文档介绍：Chapter 13
Geochemical Kinematics and Dynamics
This chapter at first is concerned with the formulation of two
fundamental dynamic and kinematic processes, diffusion and advection,
for understanding elemental movement in various geochemical systems.
Subsequently we will try to describe the bubble growth process using
diffusion and advection equations that can help understand the magma
eruption processes. We then talk about a kinematic problem: the
trajectory of a volcanic bomb during volcanic eruption. Although this
trajectory problem is not strictly geochemical, problems like this are
indeed useful for understanding the physical aspects of the eruption
process. A better understanding of physical process can improve our
understanding of chemical process, which is the spirit and the essence of
chemical geodynamics (Allegre, 1982; Zindler and Hart, 1986). In the
end, we will discuss error function that is critical for the solutions of one-
dimensional diffusion equations.
. Diffusion
. 1. Formulation
The first Fick’s law states that the flux (J ) of diffusion is proportional to
the concentration gradient (dc/dx)
dc
J=-D-, ()
dx
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where D is the diffusion coefficient of the element under consideration
and is usually expressed in surface unit per time unit (., cm2/s), c the
concentration of the element, and x is the coordinate. The negative sign
indicates that the flux moves from high concentration to low
concentration.
The second Fick's law of diffusion considers time dependent diffusion
()
Substitution of the first Fick's law of diffusion into Eq. () results in
-dc = -(a &) .
()
dt ax
More details of the derivation of the diffusiodthermal equation can be
found in Maaloe (1985) and Schubert et al. (2001).
If the diffusion coefficient D is independent of position and
spatial position, then the diffusion equation es