Physical Chemistry of Foods

would be negligible for the back fat. However, for the meat the value is somewhat
above 0: 5 c 1 , and for the fat about half that value, i.e., far from negligible. Can you
explain these results?

Answer

Above, the factors affecting the magnitude ofDhave been discussed. Factor 1 is
that part of the volume of the material is not available for transport: salt dissolves in
water and not in the dry matter of the meat. This then implies that the determined
values ofDare too small. If the volume fraction of water equals 1
j, then
D*&Dexperimental=ð 1
jÞ. Using this relation, calculate the expected values ofc=c 1
at 1 cm after 5 days brining, assuming for lean porkj¼ 0 :4 and for back fatj¼ 0 :9.
The results are 0.56 and 0.28, respectively.

5.3.3 Diffusion Through a Thin Layer

Different regions in a food may have different effective diffusion coefficients
for a solute. Moreover, the solubility of the solute may differ. A simple
example will be discussed.
Figure 5.17 depicts a situation in which a solute diffuses from left to
right because of a difference in concentration in two compartments of phase
a, which are separated by a (thin) layer of a phaseb. For sake of simplicity,
it is assumed that within each entire compartment the concentration is
everywhere the same. The solubility is not the same inaandb, and the
distribution coefficient or partition ratio (see Section 2.2.2) KD¼cb=ca.
Solution of Eq. (5.17) now yields the steady-state equation

Q¼

D*bAKD 4 c

x 2 
x 1

ð 5 : 27 Þ

whereQis the mass flux (amount of mass transported per unit time) through
an areaA. The hindrance of the diffusional transport by the layer ofbis
thus stronger for a thicker layer, a smaller value ofD*in the layer, and a
lower value ofKD—i.e., a lower solubility of the solute inb. In the example
of Figure 5.17 the distribution coefficient is about 0.5, but far smaller values
can occur. For instance, in a layer of fat (i.e., a dispersion of fat crystals in
oil) between two aqueous compartments,KDmay be as small as 0.002.
Hence such a layer will greatly impede the diffusion of hydrophilic
components from the one to the other compartment; this is commonly
applied in some kinds of pastry to slow down transport of flavor or color
substances.