual impermeable polymer protecting the system from the environment, and the other with a polymer liner containing the agent, bound to the inside of the packaging and in contact with the food. This study describes the process of agent release and consumption either by the food or by micro-organisms located in the food. The agent diffuses through the polymer liner with a constant diffusivity into the liquid food, enters the food with a finite coefficient of convective transfer at the interface, and reacts either with the food itself or with the micro-organisms. The concentration of the agent in the liquid food is uniform, resulting from the high convective effect in the liquid compared to the rate of diffusion through the liner. The rate of consumption of the agent is controlled by a first order reaction with respect to its concentration in the liquid. As the process is highly complex, with the stages of diffusion followed by consumption, two new dimensionless numbers are introduced, connecting the rate of consumption of the agent either with the diffusivity, when the process is controlled by diffusion, or with the rate of convective coefficient when it is controlled by convection. Thus from the values obtained for these two dimensionless numbers and the well known Sherwood number, it is possible to predict which factor, being limiting, the user must act upon to control the process in the desired way.