1.4 SPECIFIC DATA .1 Predictions of Density
1.4.1.2 Liquid Foods
1.4.1.2.1 Milk and Dairy Products
The density of whole and skim milk as a function of temperature can be calculated from the equations developed by Short (1955):
Whole milk:
ρa =1035 0 0 358. − . t+0 0049. t2−0 00010. t3 (1.23) Skim milk:
ρa = 1036 6 0 146. − . t+0 0023. t2−0 00015. t3 (1.24) Phipps (1969) reported an equation for the estimation of the density of cream as a func-tion of temperature and fat content with an accuracy of ±0.45%:
ρa t t f
t X
= − − − −
1038 2 0 17. . 0 003. 2 133 7. 475 5. (1.25) where Xf is the mass fraction of fat. Roy et al. (1971) reported equations for estimating the density of fat from buffalo’s and cow’s milk:
Buffalo milk: ρa = 923 84 0 44. − . t (1.26) Cow’s milk: ρa = 923 51 0 43. − . t (1.27) 1.4.1.2.2 Fruit Juices and Purees
The apparent density of a sucrose solution can be estimated as a function of sucrose con-centration (Xw: 0 to 1.0) at 20°C (Chen, 1989):
ρa j w j
j
= C X
∑
=50100 ( ) (1.28)Table 1.2 Values of Van der Waal’s Constants for Different Gases Gas a (Pa [m3/kg mol]2) b (m3/kg mol)
Air 1.348 × 105 0.0366
Ammonia 4.246 × 105 0.0373
Carbon dioxide 3.648 × 105 0.0428
Hydrogen 0.248 × 105 0.0266
Methane 2.279 × 105 0.0428
Nitrogen 1.365 × 105 0.0386
Oxygen 1.378 × 105 0.0319
Water vapor 5.553 × 105 0.0306
source: Toledo, R. T. 1993. Fundamentals of Food Process engineering.
2nd ed. Chapman & Hall, New York.
where Co = 997.2, C1 = 3.858, C2 = 1.279 × 10−2, C3 = 6.192 × 10−5, C4 = –1.777 × 10−7, and C5 = –4.1997 × 10−10, respectively. For fruit juices, the density versus the refractive index of sugar solution can be estimated as (Riedel, 1949):
ρ ϑ
a = ϑ −
+ × ×
2 2
1 2
62 4
0 206. 16 0185
. . (1.29)
where ϑ is the refractive index. For the density of tomato juice, Choi and Okos (1983) devel-oped a predictive equation based on the water (Xw) and solids (Xs) fractions:
ρa =ρwXw +ρsXs (1.30)
ρw = 9.9989 × 102–6.0334 × 10−2 t–3.6710 × 10−3 t2 (1.31) ρs =1 4693 10. × 3+ 5 4667 10. × −1t−6 9643 10. × −3 2t (1.32) Bayindirli (1992) proposed a correlation to estimate the apparent density of apple juice as a function of concentration (B: 14–39°Brix) and temperature (20–80°C) as
ρa =830 350+ exp( .0 01B) −0 564. t (1.33) Ramos and Ibarz (1998) correlated the apparent density of peach (Equation 1.34) and orange (Equation 1.35) juices as a function of concentration (B: 10–60°Brix) and tempera-ture (0–80°C) as
ρa = 1006 6 0 5155. − . t+4 1951. B+0 0135. B2 (1.34) ρa = 1025 4 6 0 3289. . − . t+3 2819. B+0 0178. B2 (1.35) Ibarz and Miguelsanz (1989) correlated the apparent density of depectinized and clari-fied pear juice as (B: 10–71°Brix and t: 5–70°C):
ρa = 988 8 5 13. + . B−0 546. t (1.36) Telis-Romero et al. (1998) correlated the apparent density of Brazilian orange juice as affected by temperature (0.5–62°C) and water content (Xw: 0.34–0.73) as
ρa =1428 5 454 9. − . Xw −0 231. t (1.37) 1.4.1.3 Density of Solid Foods
The density of food materials depends on temperature and composition. Choi and Okos (1985) presented correlations for the densities of the major food components at a tempera-ture range of –40–150°C (Table 1.3). Density of food materials varies nonlinearly with mois-ture content. Lozano et al. (1983) developed a general form of correlation to predict the density of fruits and vegetables during air drying. They found a wide variation in values and shapes of the curves when plotting the apparent density against Mw /Mwo of a carrot, a potato, a sweet potato, and whole and sliced garlic. They found that the following form of the equation can predict the density of all fruits and vegetables considered.
MAss–VoluMe–AReA-RelAted PRoPeRties oF Foods
ρ = g + hy + q[exp(−ry)] (1.38) The parameters of the models are provided by Lozano et al. (1983) for different food materials.
1.4.1.3.1 Fruits and Vegetables
The particle density of granular and gelatinized corn starches was measured in the range 0 < Mw < 1.0 and correlated as (Maroulis and Saravacos, 1990):
ρp = 1442 837+ Mw −3646Mw2 +448Mw3 −1850Mw4 (1.39) Lozano et al. (1979) correlated the apparent density of apple above freezing as
ρa = 636 102[ln+ Mw] (1.40)
Singh and Lund (1984) noted that the above correlation is not valid up to zero mois-ture content and they correlated the apparent density of apple up to zero moismois-ture content above frozen as
ρa = 852 462− [exp( .−0 66Mw)] (1.41) Again Lozano et al. (1980) correlated the apparent and particle density of apple during air drying by an exponential form of equation for whole range of moisture content above frozen as
ρa = 684 68 1+ . [ln(Mw +0 0054. )] (1.42) ρp = 1540[exp( .−0 051Mw)]−1150[exp( .−2 40Mw)] (1.43) Table 1.3 Density of Major Food Components at the
Temperaturea Range of –40–150°C
Material Equation
Air ρt = 1.2847 × 101–3.2358 × 10−3t Protein ρt = 1.3300 × 103–0.5184t Carbohydrate ρt = 1.5991 × 103–0.31046t Fat ρt = 9.2559 × 102–0.41757t Fiber ρt = 1.3115 × 103–0.36589t Ash ρt = 2.4238 × 103–0.28063t
Water ρt = 9.9718 × 102 + 3.1439 × 10−3t–3.7574 × 10−3t2 Ice ρt = 9.1689 × 102 – 0.1307t
source: Choi, Y. and Okos, M. R. 1985. In Food engineering and Process Applications, Vol. 1, transport Phenomena. Le Maguer, M. and Jelen, P., Eds. Elsevier Applied Science, London.
a t in degrees C.
Lozano et al. (1980) noted that the apparent density changed in an almost linear man-ner between full turgor and Mw = 1.5. Beyond that as moisture content decreased, the change in apparent density became steeper and showed that the apparent volume change became slower. The material density increased as moisture content decreased from full turgor to Mw = 1.5. Then it showed a sharp decrease, converging to an intercept similar to that of apparent density. Thus, one exponent form of the equation is not suitable for the entire range of moisture content. Maroulis and Saravacos (1990) measured the particle density of starch granules from Mw = 0 to Mw = 1.0 and found a similar peak at Mw = 0.15.
Madamba et al. (1994) measured the bulk density (outside void) of garlic slices and cor-related it as a function of water content (Xw: 0.03 to 0.65) and slice thickness [l: (2–5) × 10−3 m]
at room temperature as
εB = 0 865 30. − Xw −0 8 10. × 3l+2 0 10. × 3X lw (1.44) ρB = 200 6 280. + Xw+1 24 10. × 4l+ 2 0 10. × 4X lw (1.45) Bulk and particle densities of grapes as a function of water content (Mw: 0.176 to 4.0) (Ghiaus et al., 1997) are given as
ρB = 775 99 228 1. − . Mw +133 6. Mw2 −22 19. Mw3 (1.46) ρp = 1480 4 382 2. − . Mw +131 8. Mw2 −15 48. Mw3 (1.47) Table 1.4 presents coefficients of the quadratic form of density versus moisture content data. Most of the above density data were measured at room temperature; thus, a tempera-ture term was not included in developing the above correlations.
Table 1.4 Parameters of the Quadratic Equations for Density (ρ = a + bMw + cMw2)
Material Density Range a b c Ref.
Gorgon nuta Bulk Mw:0.15–0.60 369.2 1290 –1020 1
Gorgon nutb Bulk Mw:0.15–0.60 396.7 1330 –1080 1
Gorgon nutc Bulk Mw:0.15–0.60 434.0 1660 –8420 1
Gorgon nuta True Mw:0.15–0.60 995.9 830 –640 1
Gorgon nutb True Mw:0.15–0.60 1039.7 690 –420 1
Gorgon nutc True Mw:0.15–0.60 1025.7 930 –800 1
Macadamia nutd Bulk Mw:0.02–0.24 605.2 –92 800 2
Macadamia nutd Apparent Mw:0.02–0.24 1018.6 –44 1300 2
sources: Jha, S. N. and Prasad, S. 1993. Physical and thermal properties of gorgon nut. Journal of Food Process engineering 16(3): 237–245; Palipane, K. B., Driscoll, R. H. and Sizednicki, G. 1992.
Density, porosity, and composition of macadamia in shell nuts. Food Australia. 44(6):
276–280.
a Large size.
b Medium size.
c Small size.
d In-shell.
MAss–VoluMe–AReA-RelAted PRoPeRties oF Foods
1.4.1.3.2 Meat and Fish
Rahman and Driscoll (1994) correlated the density of fresh seafood by a quadratic equation (Xw: 0.739–0.856 and t: 20°C):
ρa wo
wo
X X
= 2684 3693− +2085( )2 (1.48)
The above equation was developed using the density data of different types of fresh seafood. Similarly, the density of frozen seafood at –30°C can be estimated as
ρa wo
wo
X X
= 1390 520− +31 56. ( )2 (1.49)
The density of frozen squid mantle (Xwo: 0.814) below its freezing point up to −40°C can be estimated as (Rahman and Driscoll, 1994):
ρa =1047+3 603. t+0 057. t2 (1.50) Sanz et al. (1989) proposed the density of fresh meat products above and below freez-ing as
ρa =1053 (t≥ tF) (1.51)
ρa
wo
wo F
X X t t t
= + 1053+ − <
0 9822 0 1131. . [ .0 2575 1( )] ( )
/ (1.52)