# Evaluation of the Temperature and Time in Centrifugation-Assisted Freeze Concentration
## 3 Results  
Figure 2 shows the results of the concentration of the blueberry juice (in \({}^{\circ}\)Brix) after it had been centrifuged at different temperatures and times. As presented in the figure, the highest concentration values were achieved when the time-temperature combination was lower in the first freeze concentration cycle, and this finding is consistent with the literature that demonstrates that the first drops of any thawing process are the richest in solutes [33]. On the other hand, for the lowest temperatures of those studied (5 \({}^{\circ}\)C and 10 \({}^{\circ}\)C), no significant differences in the concentration results were obtained at 15 and 20 min. However, no significant differences were noted between the treatments corresponding to 10 min and different temperatures, with the exception of the treatment at 15 \({}^{\circ}\)C, for which the concentration was the lowest for this time point. Figure 2: Results of concentration (\({}^{\circ}\)Brix) at different times and temperatures; a,b,c indicates there are significant differences at \(p\leq 0.05\), and b,d indicates there are no significant differences at \(p\leq 0.05\), both according to a least significant difference (LSD) test. Figure 3 shows the ice fractions and concentrates of two combinations studied. The fractions on the left correspond to the combination of 10 min and 5 \({}^{\circ}\)C, which was the treatment that yielded the highest value of the concentrations (49.4 \({}^{\circ}\)Brix). However, notably, the solute is retained in the ice; thus, the volume of the concentrate obtained was less than the volume corresponding to the concentrated fraction obtained with the treatment consisting of the combination of 20 min and 15 \({}^{\circ}\)C, which is shown on the right. The lowest concentration value (35.9 \({}^{\circ}\)Brix) was obtained for this combination. Table 2 shows the results of the response variables studied, including the efficiency, percentage of concentrate, and solute recovered. Regarding the efficiency (Table 2), no significant differences were noted between treatments. However, regarding the percentage of concentrate and the recovered solute, the highest values were reached with the centrifugation at 15 \({}^{\circ}\)C for 20 min for the first cycle of freeze concentration, demonstrating that these conditions represent the optimal experimental conditions to concentrate blueberry juice using the BFC technique. Figure 4 shows the effects of temperature and time on the three variables studied using Pareto diagrams for each of them. Figure 4a illustrates the effects of time and temperature on efficiency. None of the factors studied affects the efficiency response variable. However, the temperature and time have a positive effect on the percentage of concentrate and recovered solute response variables, as shown in Figure 4b,c. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Treatment**} & **Temperature** & **Time** & **Efficiency** & **Percentage of Concentrate** & **Recovered Solute** \\  & **(\({}^{\circ}\)C)** & **(min)** & **(\%)** & **(\%)** & **(\%)** & **(g Solute/g Initial of Solute)** \\ \hline
1 & 10 & 20 & 68.38 \(\pm\) 2.11 \({}^{\text{a}}\) & 17.68 \(\pm\) 3.06 \({}^{\text{a}}\) & 0.39 \(\pm\) 0.06 \({}^{\text{a}}\) \\
2 & 15 & 15 & 66. Figure 5 presents results of the regression models. The graphs illustrate the modelling results; two different scenarios for the predictor variables were considered. In the first scenario, only the temperature and time variables were used to predict target variables. In the second scenario, a third predictor variable, the amount of raw material, was added to determine whether adding this third variable improved the prediction. The quality of the predictions was measured using the MSE (\(y\)-axis) and R2 statistics (on top of each bar). Figure 4: Effect of temperature and time on the (**a**) efficiency, (**b**) percentage of concentrate and (**c**) recuperated solute.