Effect of Material Moisture Content and Temperature on the True Density of Foods

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1 International Journal of Food Properties ISSN: (Print) (Online) Journal homepage: Effect of Material Moisture Content and Temperature on the True Density of Foods Ch J. Boukouvalas, M. K. Krokida, Z. B. Maroulis & D. Marinos-Kouris To cite this article: Ch J. Boukouvalas, M. K. Krokida, Z. B. Maroulis & D. Marinos-Kouris (2006) Effect of Material Moisture Content and Temperature on the True Density of Foods, International Journal of Food Properties, 9:1, , DOI: / To link to this article: Copyright Taylor and Francis Group, LLC Published online: 06 Feb Submit your article to this journal Article views: 85 View related articles Citing articles: 10 View citing articles Full Terms & Conditions of access and use can be found at

2 International Journal of Food Properties, 9: , 2006 Copyright Taylor & Francis Group, LLC ISSN: print / online DOI: / EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE ON THE TRUE DENSITY OF FOODS Ch J. Boukouvalas, M. K. Krokida, Z. B. Maroulis, and D. Marinos-Kouris School of Chemical Engineering, National Technical University of Athens Zografou Campus, Athens, Greece 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. Keywords: Fruits and Vegetables, Shrinkage, Structure, True density. 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. [1,2] True density (ρ p ) 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. [1] 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. [3] MATHEMATICAL MODEL FOR TRUE DENSITY [2] Assuming the moist material to consist of dry solids, water and air, the following definitions are useful for the analysis: Received 18 March 2005; accepted 29 July Address correspondence to M. K. Krokida, School of Chemical Engineering, National Technical University of Athens, Zografou Campus, Athens GR-15780, Greece; mkrok@chemeng.ntua.gr 109

3 110 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS mt + ms + mw (1) where m t, m s, and m w are the total mass and the masses of dry solids and water, respectively (kg), while the mass of air is neglected. The total volume of the sample, V t, is written as: Vt = Vs + Vw + Va (2) where V s, V w and V a are the volumes of dry solids, water and air pores, respectively (m 3 ). The volume of air is referred to the internal pores only. The true density p is defined as: ρ p m t V p = / (3) where V p = V s + V w is the true (particle) volume, which is the total volume of the sample, excluding air pores. The actual densities of dry solids s and enclosed water w can also be defined as: ρ s m s V s = / (4) ρ w m w V w = / (5) The material moisture content X on a dry basis (kg water/kg db) is: X = m / m (6) Assuming that no volume interaction occurs between the water and the solids, combining Eqs. (3), (4), (5), and (6) results in: ρ p Eq. (7) shows the dependence of true (particle) density on moisture content. The parameter s (which represents the material solid density) can be calculated from relevant data for each material as linearly temperature-dependent parameters: where s 0 and s 1 are adjustable parameters. The water density is also considered temperature dependent but it can be calculated through a 2 nd degree polynomial: s w s 1+ X = 1 X (7) + ρ ρ w ρ s = s0 + st 1 (8) 2 ρ w = w0 + w1t + w2t (9)

4 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 111 where w 0, w 1 and w 2 are given by Maroulis & Saravacos, [4]. The resulting model is summarized in Table 1. DATABASE AND PROCEDURE OF REGRESSION ANALYSIS The proposed model was fitted to the selected data (Table 2) 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. [31] 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 Table 3. 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 Table 1 Mathematical model for calculating true density as a function of moisture and temperature Effect of moisture and temperature on true density Proposed Model ρ p 1+ X = 1 X + ρ ρ s w ρ w = w 0 + w 1 T + w 2 T 2 ρ s = s 0 + s 1 T where p (kg/m 3 ) the true density, s (kg/m 3 ) the dry solids density, w (kg/m 3 ) the water density, X (kg/kgdb) the material moisture content, T ( C) the material temperature, w 0 = 9.97E + 02, w 1 = 3.14E-03, w 2 = 3.76E-03 (0 150 C) Adjustable Model Parameters s 0, s 1

5 112 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS Table 2 Data used in true density parameter estimation for various foodstuffs T ρ p X w Material Ref. ( C) (kg/m 3 ) (db) Cereal products Wheat Fruits Apple Continued

6 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 113 Table 2 Continued Banana Legume Lentil Continued

7 114 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS Table 2 Continued T ρ p X w Material Ref. ( C) (kg/m 3 ) (db) Model foods Hylon Continued

8 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 115 Table 2 Continued Vegetables Carrot Garlic Onion Continued

9 116 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS Table 2 Continued T ρ p X w Material Ref. ( C) (kg/m 3 ) (db) Potato Continued

10 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 117 Table 2 Continued

11 118 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS Table 3 Parameter estimates of the model presented in Table 1 T ( C) Material Papers Data (total) Data (used) SD [kg/m 3 ] AAD% min max s 0 s 1 Cereal Products Wheat Fruits Apple Banana Legume Lentils Model Foods Hylon Vegetables Carrot Garlic Onion Potato (s 2 = 0). The assumption that the dry solids density of the materials is not strongly affected by temperature is justified by Choi & Okos, [32] where linear temperaturedependent 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. The obtained parameters for all materials are in good agreement with the ones given by Saravacos & Maroulis, [2], 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 Figs. 1 3 for selected materials studied in this work. In Figs. 1(a) to 3(a), the performance of the model is presented, along with the experimental data, at a representative temperature for comparison purposes. In Figs. 1(b) to 3(b), the performance of the model at different temperatures is presented. Figs. 4 and 5 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 Figure 6, 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.

12 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 119 (a) Apple (70 o C) Exp. Pts (70oC) Proposed Model ρp [kg/m 3 ] X w [kg/kg db] (b) Apple - Proposed model 20oC 70oC 100oC 1500 ρp [kg/m 3 ] X w [kg/kg db] Figure 1 (a) True density of Apple at 70 C and various moisture contents (Exp. Pts from Krokida et al. [9] ; Zogzas et al. [11] ). (b) True density of Apple at various temperatures and moisture contents.

13 120 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS (a) Carrot (70 o C) Exp. Pts Proposed model 1800 ρp [kg/m 3 ] ρp [kg/m 3 ] X w [kg/kg db] (b) Carrot - Proposed model 20oC 70oC 100oC X w [kg/kg db] Figure 2 (a) True density of Carrot at 70 C and various moisture contents (Exp. Pts from Krokida & Maroulis, [15] ; Zogzas et al. [11] ). (b) True density of Carrot at various temperatures and moisture contents.

14 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE 121 (a) Potato (70 o C) Exp. Pts Proposed Model ρp [kg/m 3 ] X w [kg/kg db] (b) Potato - Proposed model 20oC 70oC 100oC 1500 ρp [kg/m 3 ] X w [kg/kg db] Figure 3 (a) True density of Potato at 70 C and various moisture contents (Exp. Pts from Wang & Brennan, [27] ; Zogzas et al. [11] ). (b) True density of Potato at various temperatures and moisture contents

15 122 BOUKOUVALAS, KROKIDA, MAROULIS, AND MARINOS-KOURIS Fruits (20 o C) Apple Banana 1800 ρp [kg/m 3 ] X w [kg/kg db] Figure 4 Predicted values of true density for fruits at 20 C Vegetables (20 o C) Garlic Onion Carrot Potato 1800 ρp [kg/m 3 ] X w [kg/kg db] Figure 5 Predicted values of true density for vegetables at 20 C.

16 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE Fruits (X w (db)=1.0) Apple Banana 1300 ρp [kg/m 3 ] T [ o C] Figure 6 Predicted values of true density vs. temperature for fruits at X w (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. REFERENCES 1. Krokida, M.K.; Maroulis, Z.B. Quality change during drying of food materials. In Drying Technology in Agriculture and Food Sciences; Mujumdar, A.S.; Ed.; Science Publishers Inc.: Enfield (NH), USA, 2000, Saravacos, G.D.; Maroulis, Z.B. Transport Properties of Food. Marcel-Dekker: New York, 2001, Boukouvalas, Ch.J.; Krokida, M.K.; Maroulis, Z.B.; Marinos-Kouris, D. Densities and porosity: Literature data compilation for foodstuffs. International Journal of Food Properties. 2005, submitted for publication. 4. Maroulis, Z.B.; Saravacos, G.D. Food Process Design. Marcel-Dekker: New York, 2003, Sokhansanj, S.; Lang, W. Prediction of Kernel and Bulk Volume of Wheat and Canola During Adsorption and Desorption. Journal of Agricultural Engineering Research. 1996, 63, Teunou, E.; Fitzpatrick, J.J.; Synnott, E.C. Characterisation of Food Powder Flowability. Journal of Food Engineering. 1999, 39,

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18 EFFECT OF MATERIAL MOISTURE CONTENT AND TEMPERATURE Krokida, M.K.; Oreopoulou, V.; Maroulis, Z.B.; Marinos-Kouris, D. Deep Fat Frying of Potato Strips-Quality Issues. Drying Technology. 2001, 19 (5), Draper, N.; Smith, H. Applied Regression Analysis, 2nd Ed.; Wiley: New York, Choi, Y.; Okos, MR. Effect of temperature and composition on the thermal properties of foods. In Food Engineering and Process Applications; Le Maguer, M.; Jelen, P.; Eds.; Elsevier: London, 1986, vol. 1,

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