2.2.5. Description and Principle of DIC Treatment
Pre-dried mangoes were textured by the instant controlled pressure drop technique (DIC) under different operative parameters of saturated steam pressure (P) and processing time (t), ranging from 0.2 to 0.6 MPa and from 5 to 55 s, respectively. In the section “Experimental design description”, the adopted central composite experiment is described.
In this study, the DIC process consisted of seven steps.
Figure 2 shows the different steps of applied DIC treatment. First, 250 g of pre-dried mangoes was placed into the reactor (
Figure 2a), and to ensure rapid contact between the saturated steam and the sample, a vacuum was created (3–5 kPa) (
Figure 2b). Secondly, saturated steam was injected into the reactor until a fixed saturated steam pressure level was reached (
Figure 2c), and the target steam pressure was held for some seconds (
Figure 2d). Thus, by applying a central composite rotatable experimental design, this stage seeks the homogenization of the temperature and the water into the product; heat transfer is carried out mainly by steam condensation. Thirdly, once the temperature and water content levels were almost homogenized in the material, samples were submitted to an instant controlled pressure drop (0.55 MPas
−1) towards the vacuum (3–5 kPa) (
Figure 2e). At this stage, the autovaporization of water inside the product generates a quantity of steam and a significant mechanical tension that allows the expansion of the product. In addition, the autovaporization of the water guarantees rapid cooling, which prevents the thermal degradation of sensitive compounds and, therefore, guarantees the high quality of the treated products. Finally, after some seconds under vacuum (
Figure 2f), to recover the product from the reactor, the ambient air was introduced to return to atmospheric pressure (
Figure 2g).
For this study, the DIC MP reactor (manufactured by ABCAR-DIC Process; La Rochelle) was used.
Figure 3 shows the picture of the DIC MP reactor (A) and its schematic diagram of the reactor (B).
2.2.6. Drying Kinetics at the Post-Drying Stage
After DIC treatment, drying kinetics of the post-drying stage was carried out. For this, 20 g of mango of each experiment (DIC and CAD) was dried under the same conditions and equipment of the pre-drying stage. Weight changes were measured at 1, 5, 10, 15, 30, 60, 90, 120, 180, 240, 300, 360 and 1320 min. Samples’ weights were recorded (using an electronic balance PS 2500.3Y model Radwag, Poland). Equilibrium water content was determined until the sample’s weight changed to less than 0.01 g for 2 h.
2.2.7. Mathematical Modeling of Drying Kinetics
Dehydration involves the simultaneous application of heat and the removal of moisture from food. Then, to study the dehydration kinetics of CAD and SD mangoes, the study of Mounir and Allaf (2009) [
11] was adopted. This study focuses on the four heat and mass transfers that occurred during drying:
(1) Heat transfer from the outside to the surface of the product; the energy can be supplied by conduction, convection, or radiation.
(2) Heat transfer within the product; the energy is transmitted by conduction.
(3) Water transfer within the product, which takes place in the liquid phase by various processes including capillarity and molecular diffusivity (the driving force is the water content gradient); and/or vapor (the driving force is the vapor partial pressure gradient).
(4) Vapor transport from the surface to the outside.
Then, when the external heat and mass transfers do not limit the whole operation through adequate airflow temperature, relative humidity, and velocity, only internal transfers may intervene as limiting processes. In such conditions, the Mounir and Allaf (2009) [
11] model proposed a Fick-type relation:
By assuming any structure modification (
= constant and
= 0), the hypothesis of both structural and thermal homogeneities and a one-dimensional flow, the whole drying process is only controlled by mass transfer:
Then, in this study Crank’s solution was adopted [
12]:
where
W1 is the value of W at the time t
1 chosen as the beginning of the diffusion model obtained only for long-time experiments. Coefficients of Crank solutions Ai and qi are given according to the matrix geometry Fick’s number (
τ) defined as:
where
dp is the characteristic length (m), calculated as the relation between the volume and the surface of the parallelepipeds (
dp = V/S = a * b* c/2 (ab + ac + bc). For this case, an infinite plate is considered. Then, by limiting Equation (3) to its first term, it could be expressed as:
The logarithmic representation of Equation (5) as a straight line leads to determining
Deff from the slope
k:
where
k corresponds to:
and the effective diffusivity is:
Moreover, because the transfer mechanisms during drying are much more complex than diffusion, this model was verified experimentally by plotting the straight line given by equation 6 by excluding the points close to
t = 0. However, when the diffusion process does not control the drying operation, it cannot be possible to determine the effective diffusivity from the experimental data. In fact, if the kinetics of airflow drying depends on the velocity, it means that the water diffusion within the material is not the limiting process (Absence of Negligible External Resistance); thus, to verify that external heat and mass transfers are not limiting, the Critical Airflow Velocity (CAV) equation from [
13], could be used.
Because, in this study, we only evaluated one condition of air flow (1 m/s), we cannot calculate the CAV value, and therefore, we cannot guarantee that external heat and mass transfers are not limiting. Then, in this study, the obtained results from Equation (8) can be considered as apparent drying coefficient (Dapp), which becomes a useful tool to compare drying performance between the different drying treatments.
On the other hand, to evaluate the quantity of water dried from the surface regardless of the diffusion process, the “starting accessibility” was determined (). Then, through the extrapolation of the diffusional model, the moisture content at t = 0 (W0) can be determined, which is generally different from the initial moisture content Wi. Thus, the starting accessibility was determined as .
Finally, to determine the effect of the DIC treatment on the drying time, Equation (6) was used to calculate the time in minutes for obtaining a final moisture content of 20% d.b from an initial moisture content of 30% d.b (td20%).
2.2.8. Experimental Design
A five-level central composite rotatable experimental design was used to assess the effect of DIC operating parameters on drying kinetics. After preliminary tests, the saturated vapor pressure “P” (MPa), with a range between 0.2 and 0.6 MPa, and the treatment time of the process “t” (s) between 5 and 55 s, were used as independent variables (
n = 2). Thus, the studied design included 11 experiments: 4 factorial points (
;+1/−1, and +1/+1); 4 start trials (
; and 3 central points (0,0). The value of α (axial distance) was determined as a function of the number (
n) of operating parameters, and it was calculated as
.
Figure 4 shows the selected independent variables at five levels of (
, −1, 0, +1,
), and
Table 1 shows the applied experimental design.
To minimize the effects of unexpected variability in the observed responses due to exogenous factors, the DIC treatments were performed randomly.