Published values of food properties, such as true density, bulk density, and porosity in various foods were collected from the literature and classified in a previous work. These values of the true density were processed in order to reveal the influence of material moisture content and temperature. A simple mathematical model, relating true density to material moisture content and temperature, was developed and fitted to all examined data for each material. The data were carefully screened using residual analysis techniques. The correlation results for true density of nine materials are presented in this article.
INTRODUCTION
Structural properties of foods are affected by various factors, such as material moisture content, material morphology (continuous or granular), processing method, conditions, etc. However, true density is not affected by the method or the material morphology. On the other hand, it strongly depends on moisture content and temperature.[Citation1,Citation2]
True density (ρp) is the density excluding all pores; it is determined by the mass of the sample and its true volume. The term particle density is used for granular materials. True density increases as the water content decreases, which should be expected since it ranges between the density of water and the dry solids’ density.[Citation1]
The scope of this paper is (a) to propose a mathematical model to calculate the true density of some food materials as a function of temperature and moisture, and (b) to fit the model simultaneously to available literature data, and obtain higher accuracy in the estimation of the true density of foods.
Literature data for true density (and bulk density and porosity) for food materials were collected and presented by Boukouvalas et al.[Citation3]
MATHEMATICAL MODEL FOR TRUE DENSITY[Citation2]
Assuming the moist material to consist of dry solids, water and air, the following definitions are useful for the analysis:
The material moisture content X on a dry basis (kg water/kg db) is:
Assuming that no volume interaction occurs between the water and the solids, combining Eqs. (3), (4), (5), and (6) results in:
Eq. (7) shows the dependence of true (particle) density on moisture content. The parameter ρ s (which represents the material solid density) can be calculated from relevant data for each material as linearly temperature-dependent parameters:
Table 1 Mathematical model for calculating true density as a function of moisture and temperature
DATABASE AND PROCEDURE OF REGRESSION ANALYSIS
The proposed model was fitted to the selected data () using a non linear regression analysis method. It was fitted to all literature data for each material and the estimates of the model parameters were obtained. For data at the same temperature, the average absolute percent deviation between experimental and calculated values is calculated and the sum of these deviations is minimized. In several cases, data with relatively large deviation errors (usually greater than 20%) were excluded and the procedure was repeated until an accepted standard deviation between experimental and calculated values was obtained.[Citation31]
Table 2 Data used in true density parameter estimation for various foodstuffs
RESULTS AND DISCUSSION
Among the available data, only 7 materials have more than 10 data, which come from more than 3 publications. Apart from these, 2 more materials were considered, although the data were obtained from only 2 publications due to the relative large number of data. The regression analysis is applied to these data and the results of the parameter estimation procedure are presented in . It must be noted that this procedure was applied simultaneously to all the data of each material, regardless of the data sources. Thus, the results are not based on the data of only one author and, consequently, they are of higher accuracy and general applicability. Due to the narrow temperature range of the experimental data of three materials (banana, carrot and garlic), a temperature independent approach was adopted for dry solids density (s 2 = 0). The assumption that the dry solids density of the materials is not strongly affected by temperature is justified by Choi & Okos,[Citation32] where linear temperature-dependent correlations for pure components solid densities have been presented, but the dependency on temperature is not significant. For wheat, the temperature dependency is found to be rather significant. Although the description of the experimental data is satisfactory, the extrapolation to temperatures out of the range of the used experimental data, might give significant deviations. For potatoes, data at temperatures greater than 150°C were not taken into account for the regression procedure since the water density equation was limited at 150°C. However, the developed model with the obtained parameters was used in order to predict the true densities at higher temperatures by extrapolating up to 190°C. The results were very satisfactory since the average error was 5.2% at 170°C and 6.1% at 190°C.
Table 3 Parameter estimates of the model presented in
The obtained parameters for all materials are in good agreement with the ones given by Saravacos & Maroulis, [Citation2], with the exception of carrots (about 20% difference). However, the description of the experimental data in this material is satisfactory, which is the case for all the materials studied in this work. The typical performance of the developed model is presented in for selected materials studied in this work. In , to , the performance of the model is presented, along with the experimental data, at a representative temperature for comparison purposes. In , to , the performance of the model at different temperatures is presented. and summarize the model predicted values for various fruits and vegetables, respectively, at ambient temperature. As expected, the true density ranges between the solid density (dry material), and the density of water (infinite water content) at the examined temperature. Finally, in , the temperature dependency of true density of apple and banana at X w = 1 [kg/kg db] is presented. The decrease in true density is minor at near zero temperature, but it tends to be more significant at higher temperatures.
Figure 1. (a) True density of Apple at 70°C and various moisture contents (Exp. Pts from Krokida et al.[Citation9]; Zogzas et al.[Citation11]). (b) True density of Apple at various temperatures and moisture contents.
Figure 2. (a) True density of Carrot at 70°C and various moisture contents (Exp. Pts from Krokida & Maroulis,[Citation15]; Zogzas et al.[Citation11]). (b) True density of Carrot at various temperatures and moisture contents.
Figure 3. (a) True density of Potato at 70°C and various moisture contents (Exp. Pts from Wang & Brennan, [Citation27]; Zogzas et al. [Citation11]). (b) True density of Potato at various temperatures and moisture contents
Figure 4. Predicted values of true density for fruits at 20°C.
Figure 5. Predicted values of true density for vegetables at 20°C.
Figure 6. Predicted values of true density vs. temperature for fruits at Xw(db) = 1.
CONCLUSIONS
The values of true density in various foods were studied and analyzed statistically to reveal the influence of material moisture content and temperature. A simple mathematical model, relating true density to material moisture content and temperature, was fitted to all examined data for each material. The description of the experimental data with the aforementioned model was very satisfactory.
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