5.3.2 Effective Diffusion Coefficients
Even for such a simple case as the diffusion of a small-molecule solute, say
sugar, in a gel made of a dilute polymer solution, say gelatin or pectin, the
Stokes–Einstein relation (5.16) cannot be applied. This is because the
macroscopic viscosity of the system greatly differs from the microscopic
viscosity as ‘‘sensed’’ by the diffusing molecules: they just diffuse around the
strands of the gel. The effect is illustrated in Figure 5.14, and it is seen that
the discrepancy may be by several orders of magnitude, even for quite low
concentrations of matrix material. To be sure, the viscosity of a gel is an
ambiguous property; it concerns in fact an apparent viscosity determined at
a stress larger than the yield stress of the gel. But the example serves to
illustrate the point: the effective viscosity cannot be obtained from
macroscopic measurements. Nevertheless, diffusion in a gel is slower than
in pure solvent, the more so for a higher concentration of matrix material.
FIGURE5.14 Example of the effect of polysaccharide concentration (%) on the
apparent viscosity of the polysaccharide–water mixtureðZaÞand of the effective
diffusion coefficientðD*Þof a solute in the mixture.D 0 is the diffusion coefficient in
the absence of polymer,Zsthe viscosity of the solvent.