Geology Reference
In-Depth Information
In more complex cases, two or more of the above types of rate processes may
be identifiable as occurring simultaneously. For example, in heterogeneous
chemical reactions, both reaction and diffusion are involved. However, in such
cases, one of the constituent processes is usually rate controlling; normally, the
slowest one if the processes are sequentially dependent on each other.
3.1.2 Theory of Rate Processes
The theoretical treatment of rate processes can be approached from two points of
view, the thermodynamic and the kinetic. However, while at first sight the two
approaches
may
appear
distinct,
they
are
necessarily
eventually
related
or
equivalent.
In the thermodynamic approach, the change in the system is viewed, somewhat
formally, as a response to the system not being at equilibrium. The general con-
siderations of non-equilibrium thermodynamics, as sketched out in
Chap. 2
, are
applied. A specific process is discussed in terms of a measure of the departure from
equilibrium, a measure of the response of the system to this departure, and a
quantitative relationship between these two measures, involving some material
parameters. The linear thermodynamics of irreversible processes provides con-
straints on this relationship in cases where the system is not very far from equi-
librium. Nonlinearity appears when systems are far from equilibrium and new
phenomena may then be involved, as exemplified by the transition from laminar to
turbulent flow in fluid dynamics or by oscillations and dissipative structures in
chemical reactions (Glansdorff and Prigogine
1971
). No attempt will be made here
to deal with nonlinear systems, although they may be important in connection with
some actual geological structures (Fisher and Lasaga
1981
).
The treatment of processes taking into account the atomic structure of matter
and the existence of fluctuations in the fine-scale distribution of energy leads one
into statistical mechanics. This approach, often termed kinetic theory, especially in
connection with gases, views the change in the system directly in terms of
instantaneous or spontaneous elementary events, such as reactions between col-
liding molecules or motions of diffusing atoms, and of the macroscopic summation
of these events in time. In this approach, the primary quantities in the macroscopic
description are the concentrations of the entities involved in the elementary events,
whereas in the thermodynamic approach the primary quantities are the activities
which add a ''thermodynamic weighting'' to the concentrations through the
inclusion of the activity coefficients in order to make practical application of ideal
thermodynamic laws.
Associated with the kinetic approach and in parallel with the thermodynamic
approach, there has also been the establishment of a phenomenological or
empirical framework in what may be termed empirical kinetics. This development
has often occurred earlier and independently of the thermodynamic approach and
is illustrated in empirical relations such as the Arrhenius law and Fick's laws of
