Physical Chemistry of Foods

Note The theory does not apply for fluid particles in the absence
of surfactant, where slip occurs at the particle surface; see Section
10.8.3.
Exact calculation is intricate but has been realized for spheres, and
Figure 13.5 gives the result for spheres of equal radius (a). An approximate
relation for that case is

DðuÞ&

6 u^2 þ 4 u

6 u^2 þ 13 uþ 2

D? ð 13 : 6 Þ

which reduces for smallu(say,u<0.01) to

DðuÞ& 2 uD? ð 13 :6aÞ

Hereu¼h/aandD?is the pair diffusion coefficient at large separation, i.e.,
twice the particle diffusion coefficient.

FIGURE13.5 Value of the particle relative diffusion coefficientD/D?as a function

of the relative interparticle distanceu(¼h/a) of two equal-sized spheres. Calculated

according to Eq. (13.6).