Physical Chemistry of Foods

During several processing operations, like drying, extraction, and
soaking, diffusion is the rate determining step.
When a food is kept, it may lose substances by diffusion or leaking,
such as water or flavor components, or it may take up substances
from the environment, e.g., from packaging material.
When a food is kept, the concentration of solutes, which may at first
be uneven, becomes (slowly) evened out. This may be of
considerable importance for the eating quality if it concerns flavor
components: see the introduction to Chapter 9. Likewise, color
substances may become evenly distributed—e.g., moving from the
fruit to the surrounding yoghurt; and so may water—e.g., from the
inside of the bread to its crust, by which the crust loses its crispness.
These processes often are slow, and transport rates may be difficult to
predict. Below, a few more or less idealized cases will be considered.

5.3.1 Flow Rates

Through a porous material, liquid may flow, albeit often sluggishly. It is
useful to consider the material as a solid matrix, containing several capillary
channels or pores. In practice, the pores are always narrow enough and
liquid velocity is slow enough to ensure that flow is laminar. The rate of flow
as caused by a pressure gradient through a cylindrical capillary is given by
the law of Hagen–Poiseuille, which can be written as

vv:

Q

pr^2

¼

4 p

4 x

?

r^2

8 Z

ð 5 : 23 Þ

whereQis the volume flow rateðm^3 ?s
^1 Þ,rthe radius of the capillary,pthe
pressure, andx the distance along the capillary. The velocity profile is
illustrated in Figure 5.4a. Equation (5.23) is commonly applied in the
determination of viscosity in a capillary viscometer, where the pressure
difference mostly is caused by the weight of a column of the liquid.
For flow through a porous material, the superficial flow velocity is
given byDarcy’s law,

vv:

Q

A

¼

B

Z

?

4 p

4 x

ð 5 : 24 Þ

whereAis the cross-sectional area (perpendicular tox) through which the
liquid flows andBis the permeability. The pressure difference 4 pacting on
the liquid may be due, for instance, to