Moisture distribution of processed cheese-sponge cake system at different times (Guillard et al., 2003b). Meanwhile, the second phase shows slower moisture absorption from the center (>1 cm) to the end of the cake (Guillard et al., 2003b). The research of Jinning Qi et al. 2006) showed the increase in T2 signal when water enters the sandwich.
The study by Ramos-Cabrer et al. 2006) investigated moisture redistribution in sandwiches using 2 different MRI methods. As mentioned in the previous section, these changes in effective moisture distribution are related to changes in cake microstructure (Guillard et al., 2003d). Near saturation, moisture migration occurs mainly by liquid transport and the effective diffusion remains fairly constant due to the collapse of the porous structure (Guillard et al., 2003d).
Effective moisture diffusivity of sponge cake as a function of moisture content at 20 ℃ (Guillard et al., 2003d). Using the modeling framework used in the study, Gulati et al. 2015) confirmed that, in isothermal conditions, the main mechanism of moisture migration in multi-domain foods is capillarity. Non-thermodynamic factors of moisture migration are related to the product's composition, structure and defect (Ghosh et al., 2002) which affect the diffusion rate of water between components (Labuza & Hyman, 1998).
Meanwhile, the effect of fat content on effective moisture diffusion is suspected due to the hydrophobic nature of fat that hinders the moisture migration process through the solid matrix and pore surface (Roca et al., 2006).
External factors
Presence of surrounding air
Components contact condition
The use of a physical barrier to prevent moisture migration will be discussed in more detail in Chapter 5. Air gaps are always present in multi-domain food products, especially bakery products. A study by Roc, Broyart et al. 2008) developed and validated a moisture migration model that considered the air gap. The result demonstrates that the presence of an air gap between components results in reduced moisture migration with increasing air gap thickness.
Simulation results also suggested that a small air gap (1 mm thick) reduced the water uptake by at least 0.05 g/g d.b. 2015) also investigated the effect of the air gap between a breaded chicken sandwich. Simulated results prove that smaller gap thickness will result in a faster moisture loss by the chicken and faster moisture uptake by the bread (Gulati et al., 2015). They also mentioned that the air gap shows more resistance to moisture transfer than the resistance that exists inside the chicken and the bread, so the existence of air gaps is important to consider.
The air gap also did not affect the equilibrium as much as the amount of moisture exchanged between the chicken and the bread. The air gap only reduces the rate of moisture transport between components (Gulati et al., 2015). Similar results were obtained by Yuan et al. 2019) who compared multi-domain foods (Cookies-agar gel) in different contact conditions.
They found that the air gap reduces the rate of moisture migration but has a limited effect on the equilibrium moisture content. At longer storage, the effect of the air gap towards the final moisture content became less apparent as the full-contact and non-contact systems show nearly identical moisture contents. Moreover, increased contact distance and reduced contact area were proven to be able to reduce the rate of moisture migration (Yuan et al., 2019).
Gravity can affect the direction of moisture migration in a multi-domain system, resulting in higher moisture uptake if the dry component is located below the wet component. This comparison of moisture uptake on the top and bottom slices of bread in the sandwich system shows a higher water uptake on the bottom slice, suggesting that moisture migration is partially driven by gravity (Ramos-Cabrer et al., 2006). Two-dimensional slices of sandwiches (left processed, right untreated) obtained by 3D-MRI at different time points (Ramos-Cabrer et al., 2006).
Temperature
The dry component is initially at uniform concentration and there is no moisture gradient at the end of the dry component. Assume that the wet components have a constant and that the interface between the dry and wet components is always in equilibrium. It is assumed that the quality of the product is determined by the dry component and that the critical moisture content is low.
The model is developed based on a porous media framework, where the chicken and the bread are considered as a porous medium.
Early development of moisture migration modeling in multi-domain bakery products
Schematic model of a food system consisting of sponge cake and agar gel in a hermetic diffusion cell made of glass (Guillard et al., 2003b). Comparison between the experimental and simulated moisture profile showed that the model is an adequate tool to predict the moisture migration between the sponge cake and the agar gel (aw). The model was then found to be sufficient in predicting the moisture transfer, although the model did not match the experimental data somewhat underestimated near the interface (Guillard et al., 2003b).
The model developed in this study was also used to simulate moisture migration in other studies. The study by Roca et al. 2006) used the model to validate moisture migration between agar gel and sponge cake with varying porosity and fat content. Another study by Mavrou et al. 2018) used the model to simulate moisture migration between ice cream and a wafer cone separated by a chocolate barrier. Other studies also validated the model in a lower skewed component, i.e.
Schematic model of a food system consisting of a sponge cake and agar gel separated by a food film in a hermetic diffusion cell made of glass (Guillard et al., Moisture migration model for a two-component food system of separated from a food film by Guillard et al. 2003c) was discussed at length in the review by Bourlieu et al. Validation of the model was done using the same agar gel and sponge as previous research (Guillard et al., 2003b).
Comparison between the experiment and the simulations validated that the model has successfully predicted the local moisture content of the 3-component food system. In the study by Guillard, Broyart, Bonazzi, et al., (2004), the model was validated and found to be very suitable for predicting moisture migration profiles for different storage temperatures (5℃, 20℃ and 30℃). The model created in this study was also used in other studies comparing different edible films (Bourlieu et al., 2006; Guillard, Broyart, Bonazzi, et al., 2004).
Schematic model of a food system consisting of a sponge and agar gel separated by an air gap (Roca, Broyart, et al., 2008). In the study of Roca et al. 2008), further development of the model established by Guillard et al. (2003b) was done to simulate the presence of air gap (imperfect contact conditions) between two food components (see Table 5, Model 3). Similar to the study of Guillard et al. 2003c), the food system is assumed to be formed by three finite cylindrical components placed in contact with each other (Figure 12).
Recent development of moisture migration modeling in multi-domain bakery products
In a more recent study, the development of a new model to simulate moisture migration between multi-domain food products was done through a porous media framework (Gulati et al., 2015). The model (see Table 5, Model 5) used chicken and bread as porous medium to simulate moisture transport through liquid water and gas phases (water vapor + air). Two cases of moisture migration were investigated: (1) moisture migration occurs only in one direction along the Y-axis, without any migration through the surrounding air (1D model); and (2) some moisture migration occurs between the sandwich system and the surrounding air (2D model).
Schematic representation of the moisture migration between the bread-air-chicken system through different phases, transport modes and boundary conditions. Validation of the model was performed using the experimental result of a barbecue chicken sandwich packed in flexible high-barrier trilaminate MRE bags with a pouch of oxygen scavenger ( Gulati et al., 2015 ). Simulated (–) and experimental (•) moisture content (left) and aw (right) in chicken and bread as a function of storage time (Gulati et al., 2015).
Simulated (–) and experimental (•) yield of chicken and bread as a function of storage time and ambient air effect (Gulati et al., 2015). A more recent study by Hao et al. 2016) uses the finite element method (FEM), which uses the model created by Guillard et al. (2003b) to simulate moisture migration in a multi-domain food system (see Table 5, Model 6). In the study, the FEM is used to solve the mathematical model of Guillard et al.
The simulated moisture content also showed good agreement with the experimental results, suggesting that FEM is an effective method to predict moisture migration in multi-field food. Schematics of the geometry of the multi-domain food web model in the COMSOL Multiphysics package (Hao et al., 2016). The most recent modeling of moisture migration was done by Yuan et al. 2019) that creates moisture migration models for two-component food systems with different contact conditions (see Table 5, Model 7).
In the study, Yuan et al. 2019) creates three different models for three contact conditions (full contact, no contact and partial contact) using the second extended Fick equation. Meanwhile, due to the random distribution of air gaps and connections between two surfaces, the prediction of moisture migration under partial contact conditions according to the real situation is impossible. This suggests that the model can be used to predict food moisture migration with different contact conditions (air gap thickness and contact area) and can estimate product shelf life.
Moisture migration experiment on agar gel and biscuits under (a) full contact (b) no contact (c) partial contact conditions (Yuan et al., 2019). Discussion of moisture migration models in multidomain bakery products Almost all but one early and recent study on moisture migration modeling.
Discussion on moisture migration models in multi-domain bakery products Almost all but one of the early and recent studies on the modeling of moisture migration
