Physical Chemistry of Foods

Gravity, as in the percolation of hot water through ground coffee

An external mechanical pressure, as in ultrafiltration

Capillary suction, as in tea being taken up into a sugar cube (see

Section 10.6.3)

An osmotic pressure difference, as over the semipermeable membrane

in the apparatus of Figure 2.4 before equilibrium has been reached

An endogenous tendency of the material to shrink, as in the syneresis

of renneted milk

Thepermeabilitymay be considered as a material constant, provided
that the Reynolds number Re 5 1, which is nearly always the case
(approximately, Re¼vv?HB?r=Z). By comparing Eq. (5.24) with (5.23), it
follows thatB(unit m^2 ) is in first approximation proportional to the square
of the diameter of the pores in the material and to the surface fraction of
pores in a cross section of the material. In most real materials, the pore
diameter shows considerable spread, and Eq. (5.23) shows thatQis about
proportional tor^4 ; hence by far most of the liquid will pass through the
widest pores. Moreover, the pores tend to be irregular in shape and cross
section, they are tortuous and bifurcate, and some may have a dead end.
The permeability may even be anisotropic, i.e., be different in different
directions (see Section 9.1).
Accordingly, it is not easy to predictBfrom the structure of the
material. Numerous relations have been proposed, and the one used most is
the Kozen ́y–Carman equation

B&

ð 1 
jÞ^3

5 A^2 sp

¼

ð 1 
jÞ^3 d^2

180 j^2

ð 5 : 25 Þ

wherejis the volume fraction of matrix material andAspthe specific
surface area of the matrix (in m^2 per m^3 of the whole material). The part
after the second equals sign is only valid if the matrix consists of an
aggregate of spheres of equal diameterd. The equation was derived for
powders, and it has quite limited validity, but it serves to illustrate two
points. The permeability very strongly decreases if the volume fraction
increases (or the void volume decreases), especially for smallj;andit
decreases if the specific surface area increases, i.e., as the structural elements
in the composite material become smaller. Some very approximate
magnitudes ofBare

Ground coffee 10 
^8 m^2

Renneted milk gel 10 
^12

Polysaccharide gel 10 
^17