Physical Chemistry of Foods

transport rates through the system (Section 5.3) and capillary phenomena
(Section 10.6). The pore size is governed by the same variables as is
interparticle distance, although the relations are more complicated.

Diffusion Times. Brownian motion of molecules and particles is
discussed in Section 5.2. The root-mean-square displacement of a particle is
inversely proportional to the square root of its diameter. Examples are
given in Table 9.4. The diffusion time for heat or matter into or out of a
particle of diameterdis of the order ofd^2 /10DwhereDis the diffusion
coefficient. All this means that the length scale of a structural element, and
the time scale needed for events to occur with or in such a structural
element, generally are correlated. Such correlations are positive, but mostly
not linear.

Separability. The smaller the particles in a dispersion, the more
difficult it is to separate them from the continuous phase. This is illustrated
by the approximate pore size in various separation membranes:

paper filter 20 mm 1 kPa

microfiltration 1mm 5 kPa

ultrafiltration 10 nm 30 kPa

nanofiltration 1 nm 1 MPa

The smaller the pores, the higher the pressure to be applied to achieve
substantial flow through the membrane, as indicated. See also under
‘‘sedimentation,’’ below.

9.2.2 Forces

Internal forces. A fluid particle exhibits an internal pressure due to surface
forces, the Laplace pressure, which is inversely proportional to its diameter
(Section 10.5.1). This means that the particle resists deformation, the more
so the smaller it is. The colloidal forces that may act between particles,
keeping them aggregated, often are about proportional tod(Chapter 12).
This means that the stress (force over area) involved would, again, be
inversely proportional tod.
External forcesacting on a particle generally increase steeply withd.
For instance, the viscous stress exerted by a flowing liquid is given byZC,
whereZis viscosity andCvelocity gradient. This means that the viscous
force (stress times area) acting on a particle or aggregate is proportional to
d^2. Comparison with internal forces then leads to the conclusion that for