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transport of material may have been more directly responsible, as in the case of
stylolites (Renard et al. 2004 ). Solution transfer processes in which pressure
solution may have played a part are potentially of importance in the deformation of
rocks containing pore fluids (Rutter 1983 ).
3.4 Transport Processes in General
Thermodynamically, the relationship between the variables describing any trans-
port process can, in general, be expressed in the form
j ¼ kX
ð 3 : 14 Þ
where j is the flux density; X the thermodynamic driving force, and k a constant. The
flux density j is the amount of the extensive property or quantity, Z which passes
through a reference unit cross-sectional area in unit time, that is, j ¼ d = dA
ð Þ dZ = d ð Þ
where A is cross-sectional area, and t time. Some writers call j simply the flux but
since this term is used by others for the total flow, possible ambiguity is avoided by
calling j the flux density. The driving force X can be expressed as the negative
gradient of an intensive property or potential /, that is, X ¼ d/ = dx in a one-
dimensional situation where x is the space coordinate (/ can, in turn, generally be
expressed as the derivative of an extensive quantity with respect to another extensive
quantity see Chap. 2 ). As discussed in Chap. 2 , the driving force X conjugate to the
flux j is so defined that jX correctly expresses the rate of dissipation per unit
cross-sectional area. In effect, this requirement determines the definition of X once j is
defined as needed to describe the transport process.
In the empirical approach, the same type of relationship ( 3.14 ) is used.
However, the quantity X to which j is related is now chosen, not for reasons of
thermodynamic necessity, but for empirical reasons of convenience, as some
quantity relatively easy to measure, which can be usefully correlated with j. For
example, whereas thermodynamically the driving force X for diffusion is the
negative gradient in the chemical potential, the concentration is more conveniently
measured and its negative gradient is used as X in empirical treatments of diffu-
sion. Apart from this point, however, the formulation of theory for the two
approaches is similar.
The parameter k represents a property of the medium that may be termed a
''generalized conductivity''. For simplicity, ( 3.14 ) is given in 1D form with k as a
scalar constant but, in general, j and X are vectors and k is a second rank tensor in
which is expressed the anisotropy of the medium. Constancy of k corresponds to
linear behavior thermodynamically, a property that is common in transport pro-
cesses, and k is then identical with the kinetic coefficient L in the thermodynamic
formulation ( Chap. 2 ). The linearity can be rationalized as arising from the cir-
cumstance that over atomic distances, the scale on which the elementary transport
events occur, the change in driving potential, expressed as a molar energy, is small
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