CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 341
In dilute solutions of componentiin solutejthe diffusion coefficient may be estimated from
theEinstein relation
Dij=RT
6 π NAηjri, (10.16)
whereηj is the viscosity of solventjandriis the effective radius of the diffusing moleculei.
The relation applies on condition that the radius of diffusing molecules is much larger than the
radius of the molecules of the solvent. This relation is typically used for the diffusion of colloid
particles in a low-molecular solvent.
10.4.3 Fick’s second law of diffusion
The dependence of a component concentration on time and location is described by the partial
differential equation
∂ci
∂τ
=Dij∂^2 ci
∂z^2, (10.17)
which is referred to asFick’s second law of diffusion. By solving this equation given initial
and boundary conditions we may determine the concentration of a substance in dependence on
time and location.
Note:Compare relation (10.17) with (10.6). Both partial differential equations have the
same form. The Navier-Stokes equations describing fluid flow are more complex.10.4.4 Self-diffusion
Self-diffusion is a processes during which molecules diffuse in an environment formed by iden-
tical molecules. Fick’s first and second laws apply for self-diffusion, with the binary diffusion
coefficientDijbeing replaced with theself-diffusion coefficientD.
Note:Strictly speaking, it is impossible to measure self-diffusion because it is impossible to
distinguish the diffusing molecules from the molecules of the environment. Self-diffusion is
therefore determined using radioactive isotopes of the given substance which are considered
identical with non-radioactive isotopes.