temperature gradients. The rate of these processes depends on the diffusion
coefficient, which is inversely proportional to viscosity and to molecule or
particle radius. Heat motion is a random process, governed by statistical
laws. This causes (the root-mean-square value of) the transport distance to
be proportional to the square root of time. Consequently, diffusion is a
rapid process at very small distances and very slow at large distances. In
practice, the rate of mass transport is commonly enhanced by mixing.
Diffusional transport can generally be calculated by integration of Fick’s
laws. Also the amount of mass transported by diffusion into a lump of
material is in first approximation proportional to the square root of time.
Heat. Heat can also be transported by diffusion, also in solids. The
diffusion coefficient then is called thermal diffusivity; it has a fairly constant
value that is much larger than that of mass diffusion coefficients. This means
that temperature evens out much faster than concentration. To calculate the
transport of the amount of heat, the diffusion coefficient in Fick’s laws must
be replaced by the thermal conductivity. Under various conditions, heat can
also be transported by mixing, by radiation, and by distillation.
Composite Materials. Many solid foods can be considered as
solid matrixes, interspersed with a continuous liquid phase. Transport
through such a material may be greatly hindered. Flow of the liquid through
the matrix under the influence of a pressure gradient is proportional to a
material constant called permeability, which is about proportional to pore
diameter squared and pore volume fraction.
Transport of mass by diffusion is also hindered. Even in a liquid
solution, the effective diffusion coefficientDof a solute may be smaller
than the diffusion coefficient of a single molecule D, for a number of
reasons. On the other hand,Dis inversely proportional to liquid viscosity,
but this concerns a microscopic viscosity, as sensed by molecule or small
particle; the macroscopic viscosity as determined in a viscometer can be
much higher. Nevertheless, in materials containing fairly little liquid,D
may become quite small. Some of the factors involved are constriction (if
pore diameter is not much larger than molecule size); tortuosity of the pores
(increasing the effective path length); and electrostriction (for ions in a
matrix carrying electric charges).
The effect of molecule size on constriction also implies that large
molecules will be hindered to a greater extent than small ones. One
consequence of this is partial osmosis. If a solute molecule (A) is much
larger than the solvent molecules (mostly water), contact of the system with
a concentrated solution of A will lead to diffusion of water out of the system
and a much slower transport of A inwards. Provided that the material can