The Figure 1 shows the dehydration moisture removal rate. For conventional oven-drying, temperature significantly affected the drying process time, with the lowest drying time recorded at 70 °C. The drying time for the VMD sample also was similar to that of the 70 °C OD dried sample. This can also be ascertained from the drying rate curves for the experimental data, as shown in Figure 1a, wherein the drying rates were calculated from the drying data by taking change in moisture content for each interval and expressed as g H2O/ g dry matter /min. As expected, drying rates of OD at the three temperatures followed the order 70 °C > 65 °C > 60 °C during the entire drying process. During the initial constant rate drying period at high moisture content, VMD’s drying rate was 33–67% faster than OD at the three temperatures studied. At moisture content below 100% db moisture content, the curves made a slope with x-axis depicting a falling rate period. The falling rates of drying for all samples indicate an increase in resistance to moisture migration from inside to the surface. The dimensionless moisture content, or the moisture ration MR, kept on decreasing for all the drying processes with drying time. This has been illustrated in Figure 1b. Decreasing MR with drying time is in agreement with the drying of most biological materials and spent grain drying ^[1][2]. In this zone, VMD drying rates and slopes were similar to that of OD at 65 °C, with 70 °C OD depicting a faster drying phenomenon.

This relative slowing of the VMD drying process during the falling rate period may be attributed to the relatively higher-pressure levels (180 torr, as compared to lower than 40 torr used in other works like Kwok et al. ^[3], Wojdyło et al. ^[4]) used during the VMD process in this study to maintain the product temperature in the critical zone. A higher level of VMD pressure was used in this study to raise the critical temperature to 65 °C for simultaneous pasteurization of the BSG waste. At 180 torr, as confirmed by the temperature collected from the VMD drier, a greater than 40 min of equivalent lethality at 65 °C was recorded for the BSGs. This would tend to pasteurize the product by the generated heating.

A continuous decrease in MR with time shows that kinetics could be established based on Fick’s diffusion model, as diffusion governs the falling rate period. As already discussed, Equation (5) was obtained after solving the diffusion equation, considering a constant moisture diffusivity. When the experimental data were plotted as ln MR against time (Figure 1c), the data conformed to be linear with R² > 0.9. This allowed for linear regression analysis to use the slope (b) in Equation (6) to evaluate the effective diffusivity (D_eff), shown in Table 1. As evident, the D_eff values were profoundly affected by drying temperatures. The value of D_eff for the VMD was also within range of OD, with VMD values being slightly lower than OD at 70 °C, and larger than OD at 60 °C and 65 °C. Overall, the D_eff varied from 1.42 × 10⁻⁰⁸ to 5.45 × 10⁻⁰⁸ m²/s. The values lie well within the D_eff values of most food materials (between 10⁻⁰⁸ and 10⁻¹² m²/s) ^[5], like apricots ^[6] and pomegranate ^[7]. Using the Arrhenius relationship, the values of ln D_eff at each temperature were plotted against 1/T and showed a straight line with high linearity (R² > 0.99) (Figure 1d). The activation energy (E_a) was found to be 7095.5 J/g, whereas the pre-exponential factor for effective diffusivity (D_o) was evaluated to be 1.52 × 10¹² m²/s.

Since MR was a function of drying time, and it decreased continuously, the drying data were fitted to seven different thin-layer drying models. The fitness of the model to approximate the drying data was determined by using R², χ², SEE, and E_RMS values. In general, the R² value has to be close to 1, and χ², SEE, and E_RMS values needed to be minimized. Table 2 shows these values for various model with their parameters. The page model was seen to fit the experimental data better than other models with the highest value of R² (0.9996–0.9999) and lower values of χ² (0.0018–0.0141), SEE (0.0034–0.0143), and E_RMS (<0.0001). Figure 2a shows the fitting of the Page model on the experimental MR values for each drying treatment. The Page model had also been reported to fit drying data for several food materials, like raw mango slices ^[8] and bay leaves ^[9]. Nevertheless, Figure 2b shows a highly positive correlation between experimental and predicted MR values. Thus, the Page model was found to best represent the thin-layer drying behavior of BSGs.

The data showed that grains dried by OD at 65 °C had the highest WHC (1.52 g/g), followed by VMD (1.31 g/g) and FD (1.18 g/g). The range of oil holding capacity was from 2.27 g/g (FD) to 3.33 g/g (OD-65 °C). The values of WHC and OHC were statistically significantly higher (p < 0.05) for OD-65 °C and VMD than FD samples. Since air drying and VMD involve the application of heat for dehydration process, it can be deduced that heat application may lead to denaturation and conformational changes in protein structure, which might affect the functional properties ^[16]. Lesser values in the case of FD might be reflective of the fact that the proteins would still be in their native state, allowing minimum functionality. WHC and OHC in BSG flour varied based on the BSGs compositions after mashing process in the breweries. Replacement of wheat flour with barley flour significantly increased the water absorption capacity. Increasing the levels of barley flour in wheat flour blend insignificantly increased the oil absorption capacity of the blends ^[17]. Although the BSGs are a rich in fiber, they too affect the functionality of BSG products. Öztürk et al. ^[18] used BSGs for making cookies and observed the spread ratio (width/thickness) of cookies. This suggests that the fiber could bind the matrix together and lessen the spread. The impact of fibers of BSG chips could be a topic of further research.

Table 3 also illustrates the relevant data for foaming capacity and stability. There was no significant difference (p < 0.05) for these values in all the three different samples. The foaming capacity and foaming stability of BSG flours from three different techniques at pH 7.00 was not very noticeable and was almost the same value (1.5 mL), and the stability of foaming for all samples was low and nearly at the same value (0.5 mL). Foaming capacity and stability were affected by drying at high temperatures of 105 °C, as shown earlier ^[19]. However, no differences were observed between oven drying at 80 °C and vacuum drying by them, which supports our results. Intensity of the drying treatment affects the interfacial properties of proteins. Similarity with the FD samples meant that the treatment conditions were not so intense to affect these properties.