文档介绍：Chapter 3
Dynamic Melting
The batch melting assumes no melt extraction during melting until the
end whereas the fractional melting assumes any infinitesimal melt is
extracted from the solid as soon as it is produced. Both models are end-
member models. The reality might be in between. A more realistic
scenario is that when the degree of partial melting is smaller than a
critical value, the melt is in equilibrium with the solid and there is no
melt extraction; when the degree of partial melting is greater than this
critical value, any extra melt is extracted.
We use the physical concept of the dynamic melting model proposed
by McKenzie (1985) for the situation where the rate of melting and
volume porosity are constant and finite while the system of matrix and
interstitial fluid is moving. This requires that the melt in excess of
porosity be extracted from the matrix at the same rate at which it is
formed (the details of the model are shown in Fig. 3 of McKenzie, 1985).
The essential differences between the batch melting, fractional
melting and dynamic melting models have been given by (Zou, 1998)
and can be summarized in Table .
Table of three melting models.
Batch Fractional Dynamic
Porosity = F before extraction = 0 =F when FlcD
= 0 after extraction =@ when F >cD
X = 0 before extraction = F =o when FlcD
I I I F-cD
I = F after extraction --- when F > cD
I I I I 1-a I
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42 Quantitative Geochemistry
The mass balance of total mass and the mass of an element can be
summarized in Table .
Table . Mass balance for dynamic melting.
1 Source 1 Extracted 1 Residual melt Residual Solid
Melt
of the mass
of an element
Mass conservation for a trace element in dynamic melting requires
C,J4, (I - X )( 1 - a)+ C, M, (1 - X )O + ZM, X = C,M, . ()
The concentration in residual solid is related to the concentration in
residual melt by
c, = C,D, ()
where D is