The paper describes a mechanistic mathematical model for aroma release in the oropharynx to the nasal cavity during food consumption. The model is based on the physiology of the swallowing process and is validated with atmospheric pressure chemical ionization coupled with mass spectrometry measurements of aroma concentration in the nasal cavity of subjects eating flavored yogurt. The study is conducted on 3 aroma compounds representative for strawberry flavor (ethyl acetate, ethyl butanoate, and ethyl hexanoate) and 3 panelists. The model provides reasonably accurate time predictions of the relative aroma concentration in the nasal cavity and is able to simulate successive swallowing events as well as imperfect velopharyngeal closure. The most influent parameters are found to be the amount of the residual product in the pharynx and its contact area with the air flux, the volume of the nasal cavity, the equilibrium air/product partition coefficient of the volatile compound, the breath airflow rate, as well as the mass transfer coefficient of the aroma compound in the product, and the amount of product in the mouth. This work constitutes a first step toward computer-aided product formulation by allowing calculation of retronasal aroma intensity as a function of transfer and volatility properties of aroma compounds in food matrices and anatomophysiological characteristics of consumers.

Background: Freeze-drying or lyophilization is a dehydration process employed in high added-value food and biochemical goods. It helps to maintain product organoleptic and nutritional properties. The proper handling of the product temperature during the operation is critical to preserve quality and to reduce the process duration. Methods: Mathematical models are useful tools that can be used to design optimal policies that minimize production costs while keeping product quality. In this work, we derive an operational mathematical model to describe product quality and stability during the freeze-drying process. Model identification techniques are used to provide the model with predictive capabilities. Then, the model is used to design optimal control policies that minimize process time. Results and conclusion: Experimental measurements suggest splitting the process into two subsystems, product and chamber, to facilitate the calibration task. Both models are successfully validated using experimental data. Optimally designed control profiles are able to reduce the process duration by around 30% as compared with standard policies. The optimization task is introduced into a real time scheme to take into account unexpected process disturbances and model/plant mismatch. The implementation of the real time optimization scheme shows that this approach is able to compensate for such disturbances.

In freeze drying, the desorption step for reaching a low target moisture content may take a significant fraction of the total process duration. Because the long-term stability of freeze-dried biological products strongly depends on the current moisture content, modeling the desorption process may help safely optimize the secondary drying step. Most published models assume a first-order desorption kinetic, but experimental evidence shows that strongly bound water in the monolayer takes a much longer time to be desorbed than less bound water in multilayer. The proposed model for desorption of freeze-dried lactic acid bacteria preparation accounts for monolayer and multilayer water state in the solid matrix, with very different desorption kinetics. Results showed that the ratio of characteristic desorption times (monolayer/multilayer) was almost 30. Temperature dependence was adequately described by an Arrhenius law in the range of 15 to 40°C. Model parameter identification used simultaneously gravimetric measurements with high time resolution and direct Karl-Fisher titration, from several experiments at different, time-varying temperatures.

Lyophilizing frozen pellets, and especially spray freeze-drying, have been receiving growing interest. To design efficient and safe freeze-drying cycles, local temperature and moisture content in the product bed have to be known, but both are difficult to measure in the industry. Mathematical modeling of heat and mass transfer helps to determine local freeze-drying conditions and predict effects of operation policy, and equipment and recipe changes on drying time and product quality. Representative pellets situated at different positions in the product slab were considered. One-dimensional transfer in the slab and radial transfer in the pellets were assumed. Coupled heat and vapor transfer equations between the temperature-controlled shelf, the product bulk, the sublimation front inside the pellets, and the chamber were established and solved numerically. The model was validated based on bulk temperature measurement performed at two different locations in the product slab and on partial vapor pressure measurement in the freeze-drying chamber. Fair agreement between measured and calculated values was found. In contrast, a previously developed model for compact product layer was found inadequate in describing freeze-drying of pellets. The developed model represents a good starting basis for studying freeze-drying of pellets. It has to be further improved and validated for a variety of product types and freeze-drying conditions (shelf temperature, total chamber pressure, pellet size, slab thickness, etc.). It could be used to develop freeze-drying cycles based on product quality criteria such as local moisture content and glass transition temperature.

A mechanistic model for Debaryomyces hansenii growth and substrate consumption, lactose conversion into lactate by lactic acid bacteria, as well as lactose and lactate transfer from the core toward the rind was established. The model described the first step (14 d) of the ripening of a smear soft cheese and included the effects of temperature and relative humidity of the ripening chamber on the kinetic parameters. Experimental data were collected from experiments carried out in an aseptic pilot scale ripening chamber under 9 different combinations of temperature (8, 12, and 16 degrees C) and relative humidity (85, 93, and 99%) according to a complete experimental design. The model considered the cheese as a system with 2 compartments (rind and core) and included 5 state evolution equations and 16 parameters. The model succeeded in predicting D. hansenii growth and lactose and lactate concentrations during the first step of ripening (curd deacidification) in core and rind. The nonlinear data-fitting method allowed the determination of tight confidence intervals for the model parameters. The residual standard error (RSE) between model predictions and experimental data was close to the experimental standard deviation between repeated experiments.