Chemistry Reference
In-Depth Information
where
2
c
is the density of the concentrate (kg m
3
),
2
0
is the density of the
initial product (kg m
3
),
2
water
is the density of water (kg m
3
) and R is the
concentration factor (
¼
the ratio of the dry solids content of the concentrate
to that of the initial product). It is assumed implicitly in formulating Equation
13 that concentration causes no changes in physical state or chemical activity
coefficients (for example, hydration of proteins or insolubilization of salts)
(Sherbon, 1988).
If concentrated or unconcentrated milk or other fluid contains dis-
persed gas, such as air, the actual density will be lower than that predicted
by Equations 11, 12 or 13:
actual
¼ð
1
"
a
Þ
predicted
(14)
where
"
a
is the volume fraction of dispersed gas. This equation is easily
derived from first principles.
Dispersed gas can considerably lower density, which then becomes
appreciably pressure dependent (Walstra and Jenness, 1984). Density mea-
surement at a controlled pressure is one way of determining the gas content of
fluid milk products (Lindqvist, 1976).
Equation 11 can be transformed to the following expression:
F
þ
SNF
þð
100
TS
Þ
F
SG
fat
SG
milk
¼
(15)
þ
SNF
SG
SNF
þ
100
TS
1
where F is the % fat (w/w), SNF is the % solids-not-fat (w/w) and TS is the %
total solids (w/w). Equation 15 may be solved for TS to give
TS
¼
ð
SG
SNF
SG
fat
Þ
F
SG
fat
ð
SG
SNF
1
Þ
þ
SG
SNF
ð
100SG
milk
100
Þ
(16)
SG
milk
ð
SG
SNF
1
Þ
This equation forms the basis of the rapid determination of TS by
measuring SG
milk
using a lactometer. F must be measured separately and
suitable values assumed for SG
fat
and SG
SNF
. Modern analytical techniques
have now largely superseded this method of measuring TS.
Whitnah et al. (1957) found that the temperature of maximum density of
whole milk (which is several degrees lower than 08C) approached that of water
(48C) linearly as milk was diluted with water. They suggested that measurement
of this temperature could be used for detecting adulteration of milk by water,
but acknowledged that differences between milk samples, and changes with age
in a given sample, were serious problems in developing such an application.
The density of milk and fluid milk products decreases with increasing
temperature because of thermal expansion. The effect is due mainly to thermal
